N Schnuriger
email: nicolas.schnuriger@univ-lorraine.fr

J Flahaut

M Martinot

S D Chevrel

PSS _2019_167R2

Keywords: Moon, volcanism, domes, IMPs, mare basalts, Apollo 11

Mare Tranquillitatis corresponds to the deposit of successive Early to Late Imbrian basaltic units filling the Tranquillitatis basin on the Moon. The present study focuses on the western half of the mare, in the vicinity of the Arago crater (6.16°N, 21.42°E). High resolution datasets from recent remote sensing missions were used to reconstruct the geologic history of the area, which includes a variety of geological features such as: 8 extrusive domes, numerous wrinkle ridges, a sinuous rille and 37 Irregular Mare Patches (IMPs). We performed crater counting to date the domes emplacement and estimated the domes lava rheologic properties (plastic viscosities, lava effusion rates, and durations of effusion) using their geometric characteristics. As a result we classify the Arago domes into three groups: E1-type domes (Arago 1 and 8), H1-type domes (Arago 4 to 7), and B-type domes (Arago 2 and 3) respectively emplaced ~ 3.7 Ga, ~ 3.4 Ga, and ~ 2.8 Ga ago. IMPs are observed in the younger mare unit and on the top of the Arago 6 dome; they likely correspond to a late stage of waning mare volcanism in the area. Both IMPs and domes have a composition similar to the surrounding mare in the VNIR spectral domain, consistent with mafic materials. The exceptionally long-lived volcanism and its diversity recorded in the Arago region may be related to both a Th-rich anomaly reported nearby and to the large-scale magma center responsible for the Lamont positive Bouguer anomaly. In addition, volcanic features of the Arago region are superimposed on a Ti-rich mare unit visited by the Apollo 11 crew 175 km to the south at Tranquility Base. The geological and historical richness of this region makes it a compelling site for future science and/or In Situ Resources Utilization (ISRU) driven missions to the Moon.

Introduction

Recent studies show that the geologic and thermal evolution of the Moon is far more complex than previously thought (e.g., [START_REF] Wilson | A theoretical model for the formation of Ring Moat Dome Structures: Products of second boiling in lunar basaltic lava flows[END_REF]Head, 2003, 2017;[START_REF] Braden | Evidence for basaltic volcanism on the Moon within the past 100 million years[END_REF][START_REF] Zhao | The Mons Rümker volcanic complex of the Moon: A candidate landing site for the Chang'E-5 mission[END_REF]. This complexity is well illustrated by the diversity of volcanic landforms that are observed in the vicinity of the Arago crater, located in the western part of Mare Tranquillitatis. Mare Tranquillitatis is composed of Early to Late Imbrian geological units filling most of the ~800 km diameter impact basin of the same name with extensive basaltic flows, up to ~ 3.4 Ga (Pieters, 1978, Head and[START_REF] Head | Lunar mare volcanism: Stratigraphy, eruption conditions, and the evolution of secondary crusts[END_REF][START_REF] Staid | Mare Tranquillitatis: Basalt emplacement history and relation to lunar samples[END_REF][START_REF] Staid | The mineralogy of late stage lunar volcanism as observed by the Moon Mineralogy Mapper on Chandrayaan-1[END_REF][START_REF] Hiesinger | Ages of mare basalts on the lunar nearside[END_REF][START_REF] Hiesinger | Ages and stratigraphy of lunar mare basalts: A synthesis[END_REF]. The study area encompasses the western part of Mare Tranquillitatis (18 to 30°E, 2 to 12 °N; Figure 1a), in the vicinity of Arago and Carrel craters, 175 km north of Tranquility Base, the Apollo 11 landing site (Figure 1c).

Similarly to the Apollo 11 landing site area, the Arago region is dominated by relatively dark, ancient (> 3.6 Ga), high-Ti (> 9 wt% TiO2) mare basalt deposits (e.g., [START_REF] Pieters | Mare basalt types on the front side of the Moon: A summary of spectral reflectance data[END_REF]. The study area covers four of the geologic units previously mapped by [START_REF] Kodama | Lunar mare volcanism in the eastern nearside region derived from Clementine UV/VIS data[END_REF] and labeled Tr1 (dated at 3.85 Ga) through Tr4 (dated at 3.59 Ga), the later being the same than the Tranquility Base unit. Estimated FeO and TiO2 contents increase from Tr1 to Tr4 [START_REF] Kodama | Lunar mare volcanism in the eastern nearside region derived from Clementine UV/VIS data[END_REF].

Eight volcanic domes and 37 Irregular Mare Patches (IMPs) have been reported in this area [START_REF] Lena | Lunar Domes[END_REF][START_REF] Braden | Evidence for basaltic volcanism on the Moon within the past 100 million years[END_REF]. The Arago domes were previously studied by [START_REF] Lena | Lunar Domes[END_REF] and catalogued into two classes, based on their morphometric and spectral characteristics. Both classes of domes have low slope values and roughly circular outlines, and were therefore interpreted as likely emplaced by extrusive, effusive volcanism [START_REF] Lena | Lunar Domes[END_REF]. IMPs were recently identified based on their high albedo and paucity of craters, and are tentatively interpreted as recent volcanic units (< 1 Ga, [START_REF] Braden | Evidence for basaltic volcanism on the Moon within the past 100 million years[END_REF] and/or the result of ancient eruptions of magmatic foams (> 3.8 Ga, e.g., [START_REF] Wilson | Eruption of magmatic foams on the Moon: Formation in the waning stages of dike emplacement events as an explanation of "irregular mare patches[END_REF][START_REF] Qiao | The role of substrate characteristics in producing anomalously young crater retention ages in volcanic deposits on the Moon: Morphology, topography, subresolution roughness, and mode of emplacement of the Sosigenes lunar irregular mare patch[END_REF]. Additional volcanic and tectonic features in the study area include a 200 km long sinuous rille (named Diamondback Rille), numerous north-southtrending wrinkle ridges, and extensional grabens bordering the highlands, indicating a complex geologic history. Adding to the complexity, the region shows: i) a positive gravity anomaly centered 60 km southeast of Arago crater (tentatively interpreted as a buried impact structure; and referred to as the "Lamont" anomaly [START_REF] Evans | Identification of buried lunar impact craters from GRAIL data and implications for the nearside maria[END_REF][START_REF] Zhang | Diversity of basaltic lunar volcanism associated with buried impact structures: Implications for intrusive and extrusive events[END_REF] and ii) a high-Th content up to 6.1 ppm, which represents an anomaly for a region located outside the Procellarum KREEP Terrane (PKT) (e.g., [START_REF] Jolliff | Major lunar crustal terranes: Surface expressions and crust-mantle origins[END_REF][START_REF] Lawrence | Small-area Thorium features on the lunar surface[END_REF]Figure 1b).

The present study describes the characteristics and relative timing of the emplaced volcanic features using a variety of new high resolution datasets. We show that the Arago region is not only a promising site for science because of its long and complex geologic history, but also a potential region of interest for future In Situ Resources Utilization (ISRU) missions.

Datasets and methods

2.1/ Remote sensing datasets

A number of datasets from the Planetary Data System and SELENE archive available between 18 and 30°E, and between 3 and 12°N were processed and integrated into a Geographic Information System (GIS). The data collection includes: Kaguya Terrain Camera (TC) panchromatic images and associated Digital Terrain Model (DTM, spatial resolution of 10 m/px), both assembled in mosaics [START_REF] Haruyama | Global lunar-surface mapping experiment using the Lunar Imager/Spectrometer on SELENE[END_REF]; Lunar Reconnaissance Orbiter Camera Wide Angle Camera (LROC WAC, resolution of 100 m/px) and Narrow Angle Camera imagery (NAC, resolution < 1 m/px) [START_REF] Robinson | Lunar reconnaissance orbiter camera (LROC) instrument overview[END_REF]; Lunar Orbiter Laser Altimeter (LOLA) global Digital Elevation Model (DEM, resolution of 118 m/px) [START_REF] Smith | Summary of the results from the Lunar Orbiter Laser Altimeter after seven years in lunar orbit[END_REF]; Gravity Recovery And Interior Laboratory (GRAIL) gravity maps [START_REF] Zuber | Gravity field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission[END_REF]; Lunar Prospector Gamma Ray Spectrometry maps (GRS, resolution from 15 to 150 km/px) [START_REF] Lawrence | Global elemental maps of the Moon: The Lunar Prospector gammaray spectrometer[END_REF]; Diviner Christiansen Feature position map [START_REF] Greenhagen | Global silicate mineralogy of the Moon from the Diviner Lunar Radiometer[END_REF] and Clementine UVVIS color ratio mineral map as well as Clementine-derived FeO and TiO2 maps [START_REF] Mcewen | Clementine observations of the Aristarchus region of the Moon[END_REF]Lucey et al., 2000a, b;Heather and Duncan, 2002). Kaguya Multiband Imager data (MI, resolution from 10 to 62 m/px) were also used to build a false-color map mimicking the Clementine color ratio mineral map using following bands: R = 750/415 nm, G = 750/950 nm, B = 415/750 nm (e.g., Heather and Duncan, 2002). Moreover, the Moon Mineralogy Mapper (M 3 ) VNIR hyperspectral data were processed with the method of [START_REF] Martinot | Mineralogical Diversity and Geology of Humboldt Crater Derived Using Moon Mineralogy Mapper Data[END_REF] to provide mineralogical information for the study area. The M 3 spectroscopic data ranges from 430 to 3000 nm with 85 spectral channels and a spatial resolution from ~140 to 280 m/px [START_REF] Pieters | The Moon Mineralogy Mapper (M³) on Chandrayaan-1[END_REF]. This study makes use of geometrically, photometrically, radiometrically and thermally corrected M 3 Level 2 data [START_REF] Boardman | Measuring moonlight: An overview of the spatial properties, lunar coverage, selenolocation, and related Level 1B products of the Moon Mineralogy Mapper[END_REF][START_REF] Clark | Thermal removal from near-infrared imaging spectroscopy data of the Moon[END_REF][START_REF] Green | The Moon Mineralogy Mapper (M 3 ) imaging spectrometer for lunar science: Instrument description, calibration, on-orbit measurements, science data calibration and onorbit validation[END_REF][START_REF] Besse | A visible and near-infrared photometric correction for Moon Mineralogy Mapper (M³)[END_REF] from the OP1A and OP2C optical periods, which cover dome A7 and domes A3, A5 and A6 respectively. Because space weathering is known to weaken mineralogical absorption bands and to lower reflectance values at shorter wavelengths (inducing a red slope in the VNIR spectrum) (e.g., [START_REF] Adams | Remote sensing of lunar surface mineralogy: Implications from visible and near infrared reflectivity of Apollo 11 samples[END_REF][START_REF] Pieters | Optical effects of space weathering: The role of the finest fraction[END_REF][START_REF] Pieters | Space weathering on airless bodies: Resolving a mystery with lunar samples[END_REF], the spectral continuum was removed following the method of [START_REF] Horgan | Near-infrared spectra of ferrous mineral mixtures and methods for their identification in planetary surface spectra[END_REF] and [START_REF] Martinot | Mineralogical Diversity and Geology of Humboldt Crater Derived Using Moon Mineralogy Mapper Data[END_REF]. Both M 3 original and continuum-removed spectra were visually analyzed for definitive mineral identification, performed by comparing M 3 spectra with the Reflectance Experiment LABoratory (RELAB) reference library (http://www.planetary.brown.edu/relab/). Spectral parameters such as band centers, band depths, band areas, and band asymmetries were calculated for the 1 and 2 micron absorption bands for each spectrum [START_REF] Martinot | Mineralogical Diversity and Geology of Humboldt Crater Derived Using Moon Mineralogy Mapper Data[END_REF]. Colour composite maps generated using these parameters allow for visual detection of minerals and highlight potential spatial heterogeneities within the study area .

Previous detections of Irregular Mare Patches from [START_REF] Braden | Evidence for basaltic volcanism on the Moon within the past 100 million years[END_REF] and of the lunar domes from [START_REF] Wöhler | Formation of lunar mare domes along crustal fractures: Rheologic conditions, dimensions of feeder dikes, and the role of magma evolution[END_REF] were added to the data collection. Both the USGS geological map L-1162 [START_REF] Fortezzo | Completed digital renovation of the 1: 5,000,000 lunar geologic map series[END_REF], renovation of the [START_REF] Wilhelms | Geologic map of the south side of the Moon[END_REF] map) and the map of [START_REF] Kodama | Lunar mare volcanism in the eastern nearside region derived from Clementine UV/VIS data[END_REF] were used to map mare unit boundaries. All data are presented in equidistant cylindrical projection, with the North to the top.

2.2/ Modelling the dome rhelogical properties and ages

Kaguya TC images (Figure 2a) and their associated DTMs (Figure 2b) were used to determine the dimensions and geometry of the domes. Height and mean radius were measured to calculate slopes, areas, and volume in order to infer their rheologic properties. As domes do not always lie on a flat surface, but often straddle across topographic breaks, a minimum and a maximum height were measured and their average value was used for rheologic calculations. Crater count was performed on the domes to obtain age estimates by fitting the distribution of the largest craters, using craterstats 2 software in ArcGIS [START_REF] Michael | Planetary surface dating from crater size-frequency distribution measurements: Partial resurfacing events and statistical age uncertainty[END_REF]. Dome dimensions were entered into rheologic equations to assess the physical properties of the feeding lava flows (e.g., [START_REF] Wilson | Lunar Gruithuisen and Mairan domes, Rheology and mode of emplacement[END_REF]Wohler et al., 2007;[START_REF] Lena | Lunar domes in the Doppelmayer region: Spectrophotometry, morphometry, rheology, and eruption conditions[END_REF][START_REF] Lena | Lunar Domes[END_REF]. First order mathematic relationships (Eqs. 1 to 4) can be applied to link the geometry of volcanic landforms to the physical properties of their forming magmas (e.g., [START_REF] Hulme | The interpretation of lava flow morphology[END_REF][START_REF] Lyman | Predicting yield strengths and effusion rates of lava domes from morphology and underlying topography[END_REF]. Dome eruption can be considered as the extrusion of a Bingham fluid (the cooling magma) characterized by a yield strength τ (Eq. 1) and a plastic viscosity η (Eq. 2). Assuming that the magma spreads out onto a relatively flat surface in all directions from the vent, the dome effusion rate E (Eq. 3) and the duration of the lava effusion Te (Eq. 4) can be estimated.

The yield strength τ (expressed in Pa) is given by: τ = 0.323ℎ 2 𝜌𝑔 𝐷/2 (Eq. 1)

Where ρ is the magma density with a mean value set at 2000 kg.m -3 as in previous studies [START_REF] Wilson | Lunar Gruithuisen and Mairan domes, Rheology and mode of emplacement[END_REF][START_REF] Wöhler | Formation of lunar mare domes along crustal fractures: Rheologic conditions, dimensions of feeder dikes, and the role of magma evolution[END_REF][START_REF] Lena | Lunar Domes[END_REF], g is the acceleration due to gravity on the surface of the Moon with a value of 1.63 m.s -2 , D is the diameter of the dome in meters) and h is the average height of the dome in meters.

The plastic viscosity η (expressed in Pa.s) can then be estimated using: η(τ)= 6 × 10 -4 τ 2.4 (Eq. 2)

Although the density of terrestrial basaltic lavas is closer to 2800 kg.m -3 (e.g., [START_REF] Spera | Physical properties of magma[END_REF], previous authors have chosen a lower value as a model input for lunar lavas assuming a vesicular foam magma. Taking a density of 2800 kg.m -3 only increase the viscosity by a factor of ~2.2, and hence is not affecting the interpretation of the results discussed herafter.

Assuming that the domes have a parabolic cross-section as the advance of the lava front cools [START_REF] Wilson | Lunar Gruithuisen and Mairan domes, Rheology and mode of emplacement[END_REF], the lava eruption rate E (expressed in m 3 .s -1 ) can be estimated by: E = 0.323 1 2300𝜅(𝐷/2) 2 0.65 5/2 0.72ℎ

(Eq. 3)
Where κ is the thermal diffusivity of the lava with a value of 10 -6 m 2 s -1 [START_REF] Wilson | Lunar Gruithuisen and Mairan domes, Rheology and mode of emplacement[END_REF].

The duration of the lava effusion Te (expressed in seconds) can then be estimated with:

Te = V/ E (Eq. 4)
Where V is the dome average volume in km 3 .

The domes of the Arago region were then classified as a function of their determined morphometric, spectral and rheologic properties.

Results

3.1/ Mapping and distribution of the domes

Eight candidate volcanic domes, labelled Arago 1 to 8 (A1 to A8) were identified using the DTM derived from the TC images (Figures 2a, 2b and3). Among them, Arago 8 (4,69°N; 22,72°E) was not reported before.

All the studied domes are located within the two youngest mare units mapped by [START_REF] Kodama | Lunar mare volcanism in the eastern nearside region derived from Clementine UV/VIS data[END_REF] (Figure 3). Domes Arago 2 and 3 are located in the Tr3 unit (previously described as medium-Ti unit, dated at 3.67-3.71 Ga [START_REF] Kodama | Lunar mare volcanism in the eastern nearside region derived from Clementine UV/VIS data[END_REF]), whereas domes Arago 1, 4, 5, 6, 7, and 8 are located in the Tr4 unit (the youngest regional unit having the higher-Ti content, dated at 3.59 Ga). With the exception of dome A1 (Figure 4a) and A7 (Figure 4e), the domes are located on a topographic step (Figures 4b, c, d, andf), where the local elevation decreases from west to east. Dome A1 is located in the vicinity of a 100 km long north-southtrending wrinkle ridge (Figures 4a and5a). Besides this example, there is no obvious spatial relationship between domes, wrinkle ridges and sinuous rille (Figure 3).

Although the SE-NW alignment of domes Arago 1, 2, 4, 5, 6, and 8 does not directly crosscut any regional grabens, it suggests a regional tectonic control (see section 4).

3.2/Morphological characteristics

The domes radius, slope, area and volume that we have determined are reported in Table 1. The Arago domes range from 4.8 to 24 km in diameter, 40 to 400 m in height and 0.8 to 3 degrees in slope (Table 1, Figure 4). Four IMPs, characterized by hummocky and blocky floor terrains [START_REF] Braden | Evidence for basaltic volcanism on the Moon within the past 100 million years[END_REF] are observed on the top of dome Arago 6 (Figures 4d and5b). Pseudo-circular, shallow depressions of lower depth-to-diameter ratios than the standard values expected for fresh impact craters (between 0.11 and 0.21; e.g., [START_REF] Pike | Depth/diameter relations of fresh lunar craters: Revision from spacecraft data[END_REF]; [START_REF] Stopar | Relative depths of simple craters and the nature of the lunar regolith[END_REF]) are present on the summits of Arago 1, 7 and 8 and may represent vents, although evidence for extrusive volcanism is not obvious (Figures 4a, 4e, and5a). In addition, there is no obvious evidence supporting that these domes could be intrusive structures. [START_REF] Wöhler | Formation of lunar mare domes along crustal fractures: Rheologic conditions, dimensions of feeder dikes, and the role of magma evolution[END_REF] previously classified Arago 1 to 7 as low slope, effusive domes.

3.3/ Ages

Crater couting was performed on the domes for estimating their ages (Figure 6 and 7), spanning over ~ 1 Ga, from ~ 3.75 to ~ 2.79 Ga. Three groups of ages were derived. The older domes are Arago 1 and8 (3.75 ± 0.05/0.08 Ga and3.73 ± 0.10/0.34 Ga, respectively), followed by Arago 4 to 7 (3.19 ± 0.19/0.62 Ga, 3.34 ± 0.11/0.32, 3.68 ± 0.08/0.18 Ga and3.50 ± 0.08/0.19 Ga, respectively). The younger domes are Arago 2 and 3 (3.03 ± 0.17/0.29 Ga and 2.79 ± 0.28/0.36 Ga, respectively). These age estimates rely on the assumption that the domes are monogenetic, i.e. they were formed during a single volcanic event.

3.4/ Rheology

The domes minimum or maximum height, diameter and volume were used as inputs for estimating the dome rheologic properties (see section 2.2). Results are shown in Table 2.

Plastic viscosities η range between 1.57×10 4 and 4.05×10 6 Pa.s, and lava effusion rate E estimates range from 43 to 230 m 3 .s -1 , yielding a corresponding duration of lava effusion Te between 0.27 and 6.36 years.

3.5/ Spectroscopy

The spectral data from Clementine (Figure 1c), MI (Figure 2c), GRS (Figures 1b and2d)), Diviner (Figure 2f) and M 3 (Figure 8) do not reveal significant differences between the composition of the domes and the surrounding mare units. Dark blue tones on both the Clementine and Kaguya RGB composites are consistent with high Ti mature mare materials (Figures 1c and2c). Using the Kaguya MI RGB composite (Figure 2c), we extracted a mean value of each ratio of bands, and compared the values with those of Clementine RGB used by [START_REF] Wöhler | Formation of lunar mare domes along crustal fractures: Rheologic conditions, dimensions of feeder dikes, and the role of magma evolution[END_REF] in order to rank these domes into different categories (see section 4.1).

M 3 VNIR spectra of the different units are presented in Figure 8. The most common spectrum observed throughout the area is dominated by wide absorptions bands centered at 1.01 and 2.18 µm, consistent with the presence of high calcium pyroxenes (HCP) such as pigeonite or augite (e.g., [START_REF] Adams | Visible and near-infrared diffuse reflectance spectra of pyroxenes as applied to remote sensing of solid objects in the solar system[END_REF][START_REF] Cloutis | Pyroxene spectroscopy revisited: Spectral-compositional correlations and relationship to geothermometry[END_REF]Figures 8c, 8d). Other common lunar minerals such as plagioclase, olivine or spinel (e.g., [START_REF] Martinot | Mineralogical Diversity and Geology of Humboldt Crater Derived Using Moon Mineralogy Mapper Data[END_REF] could not be detected throughout the study area. M 3 data do not reveal major compositional differences between the domes covered by the dataset (Arago 3, 5, 6, and 7), neither between the IMPs (#1 and #7) or the surrounding mare units, all of them being also dominated by HCP signatures (Figure 8c). Spectral parameters maps (Figure 8b) show that there is little variation in the position of the pyroxene 2 µm absorption center, suggesting that the composition of the area is relatively homogeneous at the M 3 scale (140 to 280 m/px, depending on the optical period). Small craters exhibit stronger absorption features compared to the surrounding mare or dome material, as they excavate "fresher" material (meaning they were less exposed to space weathering at the lunar surface e.g., a fresh crater in Tr4 in figure 8c (blue spectrum) (e.g., [START_REF] Mccord | Progress in remote optical analysis of lunar surface composition[END_REF][START_REF] Pieters | Space weathering on airless bodies: Resolving a mystery with lunar samples[END_REF]). Spectral analyses of the largest IMPs (e.g., Sosigenes, IMP#1, sea green spectrum in Figure 8c) show that they are also characterized by higher band depth values, which indicate that they are optically less mature than the mare and dome materials.

3.6/ Dome classification

Based on their geometry (slope value) and their spectral properties (R415/R750), the domes were ranked following the classification scheme by [START_REF] Lena | Lunar Domes[END_REF]:

-H1: small domes with low slopes (< 2°) and R415/R750 values between 0.62 and 0.68 (Arago 4 to 7), -B: large scale domes with higher slopes (1.3-5.4°) and R415/R750 between 0.55 and 0.64 (Arago 2 and 3), -E1: small domes with higher slopes (2-4°) and R415/R750 between 0.58 and 0.62 (Arago 1 and 8).

Discussion.

4.1/Revisited dome classification

The use of higher resolution data from Kaguya and LRO in this study permitted to refine the domes' rank into three classes as defined by [START_REF] Lena | Lunar Domes[END_REF]:

-A2 and A3 fall in the dome category B (instead of class D: low flank slopes, high edifice volume, possibly polygenic in origin, with higher R415/R750 ratio); -A4 to A7 fall as either H1 or C2 domes (instead of class A which have a higher R415/R750 ratio). Their dimensions are smaller than C2 domes, and thus match better those of the H1 category. However, it is to be noted that A4 to A7 are not considered polygenetic domes (as previously suggested for some domes of Marius Hills which defined the H class of [START_REF] Lena | Lunar Domes[END_REF].

-A1 and the new Arago 8 are in class E1 (instead of class A: lowest slopes but higher R415/R750 ratio).

All the studied domes show relatively low slopes compared to lunar silicic domes reported elsewhere on the Moon (e.g., [START_REF] Wilson | Lunar Gruithuisen and Mairan domes, Rheology and mode of emplacement[END_REF][START_REF] Wöhler | A combined spectrophotometric and morphometric study of the lunar mare dome fields near Cauchy, Arago, Hortensius, and Milichius[END_REF][START_REF] Glotch | Highly silicic compositions on the Moon[END_REF][START_REF] Glotch | The Mairan domes: Silicic volcanic constructs on the Moon[END_REF][START_REF] Lena | Lunar Domes[END_REF]. In comparison, the silicic domes of Gruithuisen and Mairan (e.g., [START_REF] Wilson | Lunar Gruithuisen and Mairan domes, Rheology and mode of emplacement[END_REF][START_REF] Glotch | The Mairan domes: Silicic volcanic constructs on the Moon[END_REF] show slopes between 5 and 15° for a similar size range such as Arago 2 and 3 (diameters around 20 km). The low slopes of the Arago domes are more similar to those of other mare domes, such as the shallow domes present on Mons Rümker [START_REF] Zhao | The Mons Rümker volcanic complex of the Moon: A candidate landing site for the Chang'E-5 mission[END_REF], or the Hortensius, Marius Hills and Milichius domes [START_REF] Wöhler | A combined spectrophotometric and morphometric study of the lunar mare dome fields near Cauchy, Arago, Hortensius, and Milichius[END_REF]. The resolution of Diviner data is too low for a good determination of a possible silica composition. However, there is no evidence for low Christiansen Features values/high silica composition on the global map from [START_REF] Greenhagen | Global silicate mineralogy of the Moon from the Diviner Lunar Radiometer[END_REF] (Figure 2f). Both UV and VNIR spectral data indicate that the composition of the domes is similar to the nearby mare unit, i.e. that they are basaltic in composition. Some domes present a rimless crater pit on their summit (interpreted as a volcanic vent); and most domes are roughly circular in shape. Together, these observations confirm the previous assumptions that the Arago domes are likely effusive in nature (e.g., [START_REF] Lena | Lunar Domes[END_REF].

The Arago domes might represent a volcanic stage later than the normal (or typical) mare Tranquillitatis volcanism. This is supported by their emplacement on the youngest regional units (Tr4), except for Arago 2 and 3 that are within Tr3 (Figure 3). Small volumes of remaining magmas could have been emitted at the surface, possibly along fractures, after the major mare flooding episodes. As there is no evidence of high silica contents for any of the domes, the more viscous character of the dome lavas compared to the surrounding mare materials could alternatively be explained by:

-A low magma temperature, -The presence of more crystals due to progressive cooling in the magma chamber, -Magmatic differentiation (more evolved compositions), -Low rate and low volume eruptions, Or a combination of the above (e.g., [START_REF] Francis | Volcanoes[END_REF], and references therein).

4.2/Dome chronology

Based on previous observations and crater counting-derived chronology, the following chronology for the emplacement of the Arago domes is proposed.

Arago 1 and 8 are respectively dated at 3.75 ± 0.05/0.08 Ga and 3.73 ± 0.10/0.34 Ga. They would therefore be the first domes to be emplaced. A1 and A8 are emplaced over the Tr4 unit, which was dated at 3.59 Ga by [START_REF] Jerde | The origin and evolution of lunar high-Ti basalts: Periodic melting of a single source at Mare Tranquillitatis[END_REF], and should therefore be younger than Tr4. We consider this discrepancy between estimated ages to be either due to errors in crater counts (the areas counted on the domes are restricted in size and may induce large errors) or in unit mapping. Alternatively, the domes could be more ancient than Tr4 and embayed by the latest regional mare unit. The two domes have, in consideration with all domes of the area, the smaller radii, intermediate heights and volumes, the steepest slopes and are therefore both classified in the E1 category. Arago 4, 5, 6 and 7 correspond to a later stage of dome activity at ~ 3.68 to 3.19 Ga and are categorized as H1 class domes, characterized by low slopes and small volumes. Their apparent viscosities (< 2×10 5 Pa.s) yield values lower than Arago 1 and 8 (> 8×10 5 Pa.s) by an order of magnitude, indicative of less viscous magmas. Domes Arago 4, 5 and 6 are aligned along a SE-NW trend, possibly suggesting post-or syn-formation along tectonic features (e.g., fissure or fault).

Arago 2 and 3 were respectively emplaced at 3.03 ± 0.17/0.29 Ga and 2.79 ± 0.28/0.43 Ga and represent the latest dome emplacement stage in the region. Arago 2 and 3 have the largest dimensions and show intermediate slopes. Their higher apparent viscosities (4.05×10 6 and 2.75×10 6 Pa.s, respectively), compared to the earlier emplaced domes viscosities (< 8×10 5 Pa.s), might be related to either a silica enrichment of the feeding magmas, a lower temperature of the feeding magmas, or a larger amount of crystals in the magmas. Since there is no signature of high-Si contents in spectral data, the two latter hypotheses are favored. Another possible explanation related to the magma rise speed and source dike dimensions is proposed by [START_REF] Lena | Lunar Domes[END_REF]. The previous classification scheme put the domes of category B (Arago 2 and 3) in a distinct rheologic group compared to categories H1 and E1. Domes of groups E1 and H1 would display high effusion rates but low edifice volumes consistent with a short duration of the effusion process. Category B domes would be emplaced by much larger and deeper feeder dikes, and would be characterized by lower lava effusion rates but larger erupted lava products, implying a longer duration of the effusion process [START_REF] Lena | Lunar Domes[END_REF].

The proposed chronology in this work, assuming the domes to be monogenetic, disagrees with previous work [START_REF] Lena | Lunar Domes[END_REF] which suggested that Arago 2 and 3 could belong to class D (i.e., polygenetic domes). We did not find evidence of plural pulses of volcanism for domes Arago 2 and 3, as reported for some of the Marius Hills domes [START_REF] Whitford-Stark | The Procellarum volcanic complexes-contrasting styles of volcanism[END_REF] or the Gruithuisen and Mairan domes [START_REF] Wilson | Lunar Gruithuisen and Mairan domes, Rheology and mode of emplacement[END_REF][START_REF] Glotch | The Mairan domes: Silicic volcanic constructs on the Moon[END_REF]. Crater distributions on the Arago 1 to 5 and 7 domes (Figure 7) are rather uniform and do not show any slope break indicative of major resurfacing events. The lack of alignment over a single isochrone for dome Arago 6 can be explained by the superimposition of IMPs which induced partial resurfacing. Crater distributions for dome Arago 8 also do not align over an isochrone, suggesting a possible partial resurfacing, and possibly hints at a polygenetic origin (Figure 5c). [START_REF] Zhang | Diversity of basaltic lunar volcanism associated with buried impact structures: Implications for intrusive and extrusive events[END_REF] proposed that Arago 8 could correspond to a lava plateau rather than a dome, but the conclusions would remain similar in both cases, in terms of emplacement from a fissural eruption in more than a single episode.

The general lack of distinguishable units and the relatively small sizes of the other Arago domes are therefore consistent with an emplacement during a single episode. The relatively short duration of lava eruption (Te < 7 years) also make a single stage dome-forming eruptive event plausible.

4.3/Implications for the region history

A previous geologic mapping work within Mare Tranquillitatis was performed by [START_REF] Kodama | Lunar mare volcanism in the eastern nearside region derived from Clementine UV/VIS data[END_REF]. This study revealed that the Arago domes are located onto two specific geologic units: domes Arago 2 and 3 are located in the Tr3 unit (medium-Ti unit, dated at 3.67 Ga), whereas domes Arago 1, 4, 5, 6, 7 and 8 are located in the Tr4 unit (the youngest regional unit dated at 3.59 Ga with also the higher-Ti contents of the mare) (Figure 3). The region contains wrinkle ridges, one sinuous rille, and numerous extensional grabens that surround, or are part of, the Tr4 unit (Figure 3). Almost all the IMPs present in Mare Tranquillitatis are located within the Tr4 unit and they partly overlap some domes, suggesting that they are among the youngest volcanic deposits in the area. Based on these observations, the following chronology is proposed.

The emplacement of Mare Tranquillitatis basalts started more than 3.85 Ga ago (during the Early Imbrian) with the emplacement of the Tr1 to Tr3 geologic units [START_REF] Kodama | Lunar mare volcanism in the eastern nearside region derived from Clementine UV/VIS data[END_REF].

The Tr4 unit was emplaced during the Late Imbrian (3.59 Ga ago) and the region was overlain by the small, effusive domes labelled Arago 1 and 8. Unit Tr4 represent the latest, large-scale effusive mare event visible in the Arago region. Domes Arago 4 to 7 are contemporary (3.59 Ga) or younger than Tr4 and might mark the end of the Tr4 mare emplacement with effusive eruptions along local fractures. Domes Arago 2 and 3, the largest domes with intermediate slopes, were emplaced at the beginning of the Erastosthenian (~ 2.9 Ga ago), possibly from more evolved, more crystal-rich, or cooler magmas. The late formation of these two domes suggests long-lived volcanism in the region, which is however located outside the PKT, but is still associated with a GRS Thorium anomaly [START_REF] Lawrence | Small-area Thorium features on the lunar surface[END_REF] (Figure 2d).

Almost all IMPs are located on the Tr4 unit, likely representing a waning stage of dike emplacement in the region (e.g., [START_REF] Wilson | Eruption of magmatic foams on the Moon: Formation in the waning stages of dike emplacement events as an explanation of "irregular mare patches[END_REF]. IMPs were initially interpreted as young (< 1 Ga) volcanic features because of their optical immaturity and the low number of superimposed impact craters (e.g., [START_REF] Braden | Evidence for basaltic volcanism on the Moon within the past 100 million years[END_REF]. Recent studies suggest that IMPs more likely formed concurrently or slightly later than the surrounding mare lava flows (e.g., [START_REF] Garry | The origin of Ina: Evidence for inflated lava flows on the Moon[END_REF][START_REF] Wilson | Eruption of magmatic foams on the Moon: Formation in the waning stages of dike emplacement events as an explanation of "irregular mare patches[END_REF][START_REF] Zhang | Diversity of basaltic lunar volcanism associated with buried impact structures: Implications for intrusive and extrusive events[END_REF]. Similarly to the recently discovered Ring-Moat Dome Structures (RMDS) commonly observed in lunar mare regions, IMPs are indeed best explained as the result of basaltic lava flows inflation during their cooling phases(e.g., [START_REF] Garry | The origin of Ina: Evidence for inflated lava flows on the Moon[END_REF][START_REF] Zhang | Newly discovered ring-moat dome structures in the lunar maria: Possible origins and implications[END_REF][START_REF] Wilson | Eruption of magmatic foams on the Moon: Formation in the waning stages of dike emplacement events as an explanation of "irregular mare patches[END_REF][START_REF] Qiao | The role of substrate characteristics in producing anomalously young crater retention ages in volcanic deposits on the Moon: Morphology, topography, subresolution roughness, and mode of emplacement of the Sosigenes lunar irregular mare patch[END_REF][START_REF] Wilson | A theoretical model for the formation of Ring Moat Dome Structures: Products of second boiling in lunar basaltic lava flows[END_REF]. IMPs formation mechanisms are controversial, but magma degassing below a solidified lava crust as observed in Hawaiian lava lakes (e.g., [START_REF] Wilson | Eruption of magmatic foams on the Moon: Formation in the waning stages of dike emplacement events as an explanation of "irregular mare patches[END_REF] could induce cracking of the crust, resulting in the extrusion of gas-rich magmatic foams to form hummocky mounds. We favor this mechanism to explain the extrusion of IMPs onto the Tr4 unit, at the time of its emplacement or shortly after. At locations where the gas might have been able to escape from magmatic intrusions, domes could have been formed instead of IMPs. Four IMPs are, however, situated on the dome Arago 6 (Figure 5b), implying that they should have formed after the dome emplacement. The small size of the IMPs (tenth of meters) observed in this unit could be due to the important thickness of the Tr4 unit, minimizing the quantity of extruding foam and resulting in small IMPs. We infer the domes Arago 4 to 7 to be contemporaneous or younger than unit Tr4, similarly to the IMPs. Because of the gaps in age between the three groups of domes in the Arago region, it is however possible that the IMPs and dome formation periods overlapped, and that some of the IMPs predate the youngest domes Arago 2 and 3, which might have been fed by a different, deeper magma source (see section 4.2).

The emplacement of the Diamondback sinuous rille, Arago domes and regional IMPs can therefore be interpreted as the result of intrusive dikes reaching different depths within the cooling lunar crust (e.g., Zhang et al., 2018, Wilson and[START_REF] Wilson | Eruption of magmatic foams on the Moon: Formation in the waning stages of dike emplacement events as an explanation of "irregular mare patches[END_REF]. Dikes breaching the surface and erupting may create high flux effusive eruptions such as sinuous rilles, whereas dikes just reaching the near surface may extrude small amounts of lava, producing small domes. As the lunar crust cools and thickens over time, dikes may have remained trapped at shallow depths and have underdone gas exsolution. Their accumulation, and the local foam extrusion, would eventually form the IMPs.

Dikes remaining trapped at depth may result in grabens and pit chains instead. This interpretation however implies the existence of a magma storage beneath the mare to support outgassing lava eruption. Although Mare Tranquillitatis is not associated with any lunar mascon, positive Bouguer anomalies observable from the GRAIL dataset are located ~90 km southeast of dome Arago 2, just below dome Arago 8 (the "Lamont" anomaly) and another 40 km south of dome Arago 7 (the northern extension of the Lamont anomaly) (Figure 2e). This may indicate the presence of largescale magmatic intrusions at depth [START_REF] Zuber | Gravity field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission[END_REF]. The Lamont gravity anomaly was previously interpreted as a buried impact structure associated with both intrusive and extrusive volcanism (e.g., [START_REF] Evans | Identification of buried lunar impact craters from GRAIL data and implications for the nearside maria[END_REF][START_REF] Zhang | Diversity of basaltic lunar volcanism associated with buried impact structures: Implications for intrusive and extrusive events[END_REF]. These previous studies show that ancient buried impact structures such as Lamont, may be accompanied by dense dike intrusions, craterconcentric and crater-radial patterns of alignment of volcanic features such as cones, domes, rilles, linear or arc-shaped ridges and grabens (e.g. [START_REF] Zhang | Diversity of basaltic lunar volcanism associated with buried impact structures: Implications for intrusive and extrusive events[END_REF]. Figure 3 shows that most wrinkle ridges and extensional grabens in the Arago region are indeed concentric to the Lamont anomaly, whereas domes Arago 1, 2, 4, 5, 6 and 8 are aligned radially to the Lamont structure. As it is the case for several domes, some of the IMPs are aligned radially, and might represent the surface manifestation of large-scale, intrusive dikes likely connected to the Lamont structure.

4.4/The Arago region, a suitable landing site for future science and ISRU missions?

The Arago region exhibits a diversity of volcanic features and deposits, suggesting a long-lived magmatic history, possibly spanning over one billion years. These volcanic features were formed by a range of volcanic eruption styles, including flooding volcanism (rille and mare units), small shield volcanoes (domes) and outgassing process related depressions (vents and IMPs). The long duration of volcanism (> 1 Ga) is rather unusual for such locations outside of PKT. As lunar volcanism provides a window into the thermal and compositional evolution of the Moon, such regions contain a diverse and long geological record that is key to future scientific advances (e.g., NRC, 2007;[START_REF] Crawford | Back to the Moon: the scientific rationale for resuming lunar surface exploration[END_REF][START_REF] Jaumann | Geology, geochemistry, and geophysics of the Moon: Status of current understanding[END_REF]. The Arago region therefore represents a high scientific interest site for future missions of exploration (e.g., [START_REF] Flahaut | Identification and characterization of science-rich landing sites for lunar lander missions using integrated remote sensing observations[END_REF]. In addition, the Arago region offers an interesting target for future ISRU activities. The Arago region corresponds to a Thorium positive anomaly (Figure 2d) which might be of interest for nuclear power, although thorium still lacks applications compared to uranium (e.g., [START_REF] Crawford | Lunar resources: A review[END_REF]. But most significantly, the region is dominated by Ti-rich units, with estimates of 13.7 ± 0.7 wt% TiO2 for the mare unit Tr4 (where most of the domes are located) and 12.6 ±0.8 wt% TiO2 for unit Tr3 (where Arago 2 and 3 are located) [START_REF] Kodama | Lunar mare volcanism in the eastern nearside region derived from Clementine UV/VIS data[END_REF]. Unit Tr4 extends further south to the Tranquility Base where Apollo 11 astronauts collected soils with 7.5 to 12 wt% TiO2 (e.g., [START_REF] Beaty | The petrology and chemistry of basaltic fragments from the Apollo 11 soilpart I[END_REF][START_REF] Lucey | Understanding the Lunar Surface and Space-Moon Interactions[END_REF] which is mainly accommodated in the mineral ilmenite (FeTiO3). Together with Oceanus Procellarum and the western part of Mare Imbrium, Mare Tranquillitatis is one of the few vast regions of high ilmenite concentrations on the Moon. Ilmenite has long been recognized as a key resource for oxygen production through mineral reduction (e.g., [START_REF] Cutler | A carbothermal scheme for lunar oxygen production[END_REF][START_REF] Gibson | Lunar oxygen production from ilmenite[END_REF][START_REF] Taylor | Production of oxygen on the Moon: Which processes are best and why[END_REF][START_REF] Anand | A brief review of chemical and mineralogical resources on the Moon and likely initial in situ resource utilization (ISRU) applications[END_REF]. A number of reductants is possible (e.g., [START_REF] Gibson | Lunar oxygen production from ilmenite[END_REF], although hydrogen seems to be favored. Ilmenite reduction ranks high among ISRU processes to be tested and demonstrated with upcoming missions, owing to its relative simplicity and technological readiness (e.g., [START_REF] Anand | A brief review of chemical and mineralogical resources on the Moon and likely initial in situ resource utilization (ISRU) applications[END_REF][START_REF] Crawford | Lunar resources: A review[END_REF]. As noted by [START_REF] Anand | A brief review of chemical and mineralogical resources on the Moon and likely initial in situ resource utilization (ISRU) applications[END_REF], this process also yields a metal product (titanium) which may be of additional economic importance. The deposit of interest for mining appears rather wide and locally homogeneous from orbit, and the predicted content has been confirmed with ground truth.

Given its combined scientific interest and potential for resource utilization, we argue that the Arago region is a key candidate site for a future exploration mission. It would also offer the unique opportunity to fly over Tranquility Base 50 years after the first human walked on the Moon.

Conclusion

Eight volcanic domes in the Arago region, western Mare Tranquillitatis, were reported and characterized in this paper. Despite various morphometric characteristics, most domes are interpreted as single stage eruptive events, effusive in nature. High resolution observations, combined with the results of this study, suggest the following geological history of Mare Tranquillitatis. The emplacement of mare basalts older than 3.85 Ga (regional unit Tr1) was followed by the emplacement of additional lava flows (Tr2 to Tr5), volcanic domes and superimposed IMPs, a period which lasted for more than 1 Ga. Of the eight Arago mare domes, the youngest ones (Arago 2 and 3) display distinct rheological parameters and may originate from a distinct, deeper source. The Arago region is located outside of the PKT, but it is associated with a positive Thorium anomaly, which could explain its exceptional volcanic history and complexity.

The Arago region unique geologic record holds clues to the Moon's thermal and magmatic evolution. In addition, the Arago region corresponds to one of the few ilmenite-rich lunar mare deposits presenting a strong potential for future ISRU activities. A to F : Crater counts on the NAC images of domes (A1, A2 ,A3, A4-6, A7 and A8 respectively).

Figures Captions

Craters (in magenta) were counted on the entire dome area with the exception of dome A8 as the western portion of the dome is not covered by NAC imagery (counted area is indicated by a yellow outline).

Tables 683

Table 1: Morphometric properties of the eight Arago domes. Given the irregular shape of the domes, both a minimum and maximum height and radius 684

A

  . Location of the study area (white box) on the nearside of the Moon. Previously referenced lunar domes and IMPs are shown as red triangles and green squares respectively. The LROC WAC global mosaic is used as a background. B. Location of the study area (white box) on the Lunar Prospector Thorium abundance map. The outline of the Procellarum KREEP Terrane (PKT) is represented as a thick black line. C. Location of the study area (white box) on Clementine RGB mineral composite (R =750/415 nm, G = 750/950 nm, B = 415/750 nm, see text for more details). Apollo and Luna landing sites are labeled.

Figure 2 A

 2 Figure 2

Figure 3

 3 Figure3

Figure 4 A

 4 Figure 4

Figure 5 A

 5 Figure 5

Figure 6

 6 Figure 6

Table 2 :

 2 Modelled rheologic properties of the eight Arago domes. Mean heights shown in row 4 were used to perform calculations. 688

	685	were measured.
		Dome	Coordinates	Height (m)	Mean radius (m)	Slope (°)	Area (km²)	Volume (km 3 )
			Latitude (°) Longitude (°) Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum
		Arago 1	7.70	22.07	103	159	2550.25	3146.25	2.46	2.98	17.81	24.90	0.70	1.65
		Arago 2	7.57	21.55	320	398	9767.25	12021.50	1.96	1.92	240.02	395.85	31.97	60.23
		Arago 3	6.16	19.94	245	397	8411.25	12048.00	1.69	1.90	212.90	425.41	18.15	60.35
		Arago 4	8.52	21.21	38	114	2748.50	7113.25	0.82	0.93	18.36	129.19	0.30	6.04
		Arago 5	8.95	20.94	46	94	3276.50	4805.50	0.81	1.15	31.87	77.38	0.52	2.28
		Arago 6	9.27	20.76	84	129	3666.00	4068.25	1.41	1.84	35.45	43.11	1.18	2.24
		Arago 7	11.29	24.11	85	105	2427.75	2859.25	2.01	2.12	18.42	22.53	0.52	0.90
		Arago 8	4.70	22.72	116	213	3435.50	5240.00	2.54	2.62	26.96	57.97	1.43	6.12

Acknowledgments

The authors wishes to thank F. Zhang and an anonymous reviewer for their help in significantly improving our manuscript. The authors are also grateful to Sylvain Breton and Qian Huang for fruitful discussions. N. Schnuriger started this research project as a bachelor's intern at IRAP Toulouse and is now employed as a PhD student at CRPG Nancy at the time of writing. Both N. Schnuriger and J. Flahaut's contributions were and are supported by the CNES "Appels à Projets de Recherche" ExoMars and Luna attributed to J. Flahaut. J. Flahaut acknowledges funding from the CNRS Momentum, CNES APR and LUE future leader programs. This is CRPG contribution N°2719.

C. -M 3 continuum-removed spectra of domes A3, A5 and A6, of nearby mare units Tr3, Tr4 (including a spectra taken over a fresh, small crater, labeled Tr4fresh) and of IMPs #1 (Sosigenes) and #7. M 3 spectra are 3 × 3 pixel averages with the exception of the spectrum taken over IMP#7 which is a single pixel spectrum (as the IMP is smaller in size than a 3x3 pixel average). Data were processed using the algorithm developed by [START_REF] Martinot | Mineralogical Diversity and Geology of Humboldt Crater Derived Using Moon Mineralogy Mapper Data[END_REF]


Erika Cortese

Iacopo Carusotto

Raffaele Colombelli

Simone De Liberato
email: liberato@soton.ac.uk

Strong coupling of ionizing transitions

come

INTRODUCTION

When a single photon can be trapped in an optical resonator long enough to undergo multiple absorption and re-emission cycles, the coupled light-matter system is said to be in the strong coupling regime. Its physics cannot then be correctly described in terms of irreversible absorption and emission of photons; instead it becomes necessary to consider hybrid quasiparticles, half-light half-matter, named polaritons [START_REF] Kavokin | Microcavities[END_REF]. Many works have demonstrated how the hybridization with matter strongly alters not only the spectrum, but also the field profile [START_REF] Liberato | Light-matter decoupling in the deep strong coupling regime: the breakdown of the Purcell effect[END_REF][START_REF] Bayer | Terahertz light-matter interaction beyond unity coupling strength[END_REF][START_REF] Passler | Strong coupling of epsilon-near-zero phonon polaritons in polar dielectric heterostructures[END_REF], and the quantum [START_REF] Savasta | Quantum complementarity of microcavity polaritons[END_REF][START_REF] Boité | Fate of photon blockade in the deep strong-coupling regime[END_REF][START_REF] Garziano | Cavity QED beyond rotating wave approximation: photon bunching from the emission of individual dressed qubits[END_REF][START_REF] Muñoz | Emitters of N-photon bundles[END_REF] and nonlinear [START_REF] Carusotto | Quantum fluids of light[END_REF][START_REF] Gubbin | Theory of nonlinear polaritonics: X (2) scattering on a β-SiC surface[END_REF] properties of the photonic resonator. More recently, interest has also broadened toward investigating how strong coupling can be used to modify properties of the underlying matter degrees of freedom [START_REF] Galego | Cavity-induced modifications of molecular structure in the strong coupling regime[END_REF][START_REF] Cwik | Self-consistent molecular adaptation induced by strong coupling[END_REF][START_REF] Cortese | Collective optomechanical effects in cavity quantum electrodynamics[END_REF][START_REF] Luk | Multiscale molecular dynamics simulations of polaritonic chemistry[END_REF][START_REF] Flick | Cavity Born-Oppenheimer approximation for correlated electron-nuclear-photon systems[END_REF][START_REF] Keeling | Orientational alignment in cavity quantum electrodynamics[END_REF][START_REF] Khurgin | Excitonic radius in the cavity polariton in the regime of very strong coupling[END_REF][START_REF] Citrin | Microcavity effect on the electron-hole relative motion in semiconductor quantum wells[END_REF][START_REF] Brodbeck | Experimental verification of the very strong coupling regime in a GaAs quantum well microcavity[END_REF], including changes in electrical [START_REF] Orgiu | Conductivity in organic semiconductors hybridized with the vacuum field[END_REF][START_REF] Feist | Extraordinary exciton conductance induced by strong coupling[END_REF][START_REF] Hagenmüller | Cavity-assisted mesoscopic transport of fermions: coherent and dissipative dynamics[END_REF][START_REF] Paravicini-Bagliani | Magneto-transport controlled by Landau polariton states[END_REF] and photochemical [START_REF] Hutchison | Modifying chemical landscapes by coupling to vacuum fields[END_REF][START_REF] Herrera | Cavity-controlled chemistry in molecular ensembles[END_REF][START_REF] Martínez-Martínez | Polariton-assisted singlet fission in acene aggregates[END_REF] properties.

Notwithstanding a large and rapidly growing interest in polaritonic physics, until now the only transitions exploited to achieve strong coupling were those between bound electronic states. Bound-to-continuum ionizing transitions would in fact seem to be, by their very nature, irreversible, as the ionized components get separated upon photon absorption, thus not allowing for a subsequent re-emission.

In this work we demonstrate that ionizing electronic transitions can be strongly coupled to a photonic resonator, leading to the appearance of discrete polaritonic resonances below the ionization threshold. The electronic part of such resonances corresponds to bound excitons not present in the uncoupled system, and are thus generated by the coupling with the cavity-photonic field. In particular, these bound states do not rely on the Coulomb attraction between electrons and holes underlying standard excitons. Apart from its importance from a fundamental perspective, this discovery opens the way to a number of practical applications, as those novel bound states can be pathways for chemical reactions, improve the efficiency of multi-photon transitions, or push the tunability of semiconductor devices beyond that allowed by mere electronic properties.

Most of the concepts introduced in this paper are general enough to be broadly applied to any cavity quantum electrodynamics platform, including atomic and molecular systems, for which quantum electrodynamics density-functional approaches are currently being developed [START_REF] Ruggenthaler | Quantum-electrodynamical density-functional theory: bridging quantum optics and electronic-structure theory[END_REF][START_REF] Flick | Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry[END_REF]. Notwithstanding the above, henceforth we will consider the specific case of microcavityembedded doped quantum wells, sketched in Fig. 1, which have an immediate technological relevance while also allowing for a simpler and more transparent theoretical treatment thanks to their effective one-dimensional nature. In those systems the confinement along the growth (z) axis splits the conduction band into multiple discrete bound or continuous unbound subbands. The parabolic quasi-parallel in-plane dispersion then allows for the excitation of resonant coherent electronic transitions with long dephasing times. When more than one bound subband is present, the resulting narrow optical transition has been successfully strongly coupled with mid-infrared and terahertz resonators [START_REF] Dini | Microcavity polariton splitting of intersubband transitions[END_REF][START_REF] Anappara | Signatures of light-matter excitations in the ultra-strong coupling regime[END_REF][START_REF] Todorov | Ultrastrong light-matter coupling regime with polariton dots[END_REF]. The resulting quasiparticles, named intersubband polaritons, have been highlighted as a promising platform for long-wavelength optoelectronics [START_REF] Liberato | Stimulated scattering and lasing of intersubband cavity polaritons[END_REF][START_REF] De Liberato | Terahertz lasing from intersubband polariton-polariton scattering in asymmetric quantum wells[END_REF][START_REF] Colombelli | Perspectives for intersubband polariton lasers[END_REF][START_REF] Manceau | Resonant intersubband polariton-LO phonon scattering in an optically pumped polaritonic device[END_REF], with the possibility of tuning the doping in situ by optical or electrical means [START_REF] Anappara | Electrical control of polariton coupling in intersubband microcavities[END_REF][START_REF] Guenter | Sub-cycle switchon of ultrastrong light-matter interaction[END_REF]. The role of intersubband polariton formation on the electronic wavefunction has been investigated in the past [START_REF] Liberato | Quantum theory of electron tunneling into intersubband cavity polariton states[END_REF], highlighting the possibility of dramatically increasing the emission efficiency by injecting electrons into superradiant bright states. Bound-tocontinuum transitions in doped quantum wells have also been the object of theoretical [START_REF] Załużny | Bound-free intraband absorption line shape in quantum-well structures[END_REF] and experimental [START_REF] Capasso | Observation of an electronic bound state above a potential well[END_REF] investigations.

THEORY

In this section we will sketch the theory of the bound-tocontinuum strong coupling and the calculation of the corresponding resonator-induced bound excitonic states. Detailed derivations can be found in Supplement 1.

A. Spectrum

The problem of the coupling between a discrete resonance (in our case the photonic mode) and a continuum (the bound-tocontinuum electronic transitions) was initially treated by Fano in his landmark paper [START_REF] Fano | Effects of configuration interaction on intensities and phase shifts[END_REF]. In such a work, the coupled eigenfrequencies are always assumed to fall into the uncoupled continuum, leading to the characteristic asymmetric broadened absorption lineshape. The limit of a very narrow continuum, describing an inhomogeneously broadened discrete resonance, has also been investigated [START_REF] Houdré | Vacuum-field Rabi splitting in the presence of inhomogeneous broadening: resolution of a homogeneous linewidth in an inhomogeneously broadened system[END_REF][START_REF] Manceau | Immunity of intersubband polaritons to inhomogeneous broadening[END_REF]. Here we will instead consider the case of a semi-infinite ionization continuum of unbound states, in which one of the hybridized light-matter eigenmodes lies below its lowest edge. This can happen either because the uncoupled discrete resonance is not resonant with the continuum to start with, or because the coupling is large enough to push a coupled eigenmode out of the continuum.

In a planar semiconductor heterostructure, the electronic states can be indexed by the in-plane two-dimensional momentum vector k and by an index n, which runs over both bound and continuum states quantized along the growth, out-of-plane axis. The field operator for electrons of in-plane momentum k can thus be written as

Ψ k z X n ϕ n zc nk , (1)
where c nk is the fermionic annihilation operator of the nth electron level with in-plane wavevector k, frequency ω c nk , and envelope wavefunction ϕ n z. The electronic single-particle spectrum will be characterized by one or more bound levels ω c nk < 0, and a series of unbound states delocalized across the bulk ω c nk > 0. Those states can either form a real continuum or arrange themselves in a set of broadened minibands, depending on the details of the potential felt by the electrons. We will in the following use the term continuum with the understanding that it can cover both situations.

Collective electronic transitions between single-particle states can be indexed by the in-plane wavevector q and the index α ≡ nm, with m and n, respectively, the initial and final electronic levels. Narrowing down to the case of interest, we consider a system in which only bound-to-continuum transitions are optically active, by choosing the number of electrons N such that, as depicted in Fig. 1(b), the Fermi energy stands between the bottom of the last bound and first unbound subbands. A cavity photon with in-plane wavevector q thus couples to electronic transitions described by the dipole operators:

b † nmq 1 ffiffiffiffi ffi N p X k c † nkq c mk : (2)
In the dilute excitation regime, in which the number of excitations in the system is much smaller than N , those operators satisfy bosonic commutation relations [START_REF] Liberato | Stimulated scattering and lasing of intersubband cavity polaritons[END_REF][START_REF] Ciuti | Quantum vacuum properties of the intersubband cavity polariton field[END_REF][START_REF] Shammah | Superradiance with local phase-breaking effects[END_REF]:

b αq , b † βq 0 δ αβ δq -q 0 : (3)
Many-body plasmonic effects can become important at high doping densities. The Hamiltonian describing single particle transitions b αq , and their mutual Coulombic interaction, can then be diagonalized through a Bogoliubov rotation, leading to a Hamiltonian of decoupled multisubband plasmon modes p αq [START_REF] Bernardis | Breakdown of gauge invariance in ultrastrong-coupling cavity QED[END_REF][START_REF] Todorov | Intersubband polaritons in the electrical dipole gauge[END_REF][START_REF] Todorov | Dipolar quantum electrodynamics of the two-dimensional electron gas[END_REF][START_REF] Liberato | Quantum theory of intersubband polarons[END_REF]. The Bogoliubov rotation can then be inverted, writing the single particle transition operators as linear superpositions of the plasmonic ones:

b † αq b α-q X β h αβ p † βq p β-q : (4)
By introducing a † q , the bosonic creation operator for a cavity photon of in-plane wavevector q and frequency ω a q , the light-matter Hamiltonian takes the form

H X q ℏω a q a † q a q X α ℏω p α p † αq p αq X α ℏΞ αq 2 a † -q a q p † αq p α-q ,
where ω p α are the frequencies of the electronic transitions dressed by local-field effects and Ξ αq is the renormalized light-matter coupling. This Hamiltonian can be diagonalized in terms of bosonic hybrid light-matter polariton operators: d sq x sq a q z sq a † -q X α y sαq p αq w sαq p † α-q :

(5)

When the index s runs over solutions that are in the continuum, the system is equivalent to that described by Fano, and we will not explicitly discuss its solution here. We consider instead solutions with frequency ω d sq < χ, where we define the frequency of first ionization χ as the lowest ω p α belonging to a continuum part of the spectrum [see Fig. 1(a)]. The discrete nature of those polaritonic modes implies their matter component is a bound excitonic state generated by the coupling with the photonic field. This novel mechanism of binding is to be contrasted to the usual Coulomb electron-hole interaction that binds standard excitons. The eigenvalue ω d sq is shown (in this case) to obey the eigenequation (see Supplement 1)

ω a q ω a2 q -ω d 2 sq X α jΞ αq j 2 ω p α ω p2 α -ω d 2 sq 1. (6)
The existence of a solution satisfying Eq. ( 6) can be easily proved if the photonic mode lies below the frequency of first ionization (ω a q < χ). In the opposite case (ω a q > χ), however, one needs to solve the integral equation to verify whether the interaction is strong enough to push the hybrid light-matter mode out of the continuum.

B. Excitonic States

Assuming for the moment that Eq. ( 6) has at least a solution ω d sq < χ, we will now study its properties. The operator in Eq. ( 5) describes the normal mode of the system as a superposition of photonic and matter excitations but, notwithstanding the fact all electronic transitions are in the continuum, and thus all the available final states unbound, there is not enough energy to promote an electron to an unbound state. The particular linear superposition of bound-to-continuum transitions specified by the y sαq and w sαq coefficients in Eq. ( 5) thus has to describe a bound excitonic state not present in the uncoupled Hamiltonian. To visualize such a state we can define the electron density,

N z X k Ψ † k zΨ k z, (7)
and calculate its difference between the ground state jGi and the state with one excitation in an arbitrary d sq polaritonic mode:

ΔN sq z hGjd sq N zd † sq jGi -hGjN zjGi P sq jψ e sq zj 2 -jψ g sq zj 2 , (8)
where, P sq is the weight of the matter component of the polaritonic mode, and ψ g sq z and ψ e sq z, built respectively only by wavefunctions of initially full and empty electronic levels, can be interpreted as the wavefunctions of the initial (ground) and final (excited) states of the excitonic transition created by the operator d † sq .

RESULTS

We will now apply the previously developed theory to the case of n QW identical doped GaAs∕Al x Ga 1-x As quantum wells of width L QW 4 nm. The Al fraction x 0.33 then ensures that each quantum well will have a single electronic bound state.

Intersubband polaritons have been demonstrated in those structures, with doping levels up to N 2DEG 3 × 10 12 cm -2 [START_REF] Manceau | Resonant intersubband polariton-LO phonon scattering in an optically pumped polaritonic device[END_REF]. Electronic bare wavefunctions are then calculated considering a single conduction band in the effective mass approximation and using Bastard boundary conditions for the envelope functions [START_REF] Bastard | Wave Mechanics Applied to Semiconductor Heterostructures[END_REF]. These eigenfunctions are used to calculate all the electronic parameters of Eq. ( 5). The resulting multi-mode Hopfield matrix is then numerically diagonalized, leading to the determination of the eigenfrequencies ω d sq and of the eigenvectors in Eq. ( 5). Those coefficients are then used in Eq. ( 8) to calculate the ground and excited electronic densities jψ g sq zj 2 and jψ e sq zj 2 , and the matter weight P sq .

A. n QW 1
To build a good understanding of the implications of bound-tocontinuum strong coupling, we start by considering a single quantum well in a wide bulk of total width T 1 μm, aptly modeling an ionization continuum in which the electron can escape and be lost. The envelope functions in Fig. 1(a) have been calculated using these parameters. To get large values of the coupling with a single quantum well, we consider the electronic transition coupled to a subwavelength photonic resonance with an effective cavity length L c much smaller than the transition wavelength λ. In particular, we fix L c 25 nm, which for a photonic transition quasi-resonant to the frequency of first ionization χ, implies λ 2L c ≃ 125, a value that can be today achieved using various mid-infrared architectures [START_REF] Benz | Strong coupling in the sub-wavelength limit using metamaterial nanocavities[END_REF][START_REF] Caldwell | Lowloss, extreme subdiffraction photon confinement via silicon carbide localized surface phonon polariton resonators[END_REF][START_REF] Gubbin | Theoretical investigation of phonon polaritons in SiC micropillar resonators[END_REF]. Note that specific implementations could impose further constraints on the shape of the bulk (e.g., forcing the quantum well to be at a specific distance from one of the boundaries), but for the sake of definiteness we will neglect this possibility and consider the quantum well to be placed in the center of the 1 μm bulk. A microscopic model for the photonic resonator is instead considered for the case of multiple quantum wells described below.

In Figs. 234we show the results for cavity energies ℏω a q 185, 195, and 205 meV respectively. In panel (a) of each figure we plot the polaritonic spectrum as a function of the doping, clearly showing the ionization continuum around ℏχ 188.4 meV. In the case ω a q < χ, a single discrete mode below the continuum is also present for any doping. In the case of ω a q > χ, it is present only above a critical doping, since the coupling needs to be strong enough to push a polaritonic mode out of the continuum. In panels (b) we instead plot the normalized excited electronic density jψ e sq zj 2 for the lowest-lying polaritonic state in a neighborhood of the quantum well. Since we are considering a quantum well with a single initially occupied electronic state, the ground wavefunction ψ g sq z coincides with the lowest subband envelope function and thus depends neither on s nor on doping. In Fig. 5(a) we plot the ground density jψ g sq zj 2 (blue solid line) and the excited density jψ e sq zj 2 (red dashed line) corresponding to the lowest eigenmode in Fig. 3(g) in a 40 nm interval around the quantum well.

We can verify that a bound exciton forms only when a discrete polaritonic resonance below the continuum is present. The difference between the energy of first ionization and the energy of the discrete polaritonic mode plays in this case the role of binding energy for the exciton, being the excess energy the matter component of the polariton needs to dissociate into the continuum. By comparing Figs. 234, we can thus realize that the binding energy depends non-trivially on both the strength of the light-matter interaction and on the detuning between the cavity mode and the edge of the continuum. At low enough temperature, the discrete polaritonic resonance, not having enough energy to decay in the ionization continuum, is thus expected to have a linewidth of the order of few meV, determined by non-parabolicity, electron-phonon, and electron-electron scattering [START_REF] Waldmüller | Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas[END_REF], as well as by the coupling of its photonic component to extra-cavity radiative modes. The predicted coupling-induced shifts are thus sizably larger than the expected linewidths, making those resonances spectroscopically observable and individually addressable.

To prove that bound excitonic states do not exist in the continuum below the critical density, in panels (c)-(g) of Figs. 234we plot the excited electronic density jψ e sq zj 2 for all the polaritonic modes, using a cutoff of 500 meV on the single electron energies. Lines corresponding to all values of s except the lowest-lying one are all plotted in red, and their overlap forms the uniform red band that can be seen on the very bottom of each panel, of homogeneous density T -1 . Such homogeneous density, vanishing in the limit T → ∞ of a true continuum, is that expected from a standard bound-to-continuum excitation. The density of the first mode is instead plotted in blue. Those results further confirm that a bound exciton is present only when a discrete polaritonic mode appears. Note that due to the different scales of panels (b) and (c)-(g) the node of the excited density is not clearly visible in the latter.

Of course the normalized electronic densities give only partial information on the existence and observability of resonatorinduced bound exciton states, because from Eq. ( 8) they are weighted by the matter fraction P sq . In Fig. 5(b) we thus plot P sq relative to the mode plotted in panels (b) of Figs. 234as a function of doping, for the three considered values of the cavity energy. As expected, when the bare cavity mode is below the continuum (ℏω a q 185 meV, blue solid line), the discrete lowestlying polaritonic mode for a vanishing doping is just the bare cavity with a vanishing matter component. In the opposite cases (ℏω a q 195 meV, red dashed line, and ℏω a q 205 meV yellow dashed-dotted line) the lowest mode is initially purely matter (P sq 1), and only when the discrete polaritonic mode appears do we observe light-matter hybridization. In all three cases, though, a strong hybridization is observed for experimentally achievable values of the doping.

B. n QW 20

Having investigated the single-quantum-well case, and demonstrated the formation of bound excitonic resonances for suitable Weight of the matter component P sq for the lowest-lying polaritonic mode as a function of doping for ℏω a q 185 meV (blue solid line), ℏω a q 195 meV (red dashed line), and ℏω a q 205 meV (yellow dashed-dotted line). Other parameters as in Fig. 2. strength of the light-matter interaction, here we will consider the case of n QW 20 quantum wells that couple to the TM0 mode of a planar resonator as wide as the electron bulk. The relative facility to achieve strong coupling in multiple-quantum-well structures [START_REF] Dini | Microcavity polariton splitting of intersubband transitions[END_REF][START_REF] Anappara | Signatures of light-matter excitations in the ultra-strong coupling regime[END_REF][START_REF] Todorov | Ultrastrong light-matter coupling regime with polariton dots[END_REF] will allow for a rapid observation of the discrete polaritonic resonances emerging out of the continuum, heralding the generation of resonator-induced bound excitonic states.

We consider a sample with n QW 20 quantum wells, separated by barriers of 20 nm, with the same length L QW 4 nm used previously, and the bulk and the resonator have a total length L c T 0.5 μm. The filling factor n QW L QW ∕L c 0.16, which in Ref. [START_REF] Todorov | Intersubband polaritons in the electrical dipole gauge[END_REF] was shown to be the relevant figure of merit to quantify the strength of the light-matter interaction, is thus the same as in Section 3.A, allowing for a meaningful comparison.

In Fig. 6(a) we plot the eigenmodes for ℏω a q 195 meV. Notwithstanding minor differences, including a larger energy of first ionization ℏχ 192 meV, which are to be expected given the different structure of the continuum, we recover results in agreement with those in Fig. 3(a), showing that discrete resonances below the continuum are observable also in multi-quantumwell structures. In Figs. 6(b) and 6(c) we plot the excited electronic density in the lowest-lying eigenmode, for values of the doping N 2DEG 0 and 3 × 10 12 cm -2 , respectively, marked by arrows in Fig. 6(a). It can be observed that the electronic densities for the continuous (red) and discrete (blue) modes are not as spectacularly different as in Fig. 3. This was expected because, in a multi-quantum-well structure, ionized electrons will still be confined in the proximity of quantum wells, as the total space occupied by the quantum wells is now a macroscopic fraction of the total width of the bulk. Nevertheless, we can recognize the same physics at play, as the collective density, although modulated by the presence of the quantum wells, passes from a mode of the entire structure, whose intensity is maximal at the center, to a bound one in which the density is roughly the same in each quantum well.

Finally, with the objective of testing the accuracy of our quantum theory and to provide an experimentally accessible observable, we calculated the reflectivity of the same structure coupled to a planar metallic resonator, using a classical transfer matrix approach in the effective medium approximation including local field effects [START_REF] Załużny | Bound-free intraband absorption line shape in quantum-well structures[END_REF][START_REF] Załużny | Coupling of infrared radiation to intersubband transitions in multiple quantum wells: the effective-medium approach[END_REF] and considering an electronic linewidth of 4 meV. Results are shown in Fig. 7, which replicates acceptably well the modal spectrum of Fig. 6(a). Superimposed on the reflectivity map we plot, with a solid black line, the lowestlying polariton from Fig. 6(a). The small difference between the Hopfield and transfer matrix approaches, visible in the increased redshift of the reflectivity dip corresponding to the discrete polariton mode in the transfer matrix results, is due to the use of an effective medium approximation. We verified the origin of such a discrepancy by implementing the same approximation in the Hopfield model, as described in Ref. [START_REF] Todorov | Intersubband polaritons in the electrical dipole gauge[END_REF] and explained in Supplement 1, leading to the dashed white line, which instead correctly follows the reflectance dip up to high levels of doping.

CONCLUSIONS

In this work we demonstrated that an ionizing electronic transition can be strongly coupled to a photonic resonator. Spectroscopically this strong coupling manifests itself with the appearance of a discrete optically active resonance below the ionization threshold. Electronically such a discrete resonance corresponds to the generation of bound excitonic states. In contrast to the Coulomb interaction responsible for electron-hole binding in usual excitons, the bound state anticipated in this work relies on a novel mechanism due to the coupling with the cavityphotonic field.

The natural next question then is how the existence of these states can be directly probed. From the optical side, the width and the shape of the resonance bears the typical signatures of localization. For instance, the absorption of a bound-to-continuum transition has a large and asymmetric shape, while a boundto-bound transition is narrower (typically below 10% at room temperature) and Lorentzian shaped (see, for example, Ref. [START_REF] Capasso | Observation of an electronic bound state above a potential well[END_REF]). However, a truly direct way to prove the electronic localization effect would require electrical measurements. One possibility is to use scanning tunnel microscopy. An interesting alternative that can open up vaster perspectives in the long term is to develop quantum-well (QWIP) or quantum cascade (QCD) intersubband detectors operating in strong coupling. Such devices rely on polaritonic excitations tunneling out into electronic states: the study of the transport in such devices can directly prove an electronic localization effect.

Our results can find direct applications in the physics and technology of intersubband transitions in doped quantum wells, where the potential of exploiting bound-to-continuum transitions [START_REF] Faist | Quantum-cascade lasers based on a bound-to-continuum transition[END_REF][START_REF] Scalari | Terahertz bound-tocontinuum quantum-cascade lasers based on optical-phonon scattering extraction[END_REF] and of cavity-induced modifications of electronic states [START_REF] Liberato | Quantum theory of electron tunneling into intersubband cavity polariton states[END_REF] were already recognized. More broadly, this investigation, which could be extended to other cavity quantum electrodynamics systems in both solid-state and atomic physics, demonstrates a novel way strong coupling can be exploited to influence the properties of materials coupled to light, with potential impact on fields ranging from chemistry to material science.

Fig. 1 .

 1 Fig. 1. Schematic representation of the electronic structure of a quantum well of width L QW , with a single bound state below the continuum (shaded in gray). (a) Electronic density envelope functions of the different single-particle eigenmodes, shifted by their energy. The potential profile is plotted in red, with the first ionization energy ℏχ and the conduction band discontinuity V explicitly marked. The figure has been obtained using the parameters of the structure described in Section 3.A. For sake of clarity, only one continuum mode in every 10 is shown, with its density multiplied by 10. (b) In-plane dispersion of the different subbands in momentum space. The single bound state is filled with electrons (in red), up to the Fermi energy E F (dashed yellow line). The dashed-dotted blue arrows represent a collective bound-to-continuum transition.

Fig. 2 .

 2 Fig. 2. Simulation of a single quantum well of width L QW 4 nm in a bulk of total width T 1 μm, with effective cavity length L c 25 nm and cavity energy ℏω a q 185 meV, smaller than the first ionization ℏχ 188.4 meV. (a) Polaritonic spectrum as a function of the doping. The yellow line marks the cavity energy. (b) Colormap of the excited electron density jψ e sq zj 2 for the lowest lying polaritonic mode as a function of doping. Yellow dashed lines mark the boundaries of the quantum well. (c)-(g) Plots of jψ e sq zj 2 for all the polaritonic modes (all the s up to the cutoff ) relative to the five values of doping marked by dotted vertical gray lines in panels (a) and (b). The lowest lying mode represented in panel (b) is plotted in blue; all the other modes in the continuum are instead in red, forming the thin homogeneous red band of density T -1 visible at the bottom of each panel. Note that, due to the different scale, the node in the localized excited electronic density visible in panel (b) is not clearly resolved in panels (c)-(g).

Fig. 3 .

 3 Fig.3. Same as in Fig.2, but with cavity energy ℏω a q 195 meV, larger than the first ionization ℏχ 188.4 meV.

Fig. 4 .Fig. 5 .

 45 Fig.4. Same as in Fig.2, but with cavity energy ℏω a q 205 meV, larger than the first ionization ℏχ 188.4 meV.

Fig. 6 .

 6 Fig. 6. Simulation of n QW 20 quantum wells of width L QW 4 nm in a bulk of total width T 0.5 μm embedded in a planar microcavity. The TM0 mode of the microcavity is chosen to have energy ℏω a q 195 meV, larger than the first ionization energy ℏχ 192 meV. (a) Polaritonic spectrum as a function of the doping. The yellow line marks the cavity energy. (b), (c) Plots of the excited electron density jψ e sq zj 2 for the lowest-lying polaritonic mode, for values of doping equal, respectively, to N 2DEG 0 and 3 × 10 16 cm -2 , marked by arrows in panel (a). Shaded regions correspond to the locations of the quantum wells.

Fig. 7 .

 7 Fig. 7. (a) Reflectivity map for the same structure studied in Fig. 6, calculated considering an electronic linewidth of 4 meV. The horizontal dashed-dotted red line marks the first ionization energy. The solid black and dashed white lines mark instead the dispersion of the lowest polariton mode obtained using the Hopfield approach, respectively without and with the effective medium approximation. (b) A vertical cut of panel (a) for N 2DEG 3 × 10 12 cm -2 .

2334-2536/19/030354-08 Journal © 2019 Optical Society of America

Vol. 6, No. 3 / March 2019 / Optica

Acknowledgment. The authors thank Prof. J. Khurgin for useful comments on the interpretation of the results.

See Supplement 1 for supporting content.

Funding. FP7 Ideas: European Research Council (IDEAS-ERC) (GEM 306661); European Union FET (Open Grant MIR-BOSE 737017); Engineering and Physical Sciences Research Council (EPSRC) (EP/M009122/1); Provincia Autonoma di Trento; Royal Society (University Research Fellowship).