Yann ; Lebaupin
email: yann.lebaupin@estaca.fr.

Michaël Chauvin

Thuy -Quynh

Truong Hoang

Fabienne Touchard

Alexandre Beigbeder

ESTACA LAB Estaca

Michael ; Chauvin

Truong Estaca'lab

Thuy Hoang

; -Quynh

Michaël Chauvin

Thuy-Quynh Truong Hoang

Influence of constituents and process parameters on mechanical properties

Keywords: Thermoplastic resin, Flax fibres, Compression moulding, Mechanical properties, Microstructural properties

-Introduction

Green composites based on natural fibres have been gathering much attention from the standpoint of protection of the environment from plastic disposal problem and saving petroleum resources [START_REF] Yu | Biodegradable Polymer Blends and Composites from Renewable Resource[END_REF].

The introduction of natural fibres in polymer matrix can bring many advantages with regard to fibres used in traditional composites: biodegradable resource, low density, good specific strength and modulus, good acoustic and vibratory properties [START_REF] Panaitescu | [END_REF]. Various natural fibres are used as reinforcing material polymer-based composites: bagasse, flax, hemp … [3]- [5]. Many studies are focused on short natural fibre composites [6]- [9] or on non-woven mat fibre composites [10]- [12]. However, long plant fibre composites are more and more studied for improving mechanical properties, and for designing structural applications [13]- [16]. It has been shown that flax fibre present better properties than other natural fibres and is an abundant natural resource available in many countries [17].

In this study, unidirectional (UD) flax fabrics were associated with bio-based polymer matrix: Polyamide 11, to create a 100% bio-sourced composite. The Polyamide 11 is derived from castor oil, consumes less non-renewable resources to be produced and has superior thermal resistance than many other classical thermoplastic polymers [18]. This bio-based polymer has the attention of many researchers because of its potential to substitute petrochemical derivatives [START_REF] Sperling | Biotechnology and polymers[END_REF]. The combination of this high technical polymer with long UD fibres can produce a composite suitable for structural applications. As shown in literature, investigations of long fibre reinforced thermoplastic polymers are limited because thermoplastics have relatively higher viscosities than thermoset polymer ones [14].

Therefore it is difficult to impregnate long fibre yarns with thermoplastic resin [15]. In this study, composite plates were manufactured by hot press-moulding. The main advantages of this process technique are to reduce the cycle time, to limit the loss of products and to avoid high shear forces during elaboration [13]. It is well-known that the mechanical properties of the manufactured composite are affected by processing conditions such as pressure, temperature and holding time [11,16,17]. For example, Rassmann et al. have studied the effects of pressure on the mechanical behaviour of kenaf/polyester composites [22]: they found that for a low fibre volume fraction, pressurising the mould improves tensile and flexural strengths. Kobayashi processing condition role on properties of hemp/PLA composites [14]. They varied moulding conditions, including moulding temperature, pressure and time, and measured resulting tensile and shear properties. They demonstrated that for the studied materials, 190 °C-1 MPa-4 min is expected as an optimum moulding condition [14]. However, no paper was found concerning the optimisation of process parameters for elaborating UD flax fabric/PA11 composites, using the same type of hot pressmould.

Therefore, the aim of this study is to investigate the influence of process parameters on mechanical properties of flax fibre reinforced PA11 composites. In addition, different materials are used as composite constituents in order to optimise both components and process conditions. In this objective, various configurations have been tested in this study. Different temperature and pressure values have been combined. Two types of flax fabric and two types of PA11 (in the form of powder or film) have been used. Thermal and rheological measurements have been performed on the PA11 polymer. A total of ten different composites have been manufactured. They have been compared by means of tensile tests and DMA analysis. Microstructural studies including porosity measurements and SEM observations have also been employed to investigate fibre impregnation.

-Materials and techniques of characterisation

-Materials

The composite plates were made from unidirectional (UD) fabrics of flax fibres and polyamide 11 The PA11 polymer, produced from a renewable source (castor oil), was provided by Arkema in two different forms: in the form of powder "Rilsan Besno T7500" with a density of 1.2 g/cm 3 , and in the form of film "LMFO" with a thickness of 100 µm and a density of 1.02g/cm 3 . Properties of these materials are given in Table 1.

Before moulding, flax fabrics and PA11 matrix were heated during 12 hours at 80°C to reduce moisture contents from 4.5% to 0.5% for the fibres and from 0.1% to 0.05 % for the PA11. Composite plates were then produced using a stacking of PA11 in the form of powder or film and four layers of fibres, with a fibre weight fraction of 50% and a plate thickness about 2 mm depending of the pressure levels. The layers of flax fabrics and PA11 were piled up alternatively and compressed in a mould with dimensions of 450x500x2mm 3 . Different configurations have been used for hot-pressing process, varying temperature and pressure values. In order to choose adapted parameters, thermal and rheological characterization of the polymer matrix has been first performed.

-DSC tests

The Differential Scanning Calorimetry (DSC) tests were carried out using a Q20 (TA instruments) set-up. PA11 samples, in form of powder or film, were tested at a heating rate of 20°C/min, from 20 to 220 °C. Two heating ramps were made: the first ramp gives data concerning the as-received polymers. Then, the second ramp was used for comparing the two forms of PA11 samples: powder and film, after having deleted their thermomechanical history. DSC allows determining different thermal characteristics of the tested materials: glass transition temperature (Tg), melting temperature (Tm), crystallization temperature (Tc) and degree of crystallinity (χ c ). χ c has been obtained by using equation 1:

(%) = ∆ ∆ × (Equation 1)
where ∆Hm is the measured melting enthalpy, and ∆Hm 0 is the melting enthalpy of the 100% crystalline polymer (189 J / g for PA11 [23]). Viscosity of the polymer matrix was determined by rheological measurements. Information about the rheological properties of the polymers was obtained through a dynamic oscillatory characterization with a TA instruments AR 2000 rheometer using parallel-plates geometry. The distance between the plates was 1 mm, the applied stress was 100 Pa, and the oscillating frequency was taken equal to 1Hz.

-Tensile tests

Tensile tests were conducted with a mechanical testing machine (Instron 5884). Five standard specimens with cross section dimensions of 25x2mm² were tested for each configuration. Glass composite tabs of dimension 50*25mm² were glued on the specimens and were placed in the clamped area. The loading was carried out in the direction of fibres at room temperature and with a displacement rate of 2 mm/min. Strain gauges of 5 mm length were bonded on specimen surfaces.

-Dynamic mechanical analysis (DMA)

Dynamic mechanical analyses were carried out using a single cantilever bending system TA instruments DMA Q800. Samples were cut in the longitudinal direction with the dimensions of 40x10x2 mm 3 . The distance between supports was 16 mm. Specimens were tested in air atmosphere at a frequency of 1Hz and a heating rate of 2°C/min, from 25 to 100°C. DMA measurements allow determining viscoelastic properties of tested materials such as storage modulus (E') and damping parameter (Tan δ).

-SEM analysis

Two types of specimens have been observed by using a JEOL 6400 Scanning Electron Microscope (SEM). For the first type of specimens, slices of samples were cut by using a diamond wire saw. Then, they were polished with sandpapers of different roughnesses. Observations of these specimens allow checking the matrix impregnation in the different composites that have been It allows analysing the different failure mechanisms occurring in such composite materials.

-Determination of flax fibre volume fraction and porosity

Depending on the chosen process parameters, porosity in elaborated composites can vary. In order to determine porosity in each plate, composite density value ρ c was determined by the Archimedes method. Measurements have been performed with a precision balance. Then, porosity fraction V p has been calculated thanks to the following equations [14]: 2) 3) 4)

V = W ౙ (Equation
V ୫ = W ୫ ౙ ౣ (Equation
V ୮ = 1 -(V ୫ + V ) (Equation
Where W f and W m are weight fractions of fibres and matrix (equal to 50% in the elaborated composites), ρ f and ρ m are density values for fibres and matrix (given by suppliers, see in Table 1), and V f and V m are the volume fractions of fibres and matrix.

-Experimental results and discussion

-Thermal characterisation

The thermograms obtained by DSC for as-received PA11 samples are presented in figure 2 and figure 3.

The two forms of PA11 polymer have been tested: powder and film. Figure 2 3): it is about 161°C for powder and film samples, and the end of the crystallisation peak is located at about 140°C. During the second heating, melting peaks are double for both forms of polymer, as it can be seen in Figure 2. The first melting peak is located at about 182 °C for the two PA11 forms. It is probably due to the melting of the smectic phase in Polyamide 11 [START_REF] Gaudefroy | Influence de la phase smectique sur le comportement mécanique en traction uniaxiale du polyamide 11[END_REF].

These DSC results allow choosing some process parameters for composite hot-pressing. The melting temperature gives the minimum of the process temperature value: 190°C, and the ending temperature of the crystallisation peak gives the temperature value for opening the mould at the end of the process: 140°C.

-Rheological characterization

As-received Polyamide 11 polymers have also been characterized by means of a rheometer. As expected, the viscosity of PA11 in films is inferior to the viscosity of PA11 powder because of their different polymer grades. However different behaviours between film and powder can be observed in figure 4. This figure shows that the viscosity of the PA11 film remains almost constant all along the tests, whatever the temperature level is. By comparing curves for the film at different temperatures, one observes that the higher the temperature, the lower the viscosity. On the contrary, the viscosity of the PA11 powder increases significantly during the test, for all the temperature levels.

Moreover, the powder behaviour can be separated in two parts: during the first 1000 seconds, viscosity value decreases with growing temperatures, except for 220°C ; after that, the tendency is reversed.

This particular behaviour of the PA11 powder is probably due to the fact that powder is the initial state of the polymer, whereas PA11 film has already been transformed by extrusion. Therefore, the polymerization process is not completely finished in the PA11 powder, and the increase of the viscosity at the beginning of rheological tests can be explained by the increase of molar weight in the

-Different configurations for hot press-moulding

In the objective to optimize the hot-pressing conditions for flax/PA11 composites, several process parameters have been tested. For temperature level, DSC results have shown that 190°C is the minimum value. As flax fibres cannot exceed a temperature of 210°C during 5 minutes [21], three moulding temperatures were chosen: 190 °C, 200°C and 210°C. In addition, in order to investigate the influence of moulding pressure on the composite properties, three applied pressures were employed:

35, 65 and 100 bars. With higher pressure value, fibres could be damaged [12]. After the holding time of 5 minutes, composite plates were cooled at about 2°C/minute until 140°C before removing from the mould. This value of 140°C corresponds with the end of the crystallisation peak, as shown by DSC results. The process cycles that have been tested for elaborating composite panels are described in better fluidity, as it has been shown with rheological measurements, which facilitates the matrix impregnation in the composite [26], [27]. However, for configurations 2, 4 and 5, whatever the temperature level, tensile strength remains constant, around 115MPa (Table 3). The obtained results also allow comparing mechanical properties for a given value of temperature. Composite plates 4 and 6 have been manufactured with the same temperature level: 200°C. Results show that when pressure value is higher (65 bars for configuration 4 versus 35 bars for configuration 6), Young's modulus and tensile strength values increase: respectively 27GPa and 107MPa for composite 4, versus 17GPa and 73MPa for composite 6. This result can be directly linked with the degree of porosity measured in these two configurations (Table 3): porosity degree is more than twice higher in configuration 6 than in configuration 4 (26% vs 11%). It demonstrates that higher pressure level leads to lower porosity degree, and thus to better mechanical properties. Nevertheless, pressure value must not be too high.

When comparing configurations 1, 2 and 3, all elaborated with a temperature level of 190°C, one can see that the tensile strength is maximum for a pressure of 65 bars (composite 2) and this value decreases for a pressure of 100 bars (composites 3). Indeed, tensile strength value is equal to 117MPa for composite 2, and only 84MPa for composite 3. This can be explained by the degradation of plant fibres at high pressure levels [28]. It can also be noticed that composites 1 and 6 have been designed

with the same pressure level (35 bars), but with different temperature values (200°C for composite 6 and 190°C for composite 1). It leads to higher porosity ratio in composite 6 (26% versus 10% in composite 1). This can be due to the fact that, at 200°C, the matrix is more fluid than at 190°C, and for this temperature, 35 bars is too low for obtaining a good impregnation quality. According to Hong et al. [29], this phenomenon is explained by an increase in Polyamide 11 chains mobility. In addition, figure 7 shows that the highest values of E' are obtained for composite 5, which also exhibits the highest Young's modulus value (Table 3). Concerning evolution of the damping factor, one can see in figure 7 that, for all the tested samples, there is a peak located at around 55°C:

this temperature corresponds to the glass transition temperature of the resin detected by DMA.. Moreover, results show that highest Tan δ values are obtained for composite 6, while lowest values correspond with composite 5. This can be explained by the fact that Tan δ is affected by interfacial adhesion between fibres and matrix [30]. The damping factor Tan δ is an indicator of molecular motions: the lower the Tan δ values, the better the interfacial adhesion [31]. It means that, with the process configuration 5, the interface quality is better than with other configurations. This is in accordance with measured tensile characteristics: configuration 5 exhibits the best properties (figure 6). This is also in accordance with the measured values of porosity degree shown in table 3: the composite 5 presents the lowest porosity amount (8%).

Finally, the analysis of the first set of composites made of flax fabric A and PA11 powder,

shows that best properties are obtained for configuration 5, with the following hot-pressing parameters: a temperature value of 210°C and a pressure level of 65 bars.

-Analysis of the second set of manufactured composites

The second set of composites was manufactured with the optimum process parameters determined from the first set analysis: 210 °C and 65 bars. The aim is to optimize the composite constituents, for given process conditions. Different combinations of flax fabric A and B, and of PA11 powder and film have been studied. They are described in Table 2 (configurations 7 to 9). In addition, these configurations have been compared with configuration 10, elaborated with gradual pressure steps.

. 4. In terms of Young's modulus, best values are obtained for composites 7 and 10. For these configurations, the modulus value reaches 35GPa. This modulus is even higher than the one of composite 5 (30GPa, see in Table 3). It shows that, for our process conditions, the combination of flax fibre B with PA11 film gives the best composite rigidity.

Otherwise, the failure stress is maximized for the configuration 10. This configuration has been elaborated by applying gradual pressure levels. This process method allows almost doubling the strength value (174 MPa for configuration 10 vs 92 MPa for configuration 7).

Porosity measurements in the second set of composites are presented in Table 4. Results show that in the composite 8, the highest porosity fraction (16%) corresponds logically with the lowest failure stress (62 MPa) and Young modulus (27 GPa).

Each manufactured composite panel of the second set has also been tested by DMA. Results are presented in figure 9. As for the first set of composites, the highest storage modulus and the lowest damping factor are obtained for the composite which exhibits the best tensile properties (configuration 10 in the second set). It shows again that fibre/matrix quality is a key parameter for tensile properties of composites.

Finally, the analysis of the second set of composites allows determining the best choice corresponding with our process method: the best tensile properties were obtained with the composite flax B/ Polyamide 11 film manufactured with a temperature value of 210°C and using gradual levels of pressure (configuration 10).

-Microstructural observations

SEM observations have been performed on composites 7 and 10, both made of flax B and PA11 film, in order to better understand the role of the pressure gradual steps. Figure 10 presents SEM images obtained on polished cross-section surfaces for the two composites. It can be seen that, in composite 7, fibres still form bundles (figure 10a). On the contrary, figure 10b shows that, in for glass mat reinforced thermoplastics that the best impregnation of the fibre bundles was obtained with pressure steps [31].

SEM images from figure 11 show failure surface in composite 10 after tensile loading: a global view in figure 11a and a higher magnification in figure 11b. Different types of damage can be observed: fibres pulled out and fibres fracture, with some cavities left by the pulled-out fibres. In addition, it can be seen that PA11 polymer well impregnates flax fibres.

These observations show that the process with gradual pressure steps leads to a better distribution of fibres and a better adhesion at fibre/matrix interface. It explains the better mechanical properties that have been measured for this configuration (composite 10).

-Conclusion

Today, from the standpoint of the protection of the environment from plastic disposal problem

(

  PA11) polymer. Two types of non-treated UD fabrics have been used: UD fabric A and UD fabric B, with respectively 400 g/m 2 and 450 g/m 2 of area weight. The two UD fabrics are made of longitudinal fibre tows joined by some transverse flax yarns. The main difference between these two UD fabrics is their spatial distribution, as shown in figure1. In UD fabric B, the fabric is woven tightly, providing almost no gap between adjacent tows, while in UD fabric A there are gaps between adjacent tows,

  second type of observed specimens consisted in fracture surface of the tested samples.

  Tests have been performed during one hour at four different values of temperature: 190°C, 200°C, 210°C and 220°C. Viscosity values obtained for both powder and film forms are presented in figure 4.

  view of these results, and in order to save time and extra energy consumption, a holding time value of 5 minutes at high temperature has been chosen for the composite process.

Figure 5 .

 5 Figure 5. For one of the tested configurations, the moulding pressure was applied gradually: 25 bars during 2 minutes, 40 bars during 2 minutes and finally 65 bars (Figure 5).

11 Dynamic

 11 mechanical analysis of the first set of composites has also been performed and is presented in figure7. Storage modulus (E') and damping factor (Tan δ) are plotted in figure7. As expected, for each configuration, the storage modulus decreases with increasing temperature.

12 Each

 12 configuration has been tested in tensile loading. The measured mechanical properties are presented in figure8, and values are given in Table

13 composite 10 ,

 1310 many flax fibres are individually dispersed in the matrix. This observation is due to the enhancement of impregnation with gradual steps of pressure. Michaud et al. have also demonstrated

Figure1:Figure2:Figure3:Figure 4 :Figure 5 :Table 2 :Figure 6 :Table 3 :Figure 7 :Figure 8 :Table 4 :Figure9:Figure 10 :Figure 11 :

 452637841011 Figure1: Geometry of UD flax fabric A (a) and UD flax fabric B (b). 348x194mm (96 x 96 DPI)

  et al. have analysed the

	F o
	r
	P
	e e r
	R e v i e w
	4

  Analysis of the first set of manufactured compositesIn order to compare configurations of the first set, tensile tests have been performed on five samples for each manufactured composite plate. Figure6presents evolution of Young's modulus and tensile strength. All the measured values are given in Table3. Results show that, for a given pressure

	3.4 -value (65 bars), Young's modulus values increase with increasing moulding temperatures
	(configurations 2, 4 and 5). When temperature level varies from 190 °C to 210 °C, modulus value
	increases from 21 to 30 GPa. It can be explained by the fact that a temperature increase leads to a
	F o
	r
	P
	e e r
	R e v i e w
	). It will allow choosing
	best constituents for our process conditions. Finally, configuration 10 has been tested, with progressive
	levels of applied pressure (see in table 2).
	10

John Wiley & SonsPolymer Composites

John Wiley & Sons


Maxime Lecomte

Alexandre Journeaux

Loan Renaud

Jean Dalibard

Raphael Lopes

Loss features in ultracold 162 Dy gases: two-versus three-body processes

Dipolar gases like erbium and dysprosium have a dense spectrum of resonant loss features associated with their strong anisotropic interaction potential. These resonances display various behaviours with density and temperature, implying diverse microscopic properties. Here, we quantitatively investigate the low-field (B < 6 G) loss features in ultracold thermal samples of 162 Dy, revealing two-and three-body dominated loss processes. We investigate their temperature dependence and detect a feature compatible with a d-wave Fano-Feshbach resonance, which has not been observed before. We also analyse the expansion of the dipolar Bose-Einstein condensate as a function of the magnetic field and interpret the changes in size close to the resonances with a variation in the scattering length.

I. INTRODUCTION

Quantum gases are by definition relatively short-lived, as these systems are extremely sensitive to loss processes such as collisions with residual gases, photo-association or inelastic collisions. Three-body losses, for example, correspond to inelastic recombination in which three particles interact sufficiently strongly to form a two-body bound state (dimer), while the third particle ensures energy conservation by acquiring a kinetic energy equal to the potential energy difference. This energy is usually much greater than the trap depth, resulting in the effective loss of all three particles. Such a mechanism is enhanced close to a scattering resonance. In inhomogeneous gases, three-body losses are particularly damaging as they lead to the depletion of the denser part of the atomic cloud, resulting in anti evaporative cooling [START_REF] Rem | Lifetime of the Bose gas with resonant interactions[END_REF][START_REF] Eismann | Universal loss dynamics in a unitary Bose gas[END_REF]. However, while this process limits the timescales over which ultracold dense systems can be studied, it also provides an insight into the few-body physics of strongly interacting cold gases, which remains a challenging and stimulating area of research [START_REF] Chevy | Strongly correlated Bose gases[END_REF][START_REF] Greene | Universal fewbody physics and cluster formation[END_REF][START_REF] Li | Three-body recombination near a narrow Feshbach resonance in 6 Li[END_REF][START_REF] Yudkin | Coherent superposition of Feshbach dimers and Efimov trimers[END_REF][START_REF] Ji | Stability of the repulsive Fermi gas with contact interactions[END_REF][START_REF] Yudkin | The reshape of three-body interactions: Observation of the survival of an Efimov state in the atom-dimer continuum[END_REF].

Dipolar gases like chromium, dysprosium, erbium, and thulium possess a large dipolar magnetic moment, resulting in properties that markedly differ from those of alkali atoms. In these systems, long-range anisotropic dipolar interactions lead to new features of the collision potential, such as the emergence of a 1/R 4 potential [START_REF] Bohn | Quasi-universal dipolar scattering in cold and ultracold gases[END_REF] or the modification of the van der Waals C 6 coefficient [START_REF] Kotochigova | Controlling interactions between highly magnetic atoms with Feshbach resonances[END_REF]. This anisotropic dipolar interaction can lead to striking new behaviours, such as lowtemperature d-wave Fano-Feshbach resonances [START_REF] Beaufils | Feshbach resonance in d-wave collisions[END_REF]. Furthermore, the anisotropic interaction potential is responsible for the dense spectrum of loss resonances [12] in ultracold gases of erbium, dysprosium and thulium [START_REF] Baumann | Observation of low-field Fano-Feshbach resonances in ultracold gases of dysprosium[END_REF][START_REF] Frisch | Quantum chaos in ultracold collisions of gas-phase erbium atoms[END_REF][START_REF] Maier | Emergence of chaotic scattering in ultracold Er and Dy[END_REF][START_REF] Khlebnikov | Random to chaotic statistic transformation in low-field Fano-Feshbach resonances of cold thulium atoms[END_REF]. A precise characterization of loss features has recently regained interest, triggered by the determination of the temperature dependence of their chaotic statistics [START_REF] Khlebnikov | Random to chaotic statistic transformation in low-field Fano-Feshbach resonances of cold thulium atoms[END_REF][START_REF] Khlebnikov | Characterizing the temperature dependence of Fano-Feshbach resonances of ultracold polarized thulium[END_REF], the optimization of the evaporative cooling [START_REF] Krstajić | Characterisation of three-body loss in 166 Er and optimised production of large Bose-Einstein condensates[END_REF], and the identification of appropriate Fano-Feshbach resonances in dipolar mixtures [START_REF] Durastante | Feshbach resonances in an erbium-dysprosium dipolar mixture[END_REF].

In this article, we investigate the few-body processes driving the large number of low-field loss features in ultracold * raphael.lopes@lkb.ens.fr gases of 162 Dy. We recover the 9 previously reported resonances for this isotope [START_REF] Baumann | Observation of low-field Fano-Feshbach resonances in ultracold gases of dysprosium[END_REF] as well as 10 extra features, and quantitatively characterize the dependence on atom number and temperature for 11 features, indicated by the red vertical lines in Fig. 1. In addition, we identify a loss feature compatible with a d-wave Fano-Feshbach resonance, with similar characteristics to those reported for chromium in Ref. [START_REF] Beaufils | Feshbach resonance in d-wave collisions[END_REF]. We also measure the three-body loss rate parameter for a Bose-Einstein condensate near zero magnetic field. This lowfield zone is especially interesting if the objective is to establish spin-orbit coupling in a dysprosium gas, similar to [START_REF] Chalopin | Probing chiral edge dynamics and bulk topology of a synthetic Hall system[END_REF], while preventing two-body spin relaxation at increased atomic densities. Finally, we complement our analysis with a study of the BEC expansion near the different loss features, interpreting the dilatation of the cloud as a signature of enhanced two-body interactions.

II. LOW-FIELD LOSS FEATURES

Experimentally, we load about 4 × 10 6 dysprosium atoms ( 162 Dy) into a crossed dipole trap formed by laser beams operating at a wavelength λ = 1064 nm. The atoms are loaded from a five-beam compressed MOT with atom number N a ≈ 1 × 10 8 and temperature T ≈ 15 µK (see Sec. 2 for more details).

After forced evaporative cooling, we produce an ultracold thermal gas, spin polarized in the Zeeman sublevel of lowest energy |J, m J = -J⟩, with atom number N a = 2 × 10 5 and temperature T ∼ 190 nK, above the condensation threshold. The evaporation is carried out with a fixed magnetic field of 1.660 G, indicated by the green vertical line in Fig. 1. We then quench the magnetic field to a target value and hold the cloud for 2 s. We measure the atom number and temperature after time-of-flight absorption imaging, which gives us information about both the losses and heating of the cloud. The magnetic field is scanned from 0 to 6 G and we measure the atom number variation as a function of the magnetic field B. For this low temperature, we identify 10 loss features, corresponding to the atom number drops in Fig. 1 top panel. These resonances, except for one, have been reported in Ref. [START_REF] Baumann | Observation of low-field Fano-Feshbach resonances in ultracold gases of dysprosium[END_REF].

A similar experiment is performed for a hotter thermal cloud with temperature T = 2.4 µK. We recover the previous resonances and observe several new loss features (lower panel in Fig. 1), increasing the total number of loss features count to 19. This result qualitatively demonstrates the nontrivial emergence of temperature-dependent loss features in an ultracold gas of dysprosium [START_REF] Baumann | Observation of low-field Fano-Feshbach resonances in ultracold gases of dysprosium[END_REF].

To probe different temperatures T , we use a protocol that differs from most previous investigations of resonant losses in lanthanides, by preparing all of our samples in the same optical potential regardless of T . We do this by (i) cooling the atoms to very low temperature (∼ 200 nK), (ii) adiabatically recompressing the optical trap to a large depth, and (iii) tuning the temperature by parametric heating of the trapped gas. Before measuring the remaining atom number, we ensure that the cloud is in thermal equilibrium by holding it for 0.5 s, which is long compared to the elastic collision time. By contrast, many previous studies adjusted temperature by halting the evaporation process at varying laser intensities. Our protocol addresses a potential bias resulting from differences in polarizability between free atoms and the bound state involved in the loss process [START_REF] Khlebnikov | Characterizing the temperature dependence of Fano-Feshbach resonances of ultracold polarized thulium[END_REF]. Additionally, it is advantageous to operate at a high trap depth U 0 , leading to a large ratio η = U 0 /k B T . This effectively reduces the losses due to evaporation that could potentially obscure distinctive features resulting from the loss resonances we seek to examine.

III. MICROSCOPIC DESCRIPTION OF LOSS FEATURES

Before continuing with our experimental analysis, let us summarize the models developed in Ref. [START_REF] Li | Three-body recombination near a narrow Feshbach resonance in 6 Li[END_REF][START_REF] Beaufils | Feshbach resonance in d-wave collisions[END_REF][START_REF] Maier | Emergence of chaotic scattering in ultracold Er and Dy[END_REF][START_REF] Waseem | Unitarity-limited behavior of three-body collisions in a p-wave interacting Fermi gas[END_REF] that have been used to characterize loss features in dipolar gases. These models assume as an intermediate step the resonant formation of a dimer or a trimer, and they lead to different scaling laws of the maximal loss rate with density, as we show now. To keep the analysis simple, we assume here a uniform atomic density n a , but the following results can then be readily transposed to the case of a harmonically trapped gas. [START_REF] Chin | Feshbach resonances in ultracold gases[END_REF], this process leads to a sharp energy feature described by the Lorentzian of Eq. 5.

0 0 E d E ℓ = 2 ℓ = 0 Interparticle distance

A. The resonant dimer model

We describe a sequential process involving two steps (i) a quasi-resonant coupling between a state with two free atoms and a state where a dimer in some excited state A * 2 is formed:

A + A ⇄ A * 2 , (1)
(ii) the decay of the dimer with a rate Γ d . Here, this decay is essentially induced by the collision with a third atom: A * 2 + A → A 2 + A so that Γ d is implicitly a function of n a , and where A 2 is a deeply bound dimer.

In the following we restrict ourselves to the case of large Γ d , so that the dimer A * 2 decays soon after its formation by the direct process in [START_REF] Rem | Lifetime of the Bose gas with resonant interactions[END_REF], and the reverse process in (1) does not play a significant role. This scenario can happen in the case of a narrow Fano-Feshbach resonance and a sufficiently large atomic density n a . We will see that it is the relevant one for most of the resonances observed in our experimental conditions and we refer the reader to Refs. [START_REF] Li | Three-body recombination near a narrow Feshbach resonance in 6 Li[END_REF][START_REF] Beaufils | Feshbach resonance in d-wave collisions[END_REF][START_REF] Waseem | Unitarity-limited behavior of three-body collisions in a p-wave interacting Fermi gas[END_REF][START_REF] Waseem | Quantitative analysis of p-wave three-body losses via a cascade process[END_REF] for a discussion of the general case and in the limit of small Γ d . Note that the situation considered here is the opposite of that of Ref. [START_REF] Zhang | Many-body chemical reactions in a quantum degenerate gas[END_REF], where the atoms A formed a Bose-Einstein condensate and where the authors could observe a coherent oscillation between the two members of Eq. 1 thanks to bosonic stimulation.

To model the process (1), we consider a fictitious box containing two atoms, whose typical volume is thus L 3 = 2/n a , where n a is the atomic density. We work in the center-ofmass frame of the two atoms and we denote E the energy of the relative motion of the colliding atoms. We suppose that the resonant process (1) occurs for an incident partial wave ℓ and we introduce the coupling matrix element ℏκ between the relative wave function of the two free atoms and the wave function of the dimer state, of energy E d (see Fig. 2). Each wave function is supposed to be normalized to unity in the box L 3 . We will not try to provide here a detailed expression for κ and we simply note its scaling with energy and box size: κ ∝ (E ℓ /L 3 ) 1/2 [START_REF] Landau | Quantum mechanics: nonrelativistic theory[END_REF]. The hamiltonian of this fictitious two-level system is thus the 2 × 2 matrix

E ℏκ ℏκ * E d -iℏΓ d /2 (2)
where we have added the imaginary term -iℏΓ d /2 to the dimer energy to account for its instability. The two eigenvalues of this matrix are complex, which expresses the fact that the scattering state A + A is now also unstable because of its coupling to A * 2 . The imaginary part of the energy of the A + A pair in the presence of the coupling κ gives the decay rate of this pair, which reads for Γ d ≫ κ (Breit-Wigner formula):

Γ a ≈ Γ d |κ| 2 (E -E d ) 2 /ℏ 2 + Γ 2 d /4 , (3)
from which we deduce the scaling of the total loss rate in the sample with N a atoms at a given energy E:

Ṅa ∝ -N a Γ a ∝ -n a N a E ℓ L(E -E d ) (4)
where L stands for the Lorentzian function:

L(x) = 1 2π ℏΓ d x 2 + (ℏΓ d /2) 2 .
(

) 5
We now average the rate (4) over a thermal distribution of temperature T , so that the loss rate Ṅa is proportional to

+∞ 0 dE ρ(E) E ℓ L(E -E d ) e -E/kBT +∞ 0 dE ρ(E) e -E/kBT , (6)
with the density of states ρ(E) ∝ √ E for the relative motion of the A + A pair. The expression ( 6) is in general a complicated function of E d and Γ d (and thus n a ). An interesting limiting case is obtained when the resonance width ℏΓ d is very small compared to k B T , in which case the Lorentzian function L(E -E d ) can be replaced by a Dirac function δ(E -E d ) in [START_REF] Yudkin | Coherent superposition of Feshbach dimers and Efimov trimers[END_REF]. In this case, we find that the decay rate corresponds to a two-body loss process [START_REF] Beaufils | Feshbach resonance in d-wave collisions[END_REF]:

Ṅa = -L 2 n a N a (7)
with an effective two-body loss parameter L 2 given by:

L 2 (E d , T ) ∝ T -3/2 E ℓ+1/2 d e -E d /kBT . (8)
The experimental procedure involves scanning the value of E d by ramping the magnetic field at a given temperature and searching for the maximal loss rate. From the scaling of Eq. ( 8), we find that the maximum loss rate occurs for

E d = (ℓ + 1/2)k B T with L (max) 2 (T ) ∝ (k B T ) ℓ-1 . (9)
Assuming the two hypotheses above are valid, i.e. ℏκ ≪

ℏΓ d ≪ k B T , the variation of L (max) 2
with temperature thus gives immediate access to the partial wave ℓ involved in the resonant loss process. The validity of these hypotheses can be checked by verifying that Ṅa /N a scales linearly with n a (see Eq.( 7)).

B. The resonant trimer model

The second model consists in a pure three-body process [START_REF] Maier | Emergence of chaotic scattering in ultracold Er and Dy[END_REF]. Three particles that do not have resonant pairwise interactions arrive through a three-body open channel O 1 , with the quantum number λ associated with the grand angular momentum, and an incoming energy E close to the energy E t of an excited trimer state A * 3 , residing in a closed channel C:

A + A + A ⇄ A * 3 . (10)
If we neglect atom interactions at long distance, the incoming channel is purely repulsive, even for λ = 0, with the 3-body centrifugal potential V (R) ∝ λ(λ + 4) + 15 4 /R 2 , where R is the hypergeometric radius [START_REF] Delves | Tertiary and general-order collisions (ii)[END_REF][START_REF] Smith | Generalized angular momentum in many-body collisions[END_REF]. The closed channel C is coupled to other channels O f that are not directly coupled to the incoming open channel, thereby determining the decay rate Γ t of the trimer A * 3 . Note that since we do not assume resonant two-body interactions, the trimer A * 3 differs from Efimov trimers. The latter play an important role in broad Fano-Feshbach resonances and lead to the 1/T 2 dependence of the three-body loss rate L 3 [START_REF] Rem | Lifetime of the Bose gas with resonant interactions[END_REF][START_REF] Petrov | Three-body recombination in heteronuclear mixtures at finite temperature[END_REF].

The analysis of this process follows along the same general lines as for the resonant dimer model. We consider a fictitious box of volume L 3 ∼ 3/n a containing three particles. The coupling κ between the incoming state of energy E and the resonant trimer state now scales as κ ∝ E λ/2 /L 3 and the width Γ t of the trimer state A * 3 induces a non-zero width for the incoming state A+A+A, given by a formula similar to (3). We are then led to Ṅa = -n 2 a N a E λ L(E -E t ) where L is the Lorentzian function similar to [START_REF] Li | Three-body recombination near a narrow Feshbach resonance in 6 Li[END_REF] with width Γ t [START_REF] Maier | Emergence of chaotic scattering in ultracold Er and Dy[END_REF][START_REF] Incao | Scattering length scaling laws for ultracold three-body collisions[END_REF][START_REF] Wang | Numerical study of three-body recombination for systems with many bound states[END_REF] [31]. The thermal average of this decay rate involves the threeparticle density-of-state ρ(E) ∝ E 2 so that we obtain, in the limit ℏΓ t ≪ k B T :

Ṅa = -L 3 n 2 a N a (11)
with the scaling L 3 ∝ T -3 E λ+2 t e -Et/kBT . When scanning the energy of E t by ramping the external magnetic field, the maximum loss rate scales as

L max 3 (T ) ∝ (k B T ) λ-1 ( 12
)
and it is obtained for

E t = (λ + 2) k B T .
Discussion. Although the scaling of the loss rate with temperature is similar in both models of §III A and §III B, the latter is a pure three-body process and therefore cannot predict two-body dominated features of the type Ṅa /N a ∝ -n a . The reverse statement may not be true: Refs. [START_REF] Li | Three-body recombination near a narrow Feshbach resonance in 6 Li[END_REF][START_REF] Beaufils | Feshbach resonance in d-wave collisions[END_REF][START_REF] Waseem | Quantitative analysis of p-wave three-body losses via a cascade process[END_REF] indicate that the resonant dimer model can lead to an effective three-body loss rate Ṅa /N a ∝ -n 2 a in the case where the excited bound state is long-lived relative to its coupling to the incoming open channel. Let us also emphasize that the simple scaling laws (9,12) hold only when ℏκ ≪ ℏΓ d,t ≪ k B T . If this is not the case, the variation of

L (max) 2,3
with temperature is non-trivial.

IV. LOSSES VS. DENSITY AND TEMPERATURE

In this section, we present our experimental results regarding the loss rates in a harmonically trapped 162 Dy gas due to inelastic processes. We first outline our methodology ( §IV A), and then investigate the variations of the loss rate with density at a given temperature ( §IV B), and with temperature at a given atom number ( §IV C). We summarize our results for the whole set of resonances in §IV D.

A. Methodology

We recall that the microscopic nature of the process (2body or 3-body loss) of each resonance is unknown, as is the temperature variation of the associated loss rate (L 2 (T ) or L 3 (T )). Therefore, for a gas prepared with a given atom number N a and temperature T , we restrict our analysis of the decay rate to a short time interval ∆t, during which N a and T vary by less than 20% and 30%, respectively. A linear fit N a (t) = N 0 (1-βt) to the decaying atom number over this interval then allows us to derive the decay rate Ṅa ≈ ∆N a /∆t for a density na and a temperature T taken equal to the average value of these quantities over the time interval ∆t. The interval retained for the fit is indicated by a coloured zone in Figs. 3 and4.

In addition, we recall that the volume of a trapped gas in a harmonic potential is a function of the temperature. If interactions play a negligible role, one finds V = (2 √ 3πk B T /mω 2 ) 3/2 , where ω = (ω x ω y ω z ) 1/3 is the geometric mean of the trapping frequencies, and k B the Boltzmann constant. In the following, we designate by n a = N a /V the average density in the trap. For a fixed temperature, the volume does not vary, and β = -Ṅa /N a scales as β ∝ n γ a with γ = 1 (resp. γ = 2) in the case of a two-body (resp. three-body) dominated loss process [START_REF] Ji | Stability of the repulsive Fermi gas with contact interactions[END_REF] [resp. [START_REF] Beaufils | Feshbach resonance in d-wave collisions[END_REF]].

B. Examples at fixed T : 2-versus 3-body dominated losses

Here we describe a typical analysis procedure of one of the resonances featured in Fig. 1, specifically the resonance occurring at a magnetic field strength of 5.130 G. As explained in § II, we prepare a sample with an adjustable atom number at the desired temperature. The depth of the trap is sufficient to render losses due to evaporation insignificant [32]. We jump the magnetic field from its initial value (B = 1.660 G) to a magnetic field close to the target loss feature (typically 100 -200 mG away from it). We then wait for 500 ms and perform a second quench towards the magnetic field for which the losses are maximum. This sequence allows a better resolution of the initial loss dynamics.

We show in Fig. 3a,c two decay curves N a (t) for two initial atom numbers, hence two atomic densities n a . Figs. 3b,d show the corresponding changes in temperature. A linear fit of the short time variation of N a provides the decay rate β introduced in § IV A. We summarize our results for β as a function of n a in Fig. 3e. A fit β(n a ) = β 1 n γ a gives γ = 0.92 [START_REF] Kotochigova | Controlling interactions between highly magnetic atoms with Feshbach resonances[END_REF], an indication of a two-body dominated loss feature for this particular resonance.

To cross-validate our methodology, we have performed a similar loss measurement for a thermal gas at B = 1.660 G i.e. away from any loss resonance. We measure γ = 2.3(4), which is consistent with a three-body loss process, as expected for a gas with positive background scattering length. We find, for a thermal gas, L 3 = 1.2(2) × 10 -40 m 6 /s.

The same technique allows us to determine the three-body loss coefficient of a Bose-Einstein condensate (BEC) either close to B = 0 or at B = 1.660 G away from any loss resonance. For that purpose we evaporate until we produce a quasi-pure BEC, and then adiabatically recompress the trap to a final trap depth of 2.16 µK, with frequencies equal to {ω x , ω y , ω z } = 2π × {49, 152, 115} Hz. We find L 3 = 2.9(3) × 10 -41 m 3 /s and L 3 = 5.0(8) × 10 -41 m 3 /s, for the background three-body loss rate, B = 1.660 G, and the nearzero field B ≲ 50 mG, respectively. The values of L 3 are extracted for a BEC fraction going from near unity to 0.5. Compared to a thermal sample, we find a reduction of L 3 in qualitative agreement with the predicted 3! reduction for a pure BEC [START_REF] Kagan | Effect of Bose condensation on inelastic processes in gases[END_REF].

C. Example at fixed Na: T -dependent loss rate

We now turn to the temperature dependence of the atom loss rate, still taking the resonance at B = 5.130 G as an example. Following the procedure outlined in §II and §IV B, we prepare thermal samples at different temperatures but with the same atom number. We plot in Fig. 4a (resp. Fig. 4c) the atom number decay for the initial temperature T = 0.9 µK (resp. T = 1.8 µK). We show in Fig. 4b,d the corresponding time evolution of the temperature.

As explained in § IV A, we restrict to the short time evolution and extract the rate β = -Ṅa /N a from a linear fit to the measured decay of N a (t). The values of β for different temperatures are shown in Fig. 4e. We fit the relation β(T ) = β 2 T α to the temperature dependence of the loss rate, with α = -2.2(3). From the analysis of §IV B, we know that this particular resonance is likely to be due to a two-body loss decay Ṅa = -L 2 n a N a , hence β ∝ L 2 /V for a given N a . Recalling that the volume in a harmonic trap scales as V ∝ T 3/2 , we infer that L 2 (T ) ∝ T χ2 with χ 2 = α + 3/2 ≈ -0.7(3) for this particular resonance.

D. Analysis of all loss resonances

The same procedure regarding the dependence with density and temperature is applied to the 10 loss features observed in Fig. 1 (top panel) plus the loss feature at 1.755 G which emerges for hotter clouds (see Fig. 1 bottom panel). These 11 loss features are identified by the red vertical lines in Fig. 1. We report in Fig. 5a the exponent γ for each loss feature (with β = -Ṅa /N a ∝ n γ a at a fixed averaged temperature T ) and in Fig. 5b the exponent α (with β ∝ T α at a fixed initial N a ).

From the results shown in Fig. 5a, we identify 7 loss features for which the measured value of γ is compatible, within error bars, with a two-body dominated process, i.e. γ = 1. We identify a single loss feature for which γ is compatible, within error bars, with a three-body dominated process, i.e. γ = 2. We also identify three loss features that are not clearly described by either two-or three-body processes. This behaviour can emerge, for example, in the case of the two-step process discussed in § III A when the decay rate of the dimer Γ d is comparable to the rate of the process (1) producing this dimer. We will not attempt to describe the temperature dependence of those three lines.

Once the assignment of a two-body or three-body resonance has been made from the variation of β with n a , we determine the temperature dependence of the associated two-or three-body loss rates, L 2 ∝ βV or L 3 ∝ βV 2 for a given N a . Since the volume scales as T 3/2 , we write the temperature dependence of the two-and three-body loss rates as L 2 ∝ T χ2 and L 3 ∝ T χ3 , where χ 2 = α + 3/2 and χ 3 = α + 3.

In Fig. 5d we observe that six out of the seven identified two-body processes have a rate L 2 compatible with a 1/T dependence, as expected for s-wave resonances (see Eq. ( 9) for ℓ = 0). These resonances are marked with blue circles in the various panels of Fig. 5.

The only exception is the previously unobserved Fano-Feshbach resonance at B = 1.755 G, marked as a blue square in the various panels of Fig. 5. Its rate scales as L 2 ∝ T 0.5 . Although the scaling with temperature is strictly speaking not compatible with a d-wave resonance for which we would expect L 2 ∝ T , as observed for chromium [START_REF] Beaufils | Feshbach resonance in d-wave collisions[END_REF], we suggest that the deviation of χ 2 ≈ 0.5 from 1 is due to the weakness of the loss feature. As shown in Fig. 5c this resonance is an order of magnitude weaker than the other resonances, and therefore our measurements may be contaminated by other loss processes, such as forced evaporation, which could tend to weaken the observed temperature dependence.

For the six two-body loss features compatible with a swave resonance (blue circles in Fig. 5), one might expect a shift of the center of the resonance with temperature, given by ∆B = k B ∆T /δµ, where δµ, the differential magnetic moment between open and closed channels, is a priori unknown. Given the recent determination of δµ ≈ 1000 µK/G for the case of thulium [START_REF] Khlebnikov | Characterizing the temperature dependence of Fano-Feshbach resonances of ultracold polarized thulium[END_REF] we would expect a magnetic field shift ∼ mG, for our temperature range. This shift is comparable to our magnetic field stability and thus difficult to detect on our platform [34].

Finally, for the three-body dominated loss feature, identified in red in Fig. 5, we report a small positive temperaturedependence. At this stage, we cannot conclude whether this feature is caused by a direct three-body resonance as described in §III B, or whether it corresponds to an effective three-body decay resulting from a particular parameter setting in a twostep two-body loss process as proposed in [START_REF] Li | Three-body recombination near a narrow Feshbach resonance in 6 Li[END_REF][START_REF] Beaufils | Feshbach resonance in d-wave collisions[END_REF][START_REF] Waseem | Unitarity-limited behavior of three-body collisions in a p-wave interacting Fermi gas[END_REF][START_REF] Waseem | Quantitative analysis of p-wave three-body losses via a cascade process[END_REF].

V. BEC EXPANSION NEAR A LOSS FEATURE

Finally, we report a complementary measurement that allows us to determine the s-wave scattering length if we suppose that the interactions are of a two-body nature, as it seems to be the case for at least 7 out of 11 resonances. We perform a long time-of-flight expansion of a Bose-Einstein condensate (BEC) of 162 Dy and infer the scattering length from its area in the x-y plane orthogonal to the bias magnetic field pointing along z. The BEC is created in a trap with angular frequencies {ω x , ω y , ω z } = 2π × {28, 88, 66} Hz. We then quench the magnetic field to the desired value and hold the cloud for 20 ms before performing a 30 ms long time of flight. A magnetic field gradient ensures that the cloud does not fall due to gravity.

The scattering length is derived from a mean-field approach that incorporates dipolar interactions [START_REF] Eberlein | Exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions[END_REF]. We write

a ≈ a stab. + 3R x R y 2 5/2 × CN (13)
where a stab. ≈ 100 a 0 is the scattering length below which the BEC is no longer a stable solution in our trap geometry, a 0 is the Bohr radius and C ∝ a 4 ho [START_REF]Within the Thomas-Fermi approximation, C = 15a 4 ho ω2 ωxωy 5/2 , where aho = ℏ m ω is the harmonic oscillator length[END_REF]. We study the variation of the cloud size for different magnetic fields and show in Fig. 6 the resonances for which a clear dilatation is observed. We interpret this variation as a change in the scattering length using Eq. 13. Of the 11 loss features studied in this article, only 6 show a clear change in the size of the BEC. These resonances are also the ones with the highest loss rate. Since the measurements are performed with a BEC, we cannot extract negative scattering lengths and report only positive values of a. We compare our measurements with those reported in Ref. [START_REF] Tang | Anisotropic expansion of a thermal dipolar Bose gas[END_REF] and find a good agreement for the scattering length evolution near the B = 5.130 G Fano-Feshbach resonance.

Regarding the only three-body dominated loss feature at B = 5.561 G (see Fig. 6f), we draw the reader's attention to the interpretation of a BEC size change due to a variation of a. Since we do not exclude the existence of a pure threebody microscopic process for this resonance, a change in BEC size could also be due to pure three-body interactions and thus not to a change in scattering length. For harmonic traps this implies a change in the total area ∝ N 1/2 (instead of N 2/5 for two-body interactions). We have tested this hypothesis by varying the number of atoms in the BEC. Although our results are consistent with N 2/5 scaling, we cannot exclude the N 1/2 result within our experimental uncertainties. It will be particularly interesting to study this resonance in a flat-bottom trap, where the size of the BEC area after time-of-flight will be proportional to N 3 for three-body interactions instead of N 2 for two-body interactions, leading to an easier lift of ambiguity. However, this study is beyond the scope of this article.

VI. CONCLUSION

We have characterized 11 low-field resonant loss features of an ultracold thermal sample of dysprosium. From the analysis of their density and temperature dependence, we conclude that most loss features result from a resonant s-wave pairwise interaction. We also measured the corresponding change in scattering length through the expansion of a BEC. Additionally, we measured the three-body loss rate of a quasi-pure BEC near zero magnetic field, which provides valuable information for future studies aimed at exploiting spin-orbit coupling in a dense condensate of dysprosium atoms [START_REF] Chalopin | Probing chiral edge dynamics and bulk topology of a synthetic Hall system[END_REF].

Furthermore, we have evidenced (i) a possible two-body d-wave resonance, unobserved so far, highlighting the complex nature of interactions in strongly dipolar gases, and (ii) a loss resonance that may be controlled by pure three-body interactions. To go further in our quantitative description of three-body resonances, whether driven by two-body or threebody processes, we will need to better disentangle the roles of temperature and density, which should be possible with the preparation of a homogeneous sample of dysprosium in a boxlike trap [START_REF] Navon | Quantum gases in optical boxes[END_REF]. We load 3×10 8 atoms in a magneto-optical-trap (MOT), with a loading rate of 1 × 10 8 atoms, composed of five reddetuned beams (four in the x-y plane and one vertical), with detuning ∆ MOT = -43 × Γ red , with respect to the intercombination line with vacuum wavelength λ = 626.08 nm (red transition) and linewidth Γ red ≈ 2π ×136 kHz [START_REF] Ilzhöfer | Two-species five-beam magnetooptical trap for erbium and dysprosium[END_REF]. The MOT is produced with a saturation parameter s 0 = I 0 /I sat. ≈ 185 (the vertical beam has a tenth of this intensity) and a magnetic field gradient ∂ z B z = 1.72 G/cm. The cloud lies a few mm below the zero-field, which makes it fully polarized in the Zeeman sublevel of lowest energy |J, m J = -J⟩. The MOT capture velocity, determined by the linewidth of the transition and the MOT beam waist, w MOT = 15 mm, is equal to v c ≈ 7 m/s. We maximize the atomic flux reaching the main science chamber using an optical collimation. It is achieved through the cooling provided by a transverse molasses of two retroreflected laser beams with orthogonal propagation with respect to the oven's exit axis. The molasses laser beams are red-detuned, with detuning ∆ Coll. = -0.4 × Γ blue , with respect to the optical transition with vacuum wavelength of 421.29 nm (blue transition) and linewidth Γ blue ≈ 2π × 32 MHz. A saturation parameter of s 0 = 4 is used, leading to a five-fold increase in the loading rate of the MOT. The longitudinal velocity of the atomic flux exiting the oven is reduced from v x ≈ 400 m/s to ≈ 7 m/s in a 500 mm Zeeman slower in a spin-flip configuration, with a laser beam detuning of ∆ Zeeman = -14×Γ blue and a saturation parameter of s 0 ≈ 1. The blue and red laser beams are frequency stabilized through modulation frequency transfer using either the atomic flux at the output of the oven (for the blue transition), or an iodine cell (for the red transition) [START_REF] Lucioni | A new setup for experiments with ultracold dysprosium atoms[END_REF].

0 2 4 6 8 s MOT -∆ MOT |∇B| B z ODT 1 ODT 2 (1) (2) (3) (4) (5)

Compressed MOT and transfer into a crossed dipole trap

To further cool the atomic cloud, we reduce the saturation parameter of the red lasers to s 0 = 5.7, decrease the detuning to ∆ cM OT = -21 × Γ red , and increase the gradient to ∂ z B z = 4.31 G/cm, which stabilizes the position of the cloud against small fluctuations in the laser frequency and magnetic field. Although it leads to a compressed MOT (cMOT) with a temperature T ≈ 15 µK, higher than the Doppler temperature, it ensures a stable overlap with the crossed dipole trap (CDT). The cMOT has a typical size at 1/ √ e of 400 µm and atom number ∼ 1 × 10 8 . The CDT is composed of two single-mode laser beams at a wavelength of 1064 nm, with a relative angle of 144 • in the x-y plane, and a frequency difference of 180 MHz, which ensures that residual interference patterns are averaged out. As we reduce the detuning of the MOT beams, light-induced loss processes are enhanced, resulting in a short lifetime of the cMOT (∼ 200 ms). The loading of the cMOT into the CDT is therefore fast ∼ 50 ms, which allows us to load 4 × 10 6 atoms at a temperature of 60 µK. The two beams that make up the CDT, hereafter identified as ODT1 and ODT2 (see Fig. 7), have waists w ODT1 ≈ 30 µm and w ODT2 ≈ 20 µm. To optimize the loading, we enlarge the waist of ODT1 in the x-y plane by a factor of 2 with an acousto-optic deflector [START_REF] Henderson | Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates[END_REF]. The two optical dipole trap beams have maximum powers of 30 W (ODT1) and 5 W (ODT2) and the forced evaporative cooling is performed in the presence of a bias field aligned along the z-direction and with magnitude B z = 1.660 G. The maximum loading efficiency is achieved for horizontally polarized dipole beams. This is because the difference in polariz- ability between the ground and excited states of the intercombination line, ∆α = α exc.α ground , is negative at 1064 nm for a linear horizontal polarization [START_REF] Chalopin | Anisotropic light shift and magic polarization of the intercombination line of dysprosium atoms in a far-detuned dipole trap[END_REF]. This guarantees that the detuning of the cMOT cooling beam remains negative. After loading the CDT and prior to evaporative cooling, we rotate the polarization of ODT2 by 90 • .

Crossed dipole trap evaporative cooling

The first evaporation stage lasts for 1 s, during which we suppress the spatial modulation of ODT1 and reduce its power so that the two beams forming the crossed dipole trap have similar trap depths. We focus here on the second stage of forced evaporative cooling, which lasts for 3.5 s (see Fig. 8). At the beginning of this evaporation, we switch on a magnetic field gradient to partially compensate for gravity, which plays an important role in the optimization of the evaporative cooling [START_REF] Hung | Accelerating evaporative cooling of atoms into Bose-Einstein condensation in optical traps[END_REF].

We measure both temperature, atom number and trap frequencies at different times during the second evaporative cooling stage. In Fig. 9a, b we show the evolution of temperature and atom number as a function of time. Combined with our measurements of the trap frequencies, we compute the evolution of the averaged phase-space density D = n a λ 3 , where n a takes into account the averaging over the inhomogeneous density in the harmonic potential (see main text). We show in Fig. 9c We here present some examples for the BEC expansion near the B 0 = 5.130 G Feshbach resonance discussed in Fig. 6(e). We deduce the change in scattering length from the cloud dilatation in the x-y plane after a 30 ms time-of-flight. As shown in Fig. 10a, the expansion of the BEC far from the resonance, for instance B = 4.886 G (yellow dot), leads to radii of 30 -45 µm, along the two orthogonal axes of the optical dipole trap in the x-y plane. As the scattering length increases, the cloud expands significantly more, as shown in Fig. 10b for a magnetic field of B = 5.109 G. Interestingly, for B > B 0 , where the scattering length passes from large negative values to its background value, and thus crosses zero, we observe a cloud that does not expand even after a long time-of-flight (see Fig. 10c), which is a hallmark of quantum droplets [START_REF] Ferrier-Barbut | Observation of quantum droplets in a strongly dipolar Bose gas[END_REF]. Our procedure for determining the scattering length cannot be used in this case, as would need to incorporate beyondmean-field corrections to explain the stability of the cloud.

FIG. 1 .

 1 FIG. 1. Normalized atom number as a function of magnetic field for a thermal sample with temperature T = 190 nK (top panel in blue) and T = 2.4 µK (bottom panel in red). The red vertical lines indicate the 11 loss features for which we characterize the density and temperature dependence.

FIG. 3 .

 3 FIG. 3. Atom loss dynamics for varying total atom number Na at a magnetic field B = 5.130 G. The averaged temperature is constant and equal to T ≈ 2.0(1) µK. Panels (a) and (b) show the atom number and temperature evolution for the case of an initial atom number N0 = 2.3 × 10 5 . Panels (c) and (d) show the atom number and temperature evolution for N0 = 1.4 × 10 5 . (e) Variation of the initial loss rate, β = -Ṅa/Na, with the density na ∝ Na/ T 3/2 . The solid line is the fitting function β ∝ nγ a with γ = 0.92(10).

FIG. 4 .

 4 FIG. 4. Atom losses as a function of temperature T for a fixed atom number Na ≈ 1.5 × 10 5 , for the loss feature B = 5.130 G. (a) and (b) Atom number and temperature evolution, respectively, for a thermal cloud with temperature T = 1.1(1) µK. (c) and (d) Atom number and temperature evolution for T = 2.0(1) µK. (e) Variation of the initial loss rate, β = -Ṅ /N , with temperature. The solid line is the fitting function β ∝ T α , with α = -2.2(3).

FIG. 5 .

 5 FIG. 5. Summary of density-and temperature-dependence for 11 loss features between 0-6 G. (a) Determination of two-versus threebody dominated loss features. A value of γ compatible with 1 indicates a two-body dominated loss feature, while a value of γ = 2 indicates a three-body dominated feature. These values are represented by dashed horizontal lines. Loss features characterized by s(d)wave two-body dominated loss processes correspond to blue circles (squares), while red circles correspond to three-body processes. The green circles indicate loss features in a transitional regime where it is not possible to determine a 2-body or 3-body loss rate. (b) Temperature dependence of the loss rate β(T ) ∝ T α . (c) Strength of the different loss features. From the results shown in (a) and (b) we derive the two-body and three-body loss rates for a nominal density of n = 1 × 10 20 m -3 and temperature T = 1 µK. (d) Temperature dependence of the two-and three-body loss coefficients χ2 = α + 3/2 (blue) and χ3 = α + 3 (red). The 11 loss features studied in this article are marked by vertical bars.

FIG. 6 .

 6 FIG. 6. Variation of the scattering length with magnetic field, in the vicinity of six loss features. Central magnetic field: (a) B = 2.655 G, (b) B = 3.138 G, (c) B = 3.881 G, (d) B = 4.620 G, (e) B = 5.130 G, (f) B = 5.561 G.

Appendix: Details of the experimental setup 1 .

 1 Production of a 162 Dy MOT

FIG. 7 .

 7 FIG. 7. Schematic representation of the experimental setup. The atoms are optically collimated at the output of the oven (transverse cooling) and then decelerated in a spin-flip Zeeman slower. The atoms are then confined in a magneto-optical trap (MOT), which comprises 5 laser beams and a magnetic field gradient. We compress the MOT and capture approximately 4 × 10 6 atoms into a crossed dipole trap (CDT) made up of two beams (ODT1 and ODT2) with a relative angle of 144 • .

FIG. 8 .

 8 FIG. 8. Schematic representation of the experimental sequence used to produce a degenerate gas of dysprosium. (1) MOT loading stage. (2) Compressed MOT. (3) First stage of evaporative cooling. (4) Second stage of evaporative cooling. (5) Plain evaporation in the CDT to purify the quantum gas. (ToF) Time-of-flight expansion and absorption imaging acquisition.

FIG. 9 .

 9 FIG. 9. Efficiency of evaporative cooling. (a) Temperature as a function of time in log-linear scale. (b) Atom number as a function of time in log-linear scale. (c) Phase-space-density (D) as a function of atom number, Na, in log-log scale. We fit our with D ∝ N -ϑ a and retrieve ϑ ≈ 4.0. The gray region indicates the points for which a non-negligible condensed fraction is already present and the estimation of D is no longer quantitative. The horizontal dashed line corresponds to the non-interacting prediction for the emergence of a BEC at D ≈ 2.612.

FIG. 10 .

 10 FIG. 10. Scattering length in the vicinity of B0 = 5.130 G resonance (vertical red line). Expansion of a BEC in the x-y plane after 30 ms time-of-flight, (a) far from the Feshbach resonance and near the resonance with B < B0 (b) or B > B0 (c). We interpret the strong expansion of the BEC for B < B0 resulting from a large scattering length, while for B > B0 we observe a dense cloud compatible with the formation of a quantum droplet.

  the evolution of D as a function of N a in log-log scale. From the fit function D ∝ N -ϑ a , we determine the evaporative cooling efficiency ϑ ≈ 4, at the upper end of typical values in optical dipole traps (2 ≲ ϑ ≲ 5) [43]. Appendix: Examples of expanded clouds in the vicinity of the 5.130 G Feshbach resonance

Acknowledgements:

We thank Sarah Wattellier, Jean-Gabriel Pipelin, Louis Chambard, Virgin Durepaire, and Julie Veschambre for early contributions to the experimental setup. We acknowledge fruitful discussions with the members of the Bose-Einstein condensate team at LKB, and with F. Werner, D. Petrov, F. Chevy, R. P. Smith, O. Dulieu and M. Lepers. This work was supported by Grant No. ANR-20-CE30-0024, and by Region Ile-de-France in the framework of DIM Quan-TiP.