Olivier Llopis
email: llopis@laas.fr

Pierre Martinet

Pierre-Henri H Merrer

Khaldoun Saleh

50 GHz to 60 GHz local oscillator transmission over fiber using optical frequency multiplication

Keywords: Microwave optical systems, millimeter wave generation, phase noise, frequency reference, optical modulator, nonlinear modeling, CAD of microwave optical systems. I

published or not. The documents may come

50 GHz to 60 GHz local oscillator transmission over fiber using optical frequency multiplication

INTRODUCTION

Frequency generation and distribution using optical techniques is an interesting approach, particularly at very high frequencies. Millimeter wave local oscillator distribution using optics is implemented in many applications, going from telecommunications to radio-astronomy, and on distances which can vary from a few meters (ex : plane or satellite) to a few kilometers (ex : antenna network) or even much more (ex: clock comparison between laboratories) without any significant attenuation. Moreover, the high Q factor of optical delay lines or resonators can be used to realize low phase noise microwave sources [START_REF] Yao | Progress in the optoelectronic oscillator -a ten year anniversary review[END_REF] such as OEOs (Optical Electric Oscillators), and the frequency reference signal delivered by such OEOs is readily available for its distribution using optical fiber. The equivalent RF Q factor of OEOs is proportional to the RF frequency, and it is thus much higher in the millimeter wave range than in the low microwave range were most of the systems are today designed because of greater availability of devices (photodiodes, modulators, amplifiers…). It is thus interesting to investigate on low cost solutions which could be able to generate a millimeter wave signal carried by optics with a high signal to noise ratio.

Two techniques are today well known for signal generation in the millimeter wave range using optics : dual frequency (or mode locked) lasers [START_REF] Pillet | Dual-Frequency Laser at 1.5 m for Optical Distribution and Generation of High-Purity Microwave Signals[END_REF] and frequency multiplication [3 to 5]. Dual frequency lasers are particularly interesting to get a high output power and a high signal to noise ratio at very high frequencies. However, to get a sufficient close to carrier phase noise performance for the above described applications, the two modes have to be locked in some way (either optically, or electrically, or both). Such systems are difficult to set up, and require specific devices which are not commercially available. Frequency multiplication is, on the contrary, quite easy to set up and only requires a Mach Zehnder (MZ) modulator. In some cases, the modulator is specifically designed for this application, but a good performance can be obtained from a conventional MZ modulator (such the one used in this study). With this approach, the optical components are of course strongly correlated and the only problem is in the low level output signal, and the resulting degraded signal to noise ratio. It is thus interesting to try to improve this performance using CAD, investigating on various nonlinear modulation techniques and nonlinear orders for the frequency multiplication.

In this paper, various techniques to generate a 50 GHz or 60 GHz sinusoidal signal carried over fiber are compared, both theoretically (CAD) and experimentally. Four cases are more deeply studied, including phase noise measurement of the recovered millimeter wave signal. Finally, it is concluded on the interest of frequency multiplication by three for applications in this frequency bandwidth.

II. CAD APPROACH

The optical link under study is described in Figure 1. It uses a 20 mW (max.) 1.55 m DFB laser (Mitsubishi) and a 10 Gb/s MZ modulator (JDSU), so relatively low cost material, on the emitter side. On the receiver side, a 75 GHz photodiode (U2T) is used.

The frequency multiplication is obtained thanks to the nonlinearity of the MZ characteristic (Figure 2). Two bias points are classically used : V /2 , which corresponds to the normal bias for linear modulation (LM), and V  , which corresponds to the carrier suppression (CS) and which is often used for frequency multiplication by two.

However, in both cases, higher order multiplication orders can be reached with these two bias conditions when a high power RF signal is superimposed on these bias points. Around V /2 , the transfer function is odd, and only the odd harmonics of the RF input signal are generated : 1, 3, 5… Near V  , it is an even function, and the even harmonics are generated : 2, 4… The question is: how efficient is this process ?

In order to model this behavior, a CAD approach has been used. This approach is based on Agilent ADS software and uses an already described modeling approach of the optical link [START_REF] Brahimi | A CAD approach of microwave optical systems including noise performance[END_REF]. Because Agilent ADS does not include optical or optoelectronic devices, these devices have been implemented using mathematical equations and the symbolically defined devices (SDD) module of ADS. The optical frequency is simply an RF source, with a 194 THz frequency (!), which is not a problem for the harmonic balance approach of ADS. The system handles three main frequency ranges : DC, RF frequency and its harmonics (ex : 10 GHz, 20 GHz…) and the optical frequency (194 THz). Thanks to the conversion matrices approach implemented in the harmonic balance software, it is also possible to study the nonlinear noise conversion mechanisms between the sidebands of all these carriers. This is particularly interesting, as an example, for investigating on how the laser AM and FM noise may affect the RF carrier. The results obtained with this approach have been compared to more classical analytical approaches of MZ modulators models [START_REF] Wooten | A review of lithuim niobate modulators for fiber optic communications system[END_REF][START_REF] Zandano | A new compact model for high-speed electro-optic modulators fully integrated within a microwave CAD environment[END_REF][START_REF] Chung | Modeling and optimization of traveling wave LiNbO3 interferometric modulators[END_REF][START_REF] Hilt | Microwave harmonic generation in fiber-optical links" Microwaves, Radar and Wireless Communications[END_REF].

Figures 3 and4 represent the simulated and measured transfer function of the optical link, for the two bias cases under study and for two different input frequencies (10 GHz in LM and 15 GHz in CS). The agreement between simulated and measured power is excellent, at least in the power range which was available during the experiment. Only the 5 th harmonic is underestimated in case of V /2 bias.

III. OPTIMISATION OF 50-60 GHZ GENERATION

Our OEO application is focused in this frequency range. We have thus investigated four cases: frequency multiplication by 3 in LM mode, with an input frequency at 16.66 GHz (output at 50 GHz) and an input frequency at 20 GHz (output at 60 GHz) ; frequency multiplication by 4 in CS mode, with an input frequency at 12.5 GHz (output at 50 GHz) and an input frequency at 15 GHz (output at 60 GHz). In all these cases, the input frequency remains low enough to avoid prohibitive attenuation by the MZ modulator. Moreover, relatively low cost medium power amplifiers are available in this frequency range (10 GHz to 20 GHz).

Figure 5 represents the simulated and measured results obtained in these four cases. At low input power, the frequency multiplication by three is much more efficient than the frequency multiplication by four. At high level, this difference is not so clear, but it has to be noticed that the modulator manufacturer limits the input power at about 27 dBm. Because of these results, we have bought a 25 dBm output power amplifier for the more recent experiments.

However, the most important parameter for our application is not the output signal power but the carrier to noise ratio (CNR), which is related to the far from carrier phase noise. Including in the model the laser RIN parameter and the photodiode schottky noise, it is possible to compute this CNR. The result is depicted in Figure 6. The model shows that a CNR between 120 to 130 dB can be obtained with this technique with a 25 dBm RF input signal.

The last remaining test corresponds to the transmission of a high spectral purity signal and to the measurement of its phase noise at the output of the system. To this purpose, a low phase noise synthesizer (Anritsu) is used and the output from the optical link is measured thanks to an Agilent E5052B signal source analyser. This system allows a cross-correlation approach which ensures a very low phase noise floor, even in the millimetre wave range were two external mixers are used. Figure 7 represents the system configuration, with the various elements of the optical link and the millimeter wave mixers of the E5052B. Between the photodiode and the mixers, a low noise amplifier has been added (Spacek Labs). Figure 8 depicts an example of such phase noise measurement. No noise is added to the synthesizer phase noise, which is simply multiplied with the same factor than the frequency, up to a relatively high frequency offset of about 3 MHz, above which the noise floor of the optical link can be measured. Table 1 summarises the results obtained in this type of experiment for both the signal (photodiode output) and the phase noise.

Finally, it is clear that there is an advantage of more than 5 dB in terms of additive phase noise (and CNR) for the multiplication by 3 approach, compared to the multiplication by 4 (carrier suppression) approach.

IV. CONCLUSION

The theoretical and experimental evaluation of a frequency multiplication technique to generate high spectral purity signals in the microwave range has been presented. The theoretical model uses an original CAD approach implemented on a software originally dedicated to microwave systems modeling. A good agreement is found with the experimental results, and a phase noise floor of about -130 dBc/Hz in the 50-60 GHz range has been demonstrated, which is largely sufficient for most time and frequency applications.

Figure1:Figure 2 :

 2 Figure1 : Schematic diagram of the experimental set-up

Figure 3 :

 3 Figure 3 : Simulated and measured output power of the 1st, 3rd and 5th harmonics in LM modulation with a 10 GHz RF input

Figure 4 :

 4 Figure 4 : Simulated and measured output power of the 2nd and 4th harmonics in CS modulation with a 15 GHz RF input

Figure 5 :

 5 Figure 5 : Simulated (lines) and measured (dots) output power level at 50 GHz and 60 GHz. At low input power, the higher level is measured for a 50 GHz signal obtained from 16.66 GHz muliplied by 3, then a 60 GHz signal obtained from 20 GHz (X3), then a 50 GHz signal obtained from 12.5 GHz (X4) and finally a 60 GHz signal obtained from 15 GHz (X4).

Figure 6 :

 6 Figure 6 : Carrier to noise ratio (CNR) simulated for 3rd harmonic in LM and 4th harmonic in CS modulation

Figure 7 :

 7 Figure 7 : Overview of the experiment, including the output amplifier and external mixers used for the millimeter wave phase noise measurement

Figure 8 :

 8 Figure 8 : Phase noise spectrum of the output 60 GHz signal (top curve) compared to the phase noise spectrum of the 20 GHz source (bottom curve) in case of a multiplication by 3. The two curves are perfectly parallel, with a difference of 9.5 dB corresponding to the multiplication factor. Above 3 MHz offset, the noise floor of the optical link can be observed

Table 1 :

 1 Summary of the results obtained in the four cases (signal and noise)

ACKNOWLEDGEMENTS

This study is part of a project of the French national research agency ANR « ORA » 2010 BLAN 0312 03.


H S Nguyen

G Sallen

C Voisin

Ph Roussignol

C Diederichs
email: carole.diederichs@lpa.ens.fr

G Cassabois

Ultra-coherent single photon source

We present an original type of single photon source in solid state, based on the coherent laser light scattering by a single InAs quantum dot. We demonstrate that the coherence of the emitted single photons is tailored by the resonant excitation with a spectral linewidth below the radiative limit. Our ultra-coherent source opens the way for integrated quantum devices dedicated to the generation of single photons with high degrees of indistinguishability.

Semiconductor quantum dots (QDs) are promising candidates for the realization of reliable single photon emission devices in the contexts of fundamental quantum optics experiments or quantum information applications. In the pioneering work of Michler et al., intensity correlation measurements on the photoluminescence signal of single QDs brought the experimental evidence of the quantum nature of the QD radiation [1]. Subsequent experiments demonstrated the possibility to use single QDs for the generation of polarization-entangled single photon pairs [2][3][4], or indistinguishable single photons [5,6]. An important general issue is to reach the socalled fundamental radiative limit T 2 = 2T 1 , with T 1 the population lifetime and T 2 the coherence lifetime, where the linewidth of the photoluminescence spectrum corresponds to its lower limit 2 /T 2 = /T 1 . Several strategies have been followed in that sense such as the shortening of population lifetime induced by the Purcell effect [5,7], or the reduction of pure dephasing by resonant excitation [6,8]. Up to now, all the measurements reported in the literature focus on the incoherent photoluminescence signal for achieving single photon emission.

In this letter, we present an original type of single photon source based on the coherent laser light scattering by a single semiconductor QD. Besides the anti-bunching effect showing the non-classical nature of the emitted light, we observe that the QD emission spectrum is determined by the spectrum of the resonant excitation laser. This intrinsic striking feature of our system demonstrates the generation of single photons within a spectral linewidth below the radiative limit, resulting in a so-called ultracoherent character. Our study brings the evidence in a solid state system of the peculiar physical phenomenon where the radiated electric field has the classical character of the resonant excitation source while the emission statistics exhibit the quantum nature inherited from the light-matter coupling at the scale of a single system. Our ultra-coherent single photon source opens the way for in-tegrated quantum device where the generation of indistinguishable single photons is tailored by the excitation laser source.

Resonant excitation experiments on single QDs were performed in an orthogonal excitation-detection geometry [8]. The sample consists of a low density layer (0.01 µm -2 ) of self-assembled InAs/GaAs QDs embedded in a planar λ 0 -GaAs microcavity formed by two distributed-Bragg reflectors. The top and bottom Bragg mirrors are respectively made of 11 and 24 pairs of λ 0 /4 layers of AlAs and AlGaAs which leads to a microcavity quality factor of 2500. Resonant excitation of the QD is performed by a tunable cw external cavity diode laser. A Michelson interferometer allows highresolution Fourier transform spectroscopy of the QD resonant emission (RE), where the first-order correlation function g (1) (τ ) is deduced from the contrast of the interferences [9]. A Hanbury-Brown and Twiss (HBT) setup is also used to perform intensity correlation measurements under resonant excitation [1] and to measure the secondorder correlation function g (2) (τ ).

Figures 1(a) and 1(b) show micro-photoluminescence (µPL) spectroscopy on a single QD at 10K. Figure 1(a) is a quasi-resonant µPL spectrum, where the energy of the resonant diode laser E L is slightly detuned from the mean exciton energy E X (δ = E L -E X = -74 µeV ). We observe that the laser light scattering is highly reduced in the orthogonal excitation-detection setup and it is here comparable to the intensity of the excitonic emission. When the laser is strictly resonant with an exciton line in figure 1(b), the intensity is enhanced by a factor 60 due to the resonant excitation and this enhancement is here only limited by the QD saturation properties. Figure 1(c) is the RE spectrum of the same single QD where the intensity of the exciton emission under resonant excitation is plotted as a function of the laser detuning δ. In comparison to the previous µPL spectrum where the exciton linewidth is not resolved, we now observe two Lorentzian lines of width 4.4 µeV and 5.0 µeV, separated by 12 µeV. Polarization-resolved measurements show that they correspond to two linear orthogonal polarizations, hereafter called A and B, as expected for the fine structure splitting of the neutral exciton [10]. In the following, we investigate the different contributions in the RE signal. It is in fact known that the RE signal consists of the superposition of the coherent resonant Rayleigh scattering (RRS) and the incoherent resonant photoluminescence (RPL). The RRS component has a spectrum exactly corresponding to the one of the resonant excitation laser. The incoherent RPL has a more complex profile evolving from a single Lorentzian of linewidth 2 /T 2 to the so-called Mollow triplet on increasing the excitation power [START_REF] Cohen-Tannoudji | Atom-Photon Interactions: Basic Processes and Applications[END_REF]. Note that in figure 1(c), for a given detuning, the recorded intensity consists in the sum of these two components. In fact, one expects the RE signal to be dominated by the coherent RRS at low incident power, and on the contrary by incoherent RPL close to the QD saturation power. This latter regime has already been well studied in single QDs [6,8,[START_REF] Melet | [END_REF]13] with the evidence of the Mollow triplet [13], characteristics of this peculiar high power regime.

Our study focuses on the low excitation regime determined by the coherent RRS. Figure 2(a, b &c) shows high-resolution measurements by Fourier transform spectroscopy of the RE, for resonant excitation of the exciton line B (δ = 6 µeV), for three excitation powers corresponding to Ω 2 = 155 ns -2 , 64.6 ns -2 and 11.6 ns -2 , where Ω is the Rabi frequency. Our data are fitted (solid lines in Fig. 2(a, b &c)) to the first-order correlation function g (1) (τ ) of the RE of a two-level system:

g (1) (τ ) ∝ e -τ T L + A [ e -τ T 2 + e -ατ (B cos(βτ + ϕ)) ] (1)
where T L is the coherence time of the resonant laser, A, B and ϕ are three constants which depend on Ω, T 1 and T 2 , and α = 1 2

( 1 T1 + 1 T2 ) , β = √ Ω 2 -1 4 ( 1 T1 -1 T2 ) 2 .
The first term in the g (1) (τ ) function corresponds to the coherent RRS whereas the second one is related to the incoherent RPL. The experimental data are fitted by taking for T 1 and T 2 the experimental values determined by independent experiments (not shown here). Time-resolved measurements of the RE signal intensity first lead to an exciton lifetime T 1 = 320 ± 20 ps. Power-dependent experiments of the RE signal exhibit the standard powerbroadening effect of a two-level system [START_REF] Cohen-Tannoudji | Atom-Photon Interactions: Basic Processes and Applications[END_REF] from which we deduce a decoherence time T 2 = 410 ± 10 ps. As seen in Fig. 2(a, b &c), with T 1 = 320 ps and T 2 = 410 ps, we fairly reproduce our experimental data. In particular, we account for the smooth transition from a nonmonotonous decay corresponding to the Mollow triplet in the incoherent RPL regime, to a bi-exponential one where the long time component is determined by the coherence time T L of the resonant laser in the coherent RRS regime (the value of 10 ns is a lower bound of the coherence time which is not experimentally resolved).

The inverse Fourier transform of the theoretical g (1) (τ ) function allows a direct comparison, in the spectral domain, of the different RE emission profiles (Fig. 2(d, e &f)). The radiative-limit /T 1 of 2 µeV is also displayed on each spectrum as a guide of the eye of rectangular form. At high power (Fig. 2(d)), the incoherent RPL consists in a well-developed Mollow triplet with side bands separated by 8 µeV from the central peak of width 3 µeV. The RRS signal appears as a superimposed weak line, much narrower than the radiative limit. Upon reducing the resonant excitation power (Fig. 2(e &f)), the Mollow triplet shrinks to a single Lorentzian line with sidebands, while the relative intensity of the narrow RRS peak increases and tends to overwhelm the RE spectrum. FIG. 3. Intensity correlation measurements of the RE under resonant excitation of the exciton line B, for a power corresponding to Ω 2 = 2 ns -2 . Fit (solid line) to the second-order correlation function g (2) (τ ) with T1 = 320 ps and T2 = 410 ps.

An important question is the existence of an upper limit for the RRS fraction and the corresponding physical parameters conditioning it. We have theoretically investigated the spectral distribution of the coherent and incoherent components of the RE signal by considering the optical Bloch rate equations. One can deduce the intensity of these two components under resonant excitation, and further calculate the ration between the RRS contribution and the total RE signal (RRS+RPL), which is given by:

I RRS I RE = T 2 2T 1 × 1 1 + Ω 2 T 1 T 2 (2)
In the case of an ideal two-level system at the so-called radiative limit (T 2 = 2T 1 ), one can see that the RE signal is completely dominated by the RRS for excitation powers such as Ω 2 T 1 T 2 ≪ 1. On the contrary, as soon as pure dephasing appears leading to T 2 < 2T 1 , the highest fraction of RRS in the RE signal is given by T 2 /2T 1 .

In our system where T 2 = 1.3T 1 (which is very closed to the radiative-limit), the RRS fraction can intrinsically not exceed 65% of the RE signal. In Fig. 3, we display the normalized intensity auto-correlation measure-ments by the HBT setup under resonant excitation of the exciton line B, for an excitation power corresponding to Ω 2 = 2 ns -2 (I RRS /I RE =50%). After subtracting the noise contribution and taking into account the system response function of 400 ps, the experimental data are well fitted by the theoretical second-order correlation function g (2) (τ ) of the RE of a two-level system, given by g (2) (τ ) = 1 -( cos(βτ ) + α β sin(βτ ) ) e -ατ [13,[START_REF] Scully | Quantum optics[END_REF]. In particular, for low excitation powers (Ω ≪

1 2 1 T1 -1 T2
), the second-order correlation function follows the simple dependence on T 1 and T 2 , g (2)

(τ ) = 1 -1 T2-T1 ( T 2 e -2τ /T2 -T 1 e -2τ /T1 )
. The pronounced dip at zero time delay (g (2) (0) = 0.3), which is only limited by the system time response, shows that our system is indeed a very efficient single photon source, as expected in the regime where the RE spectrum is dominated by the RRS component [13,[START_REF] Scully | Quantum optics[END_REF]. Moreover, even at this uncommon low-power regime, the RE intensity reaches 30 kcounts/s which is comparable to the emission rate of other complex devices [4,[START_REF] Claudon | [END_REF]. The resonant excitation of a single QD thus leads to this very peculiar situation where the first-order correlation function of the radiated electric field has the classical character of the excitation laser, whereas the second-order correlation function has a quantum nature inherited from the light-matter interaction at the scale of a single QD [START_REF] Walther | Proc. R. Soc. Lond. A[END_REF]. As a matter of fact, this system represents an original type of quantum device with ultra-coherent single photons controlled by the linewidth of the resonant excitation source and the photon statistics controlled by the QD properties.

In conclusion, we have demonstrated that when the RE of a single QD is dominated by the coherent laser light scattering, anti-bunching is observed together with a narrow emission spectrum below the radiative limit. This implies that single QDs can produce single photons with a decoherence time that is not limited anymore by the QD electronic properties. This ultra-coherent single photon source promises high degrees of indistinguishability of the emitted photons which is a crucial requirement for quantum information applications.

This work was supported financially by the "Agence Nationale pour la Recherche" project CAFE (ANR-09-NANO-022).

FIG. 1 .

 1 FIG. 1. Micro-photoluminescence spectrum for a laser detuning with the exciton energy δ = EL -EX of -74 µeV (a) and -6 µeV (b). (c) Intensity of the QD resonant emission as a function of δ. The solid line is the sum of two Lorentzian fits (dashed lines) of width 4.4 µeV and 5.0 µeV, separated by 12 µeV, corresponding to the two linear orthogonal polarizations A and B, of the neutral exciton. Inset: Scheme of the tilted QD axis A and B with respect to the main crystallographic axis [110] and [110], labeled as X and Y.

2 FIG. 2 .

 22 FIG. 2. (a), (b) and (c) High-resolution Fourier transform spectroscopy of the resonant emission of the exciton line B, at δ = 6 µeV, for decreasing powers corresponding respectively to Ω 2 = 155 ns -2 , 64.6 ns -2 and 11.6 ns -2 . Fit (solid line) to the first-order correlation function g (1) (τ ) with T1 = 320 ps, T2 = 410 ps and TL = 10 ns. The background level is indicated with a dashed line. (d), (e) and (f) Corresponding calculated resonant emission spectrum deduced by inverse Fourier transform of the g(1) (τ ) function (Ω 2 = 155 ns -2 , 64.6 ns -2 and 11.6 ns -2 respectively). The radiative-limit of width 2 µeV is schematized in grey and superimposed on each spectrum.


H S Nguyen

G Sallen

C Voisin

Ph Roussignol

C Diederichs
email: carole.diederichs@lpa.ens.fr

G Cassabois

Optically-gated resonant emission in single quantum dots

We report on the resonant emission in coherently-driven single semiconductor quantum dots. We demonstrate that an ultra-weak non-resonant laser acts as an optical gate for the quantum dot resonant response. We show that the gate laser suppresses Coulomb blockade at the origin of a resonant emission quenching, and that the optically-gated quantum dots systematically behave as ideal two-level systems in both regimes of coherent and incoherent resonant emission.

Semiconductor quantum dots (QDs) are commonly considered as artificial atoms [1], and this analogy has led to an important development of experiments in the field of cavity quantum electrodynamics with semiconductor systems. These nanostructures are very promising for the realization of integrated devices such as single photon sources for quantum cryptography applications. The corresponding photon antibunching effect was observed by photoluminescence experiments in single QDs under non-resonant excitation [2], and more recently under strictly resonant excitation of the fundamental interband transition [3,4]. In particular, the application of this technique to single QDs in the weak coupling regime has led to the generation of indistinguishable photons thanks to the shortening of the radiative lifetime due to the Purcell effect, and to the reduction of the dephasing processes due to the strictly resonant excitation of the QD [4]. In fact, this configuration minimizes the residual excitation of the QD environment that acts as a fluctuating reservoir for spectral diffusion [5,6]. In this context, the intrinsic properties of a two-level system can be studied such as the Rabi oscillations [3,7,8] or the Mollow triplet in the resonant fluorescence regime [8].

In this letter, we show that experimental studies of the resonant emission (RE) of single QDs can be strongly limited, even impossible, since most of the QDs show a very strong quenching of the RE of the neutral exciton. This issue is a broadly met experimental situation [9,10] which is highly problematic for cavity quantum electrodynamics experiments in single quantum dots. We propose an efficient way to overcome this issue based on the use of an ultra-weak non-resonant laser that optically gates the QD resonant response. The optical gate induces a complete recovery of the properties of an artificial atom, and the single QDs behave as ideal two-level systems. We show that the QD RE is in fact quenched by Coulomb blockade, and that the non-resonant gate laser controls the QD ground state, even in the coherent regime of Rayleigh scattering. The optical gate effect results from radiative recombination in the QD in an unprecedented explored regime of ultra-slow carrier capture.

Resonant excitation experiments on single QDs are performed at low temperatures at 10 K with an orthogonal excitation-detection setup [3,7]. The sample consists of a low density layer (0.01 µm -2 ) of self-assembled InAs/GaAs QDs embedded in a planar λ 0 -GaAs microcavity formed by two distributed-Bragg reflectors. The top and bottom Bragg mirrors have 11 and 24 pairs of λ 0 /4 layers of AlAs and AlGaAs, respectively. The QD emission is detected in the microcavity mode, which has a quality factor Q of 2500 and a central energy of 1.27 eV, by means of a conventional confocal setup. The excitation laser is injected into the in-plane guided mode supported by the planar microcavity. The QD resonant excitation is performed either by a tunable cw external cavity diode laser for experiments in the spectral domain with an overall resolution of 1 µeV, or by a cw modelocked Ti:Sa laser for time domain measurements with a temporal resolution of 90 ps. Fourier transform spectroscopy enables high spectral resolution measurements of the QD emission [6]. The non-classical properties of the QD resonant emission is further investigated by a Hanbury-Brown and Twiss (HBT) setup for intensity correlation measurements [2]. Finally, the optical gate at the heart of our study is provided by a cw HeNe laser at 632 nm (1.9 eV) that is vertically injected into the planar microcavity via the confocal setup.

The implementation of the resonant excitation technique appears to be successful for very few QDs. The reproduction of the typical results reported by Muller et al. in Ref. [3] is achieved for 1 QD over 50, and the most frequent case corresponds to no resonance in the RE spectrum of the neutral exciton (Fig. 1(a), open circles •). Since the excitation laser is strictly at the energy of the QD fundamental interband transition, our observation strongly contradicts the expectations for having a quasi-ideal two-level system, which are based on the upmost reduction of the environment fluctuations under resonant excitation of the QD [5,[11][12][13]. We demonstrate below a solution with an optical gate.

We optically control the QD resonant response by means of a non-resonant laser that systematically restores the RE response of the neutral exciton in the studied QDs. Figure 1(a) shows the RE spectrum of a single QD when the optical gate is switched on (•) and off (•), and we stress that this result corresponds to the general behavior. The intensity of the RE is measured as a function of the laser detuning δ = E L -E X , where E L and E X are the laser and the exciton energies. While almost all the QDs show no resonance when the optical gate is switched off, a clear resonance appears at zero detuning when the optical gate is switched on. The opticallygated RE spectrum is fitted with a Lorentzian line of width 3.2 µeV, comparable to the typical linewidths measured under resonant excitation with various techniques [3,12,13]. We stress that the power of the additional non-resonant laser is typically of few nanowatts, that is more than four decades lower than the power required to saturate the QD. The contribution of the photoluminescence that is non-resonantly excited by the optical gate is therefore completely negligible.

In the following, we present a complete experimental study on the optically-gated RE in single QDs. We show that the intrinsic properties of a two-level system under resonant excitation are recovered when the optical gate is switched on. Figure 1(b) first presents time-resolved measurements of the optically-gated QD emission under resonant excitation (•). A typical exponential decay is observed in the temporal trace and a fit (solid line) gives the QD lifetime T 1 = 330 ± 20 ps. This estimate is a standard value for epitaxially grown semiconductor QDs [1].

We now turn to the power-dependence of the opticallygated RE, which allows for the evaluation of the decoherence time T 2 . Figure 2 displays the intensity at zero detuning (δ = 0) (Fig. 2(a)) and the linewidth ∆ (Fig. 2(b)) of the optically-gated RE spectrum as a function of the power of the resonant diode laser. The intensity of the RE signal first increases linearly with the excitation power, and then displays the typical saturation expected at high powers. In parallel, we observe the text-book power-broadening of the RE spectrum, with a linewidth increasing by a factor of three in our investigated range of excitation power. The theoretical expressions of the emission intensity I at zero detuning (δ = 0) and the linewidth ∆ of a two-level system under resonant excitation are [START_REF] Cohen-Tannoudji | Atom-Photon Interactions: Basic Processes and Applications[END_REF]:

I ∝ Ω 2 T 1 T 2 1 + Ω 2 T 1 T 2 ∝ P P + P 0 (1)
∆ = 2 T 2 √ 1 + Ω 2 T 1 T 2 = 2 T 2 √ 1 + P P 0 ( 2
)
where Ω is the Rabi frequency, T 1 the population lifetime, T 2 the decoherence time, P the power of the resonant laser and P 0 the saturation power. The experimental data presented in Fig. 2 are perfectly well fitted to equations ( 1) and ( 2), with T 2 = 480 ± 10 ps and P 0 = 16.5 ± 1.5 µW. We then deduce from the extracted value of T 2 that T 2 ∼ 1.5T 1 , which means the QD homogeneous linewidth is very close to its radiative limit (T 2 = 2T 1 ). More precisely, our experimental data indicate that the pure dephasing time T ⋆ 2 is of the order of 1.8 ns, T ⋆ 2 being defined by 1/T 2 = 1/2T 1 + 1/T ⋆ 2 . Such a pure dephasing time attests for the reduction of the environment fluctuations under resonant excitation where spectral diffusion effects are minimized [5,6]. We further conclude that the intrinsic features of a two-level system under resonant excitation are clearly restored by the ultra-weak optical gate. In particular, our technique is validated in both regimes of coherent and incoherent RE. For P ≪ P 0 , it is known that the RE consists in the coherent signal of Rayleigh scattering, whereas at saturation, the incoherent photoluminescence dominates the RE [START_REF] Cohen-Tannoudji | Atom-Photon Interactions: Basic Processes and Applications[END_REF]. In figure 1(a), for a given detuning, the recorded intensity consists in the spectrally integrated signal of both components. High-resolution measurements by Fourier transform spectroscopy of the RE at zero detuning (δ = 0) for P/P 0 = 2.4 show the superposition of the coherent and incoherent components of the RE (Fig. 3(a &b)). Our data are well fitted (solid lines in Fig. 3(a &b)) to the first order correlation function g (1) (τ ) of the RE of a twolevel system [15]:

g (1) (τ ) ∝ e -τ T L + A [ e -τ T 2 + e -ατ (B cos(βτ + ϕ)) ] (3)
where T L is the coherence time of the resonant laser, A, B and ϕ are three constants which depend on Ω, T 1 and T 2 ,

α = 1 2 ( 1 T1 + 1 T2 ) , and β = √ Ω 2 -1 4 ( 1 T1 -1 T2 ) 2
. The first term in the g (1) (τ ) function corresponds to the RE signal that is coherent with the excitation laser, whereas the second one is related to the incoherent part. In Fig. 3(b), we display the Fourier transform of the theoretical g (1) (τ ) function which gives the RE signal in the spectral domain. The incoherent component (dashed line in Fig. 3(b)) is broader than the radiatively-limited emission line (gray line in Fig. 3(b)) of 2 µeV width. On the contrary, the central peak of the coherent resonant Rayleigh scattering is much narrower than the natural line. Indeed, we demonstrate that the ultra-weak nonresonant optical gate induces the recovery of the properties of an artificial atom even in the coherent regime of Rayleigh scattering.

We finally discuss the quantum properties of the optically-gated RE signal in single QDs. Figure 3(c) presents the normalized intensity auto-correlation measurements by the HBT setup under resonant excitation at zero detuning (δ = 0), when the optical gate is switched on. After subtracting the noise contribution, we observe a pronounced dip at zero time delay with g (2) (0) = 0.06. This is a clear evidence of the characteristic photon antibunching in a single photon source [2][3][4]. Most importantly, it further shows that the ultra-weak gate laser does not degrade the non-classical properties of a single QD emission. Our data are well fitted by the convolution of the system response function of 150 ps resolution with the theoretical intensity auto-correlation function g (2) (τ ) of the RE of a two-level system, given by g (2) (τ ) = 1 - [8,[START_REF] Scully | Quantum optics[END_REF]. Taking into account the previous measured values of T 1 and T 2 , the data are fitted with Ω = 1.4 ± 0.1 µeV . The QD dipole moment, defined as µ = Ω/E with E the electric field amplitude, is then deduced from the fitted value of the Rabi frequency. From the power of the resonant excitation laser P = 11.5 µW (measured before coupling into the optical setup) and the waveguide cross-section S = 0.83 µm -2 , we deduce E ∼ 0.013 kV/cm from which we obtain an estimation of µ ∼ 50 D. This dipole moment is in agreement with other estimations in similar InAs QDs ranging from 20 to 60 D [START_REF] Muller | [END_REF][18][19][20]. We interpret the optical gate-effect within a model where the QD RE is quenched by Coulomb blockade because of the tunneling of a hole from a structural deep level (inset of Fig. 4(b), [15]). The optical gate suppresses Coulomb blockade by switching back the QD into a neutral state. This interpretation is supported by additional measurements of the QD RE, for the two spectral windows of the neutral exciton (X) and positively charged exciton (X + ), centered at E X and E X + (see [15] for the identification of the two lines). When the optical gate is switched off, no resonance is observed for the neutral exciton, as displayed in Fig. 4(a, top left) (and already shown in Fig. 1(a)), whereas RE is observed for the charged exciton (Fig. 4(a, top right)) (the higher background signal for X (Fig. 4(a, top) comes from the different detunings of the neutral and charged emission lines with the cavity mode, the X line being in resonance with the cavity mode in the present case). On the contrary, when the optical gate is switched on, the RE of the neutral exciton (Fig. 4(a, bottom left)) appears and becomes more intense than for the charged one (Fig. 4(a, bottom right)). These experimental data indicate that the optical gate controls the residual charge q in the QD. When the optical gate is switched off, the q value is close to +e whereas q becomes closer to 0 when the optical gate is switched on.

( cos(βτ ) + α β sin(βτ ) ) e -ατ
A deeper insight into the physics of the optical gateeffect is gained by investigating the switching dynamics of the RE signal. In Fig. 4(b), we observe that the RE intensity increases exponentially with a time constant t on = 5.1 ± 0.2 µs when the gate laser is switched on, at a power of 3 nW. Within the time constant t on , an electron that was non-resonantly photogenerated by the gate laser is captured into the QD and radiatively recombines with the residual hole in the QD. Since we use an ultra-weak non-resonant laser for the optical gate, the limiting process for the QD neutralization appears to be the carrier capture into the QD (this interpretation is further supported by a quantitative analysis of an extensive experimental characterization of the optical gate-effect, which will be the subject of a forthcoming publication). Contrarily to the standard configuration of photoluminescence spectroscopy under non-resonant excitation where the capture rate is in the range of tens of ps, the optical gate-effect occurs in an unprecedented explored regime of ultra-slow capture on µs time scales. We are led to a picture of a coherently-driven QD where the carriers injected by the gate are slowly captured oneby-one into the QD prior to quasi-simultaneous radiative recombination of an electron-hole pair. The QD neutralization is therefore limited by the recapture of a hole, thus leading to a RE intermittency very similar to the blinking phenomenon reported for the nanocrystals [21]. Finally, when the gate laser is switched off, the QD ground state evolves to a stationary hole excess because of the defect in the QD environment.

The electrical space-charge technique of deep level transient spectroscopy brought evidence that the growth process of self-assembled QDs results in the intrinsic coexistence of structural deep levels and QDs [22]. In fact, the photophysics of defects in arsenide semiconductors presents a rich phenomenology. For instance, in fractional quantum Hall effect experiments, the mobility of two-dimensional electron systems is increased to the highest values by using a weak non-resonant laser [23]. In bulk semi-insulating samples, persistent photoconductivity arises from the metastability of the arsenic antisite, due to the complex bond-breaking structural rearrangement in GaAs [24][25][26]. In our case, the structural defects around the QD contribute to the presence of residual charges inside the QD, which lead to the coexistence of neutral and charged exciton lines [15]. Such a feature is routinely observed in QD samples from different growth facilities [27][28][29] or made of various materials [30,31]. Several papers reported the optical control of the QD residual charge in photoluminescence spectroscopy under non-resonant excitation [28,30]. Although analog to our optical gate-effect, it strongly contrasts with our experiments. The techniques used in Ref. [28,30] refer to a complete incoherent regime where the photoluminescence is non-resonantly excited. Our work demonstrates a novel approach for coherently-driven single QDs. In particular, even in the regime of coherent Rayleigh scattering, where no energy is absorbed in the QD [START_REF] Mukamel | Principles of Nonlinear Optics and Spectroscopy[END_REF], the non-resonant gate laser finely controls the QD ground state. This configuration opens the way for conditional quantum measurements time-controlled by the gate laser.

In summary, we have shown that experimental studies of the resonant emission of coherently-driven single QDs can be strongly limited, even impossible, since most of the QDs show no resonance in the resonant emission spectrum of the neutral exciton. We demonstrate a solution based on an ultra-weak non-resonant laser that optically gates the QD resonant response. The optical gate induces a complete recovery of the properties of an artificial atom, and the single QDs behave as ideal twolevel systems. We show that the QD resonant emission is in fact quenched by Coulomb blockade, and that the non-resonant gate laser controls the QD ground state, even in the coherent regime of Rayleigh scattering. I. Coherent and incoherent contributions in the resonant emission.

Figure 3(a & b) display high-resolution measurements by Fourier transform spectroscopy of the resonant emission (RE). The coherent and incoherent components of the RE are fitted by the first order correlation function g (1) (τ ) of the RE of a two-level system:

g (1) (τ ) ∝ e -τ T L + A [ e -τ T 2 + e -ατ (B ′ cos(βτ ) + C ′ sin(βτ ))
] where α = 1 2

( 1 T 1 + 1 T 2 ) β = √ Ω 2 - 1 4
( 1 T 1 - 1 T 2 ) 2 A = T 1 T 2 (1 + Ω 2 T 1 T 2 ) B ′ = 1 - T 2 T 1 (1 + Ω 2 T 1 T 2 ) C ′ = Ω 2 T 1 (3T 2 -T 1 ) -(T1-T2) 2 T1T2 2βT 1 (1 + Ω 2 T 1 T 2 )
The Fourier transform of the g (1) (τ ) function gives the RE signal in the spectral domain I(ω), which is the sum of the coherent and incoherent components, I coh (ω) and I incoh (ω) respectively, in the RE spectrum:

I coh (ω) ∝ Ω 2 T 2 2 (1 + Ω 2 T 1 T 2 ) 2 2 TL (ω -ω L ) 2 + 1 T 2 L I incoh (ω) ∝ Ω 2 T 1 T 2 1 + Ω 2 T 1 T 2 [ 2 T2 (ω -ω 0 ) 2 + 1 T 2 2 + αB ′ + (ω + β -ω 0 )C ′ (ω + β -ω 0 ) 2 + α 2 + αB ′ -(ω -β -ω 0 )C ′ (ω -β -ω 0 ) 2 + α 2
] * Present address: Laboratoire de Physique et Chimie des Nano-Objets, 135 avenue de Rangueil, 31077 Toulouse, France. † carole.diederichs@lpa.ens.fr with E L = ω L the laser energy and ω 0 the energy of the resonantly-excited fundamental transition. In particular, I coh (ω) corresponds to the central peak of the coherent resonant Rayleigh scattering observed in Fig. 3(b). Moreover, in the configuration where P ∼ P 0 , the incoherent part of the RE signal is limited to the first term of I incoh (ω).

II. Identification of the neutral and charged excitons.

The inset of figure S 1(c) displays a typical microphotoluminescence spectrum under non-resonant excitation showing two lines. The lower and upper lines are labelled X and CX, respectively. We show below by autoand cross-correlation Hanbury-Brown and Twiss (HBT) measurements (Fig. S 1) that the X line corresponds to the neutral exciton, and the CX one to the charged exciton. The g (2) correlation functions are displayed in Fig. S 1 after deconvolution by the system response function. We observe a pronounced dip at zero time delay for all three measurements, with g (2)

X-X (0) = 0.08 and g

(2)

CX-CX (0) = 0.09 for the auto-correlation functions of X and CX, respectively, and g X-CX corresponds to the probability of detecting one CX photon after one X photon for positive time delays, the bunching at negative time delays allows us to identify the CX line as corresponding to a charged state of the X line [1]. All the results are well fitted by using the rate equations corresponding to the model in Ref. [1]. In a simple manner, the long time part of g (2) (τ > 0) is attributed to a three charges capture process whereas the short time part of g (2) (τ < 0) is attributed to a single charge capture process. Finally, from the the positive detuning of the charged exciton state (CX) with respect to the neutral one (X), the CX line is attributed to the positive trion made of two holes and one electron [2,3].

III. Model of the optical gate-effect

We interpret the optical gate-effect within a model where the QD resonant emission (RE) is quenched by Coulomb blockade because of the tunneling of a hole from a structural deep level (DL). The optical gate suppresses Coulomb blockade by switching back the QD into a neutral state.

The processes governing the optical gate-effect are represented in the model sketched in figure S 2. The defect state is assumed to be close to the QD confined hole state. When the resonant laser and the optical gate are switched off (Fig. S 2(a)), the hole tunnels from the structural deep level to the QD with a time constant τ in , and from the QD back to the deep level with a time constant τ out , the deep level being filled with a rate 1/t off . This leads to a residual charge q close to +e in the QD. When the QD is resonantly excited by the resonant laser (Fig. S 2(b)), only the RE of CX is observed since the residual hole in the QD blocks any optical transition at the energy E X of the neutral exciton because of Coulomb blockade [4].

When the optical gate is switched on (Fig. S 2(c)), the residual hole is ejected from the QD through radiative recombination with one electron photogenerated by the optical gate in the GaAs barrier. The inverse of the t on time thus characterizes the corresponding rate of neutralization. This process is extremely rare since the optical gate is more than four orders of magnitude lower than at the QD saturation. However, when it occurs, it switches the QD back into a neutral state where the RE of the neutral exciton is observable (Fig. 1(a) and 4(c)). The probability of having no residual hole in the QD is then limited by the recharging of the deep level with a time constant t off . This phenomenology is well described by a simple rate equations model which gives a rough estimation of the transient time constants t on and t off measured with timeresolved experiments (these results on the switching dy- namics of the optical gate-effect and its power dependence will be the subject of a forthcoming publication with a more detailed model with P sat G the QD saturation power of few tens of µW. In the experimental conditions where P G ∼ few nW, we get a rough estimate of t on of 5 µs, fully consistent with the measured one. Moreover, measurements on increasing the optical gate power (not shown here) show (i) a decrease of t on as a function of P G , and (ii) an approximately constant t off value, as predicted by our model. Finally, the higher the ratio t off /t on , the lower the residual q in the QD and the more intense the RE of the neutral exciton.

We stress the suggested model could be rewritten taking into account a residual electron in the QD which comes from a residual donor in the vicinity of the QD confined electron state.

Eventually, we discuss other additional measurements as a function of the energy of the optical gate (not shown here). Remarkably, the intensity of the QD RE varies with the optical gate energy exactly as the QD photoluminescence non-resonantly excited by the intense optical gate. This similarity of the excitation spectra of the RE and non-resonant photoluminescence confirms the assumption of radiative recombination as the process involved in the neutralization of the QD by the optical gate.

FIG. 1 .

 1 FIG. 1. (a) Resonant emission (RE) spectra of the exciton with (•, gate ON) and without (•, gate OFF) the additional non-resonant laser, in a single QD at 10K. The RE intensity is measured as a function of the laser detuning with the exciton energy, δ = EL -EX . The powers of the optical gate and the resonant laser are respectively equal to 3 nW and 4 µW . Lorentzian fit (solid line) of width 3.2 µeV . (b) Time-resolved RE of the QD when the gate is switched on (•). The solid line is a fit with a decay time T1 = 330 ± 20 ps.

FIG. 2 .

 2 FIG.2. Intensity (a) and linewidth (b) of the optically-gated resonant emission spectrum versus the power of the resonant laser, P. The experimental data are fitted by using Eq.1 and 2 corresponding to a two-level system model (solid line).

FIG. 3 .

 3 FIG. 3. (a) High-resolution Fourier transform spectroscopy of the optically-gated RE, at zero detuning (δ = 0), for P/P0 = 2.4. The background level is indicated with a dashed line. Fit (solid line) by using Eq. 3 with TL = 100 ns, Ω = 2.5 µeV, T1 = 330 ps and T2 = 480 ps. (b) Theoretical RE signal in the spectral domain (red solid line) together with the incoherent contribution (dashed line) and the radiatively-limited emission line of width 2 µeV (gray solid line). (c) Intensity auto-correlation measurements under resonant excitation at δ = 0, for P/P0 = 0.7, when the optical gate is switched on.

FIG. 4 .

 4 FIG. 4. (a) RE intensity as a function of the energy detuning between the resonant laser and the neutral exciton X (left row), and positively charged exciton X + (right row), when the gate laser is switched off (top) and on (bottom). (b) RE intensity as a function of time (•) when the gate laser is switched on at t=0. The theoretical fit (solid line, red) is the convolution of the system response function (•) with an exponential of time constant ton = 5.1±0.2 µs. Inset: Scheme of the electronic states (|v⟩: empty QD; |+e⟩: one hole in the QD; |X⟩: neutral exciton; |X + ⟩: positively charged exciton) and the transitions involved in the optical gate-effect (dotted arrow: neutralization of the QD by the optical gate; solid arrows: optical transitions under resonant excitation of the neutral exciton).

  The authors gratefully acknowledge P. M. Petroff for the sample fabrication, as well as G. Bastard, R. Ferreira and C. Delalande for stimulating discussions. The work was supported financially by the 'Agence Nationale pour la Recherche' project QSWITCH.Supplemental material for: Optically-gated resonant emission in single quantum dots H. S. Nguyen 1 , G. Sallen 1 , * C. Voisin 1 , Ph. Roussignol 1 , C. Diederichs 1 , † and G. Cassabois1,2,3

FIG. S 1 .

 1 FIG. S 1. Intensity auto-(a & b) and cross-(c) correlation measurements of the X and CX lines observed in the microphotoluminescence spectrum under non-resonant excitation (inset). The experimental data are fitted by using the rate equations corresponding to the model in Ref. [1] (solid lines). The X and CX lines are identified as the neutral and charged excitons, respectively.

( 2 )

 2 X-CX (0) = 0.05 for the cross-correlation function between the two lines. The anti-bunching in the cross-correlation experiment (Fig.S1(c)) is a clear evidence that the two lines observed in the micro-photoluminescence spectrum correspond to the same quantum dot (QD). Moreover, since g(2)

FIG. S 2 .

 2 FIG. S 2. Scheme of the valence (v) and conduction (c) bandedges in the growth direction of the heterostructure, showing together the InAs wetting layer (WL), the GaAs barrier, the single QD and a deep level (DL) assumed to be close to the confined hole state of the QD, with electrons (•) and holes (•). (a) The resonant laser and the optical gate are switched off. A hole tunnels from the DL to the QD and vice-versa, with characteristic times τin and τout, respectively. The DL filling with a rate 1/t off leads to a residual hole in the QD. (b) The resonant laser (shown by the up solid arrow) is switched on. The QD resonant emission (RE) is observed only at the energy ECX of the positively charged exciton CX. (c) The resonant laser and the optical gate (long solid arrow) are switched on.The residual hole is ejected from the QD after radiative recombination with one electron photogenerated by the optical gate, with a time constant equal to ton. The DL recaptures a hole with a time constant equal to t off . ton < t off leads to a neutral QD state, and the QD RE is predominantly observed at the energy EX of the neutral exciton X.

1

  Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS (UMR 8551), Université P. et M. Curie, Université D. Diderot, 24, rue Lhomond, 75231 Paris Cedex 05, France 2 Université Montpellier 2, Laboratoire Charles Coulomb UMR5221, F-34095, Montpellier, France and 3 CNRS, Laboratoire Charles Coulomb UMR5221, F-34095, Montpellier, France (Dated: December 19, 2011)

  QD and p DL are the probabilities to have one hole in the QD and DL, respectively, G the capture rate of one hole in the DL (assumed to be constant at low optical gate powers), and µP G the effective radiative recombination rate of the residual hole in the QD, P G being the optical gate power. This model leads to a transient time t on of the order of 1/µP G , and to a t off time of the order of 1/G. In the limit of the QD saturation by the optical gate, µP G corresponds to the neutral exciton recombination rate γ R , with 1/γ R = T 1 ∼ 500 ps. Therefore, we rewrite µP G as γ R

					). The corresponding rate
	equations are:
	dp DL dt	=	p DL (1 -p QD ) τ in	+	p QD (1 -p DL ) τ out	+ G(1 -p DL )
	dp QD dt	= +	p PG
					P sat G

DL (1 -p QD ) τ in -p QD (1 -p DL ) τ out -µP G p QD

where p