Mollow triplet in cold atoms
Luis Ortiz-Gutiérrez, Raul Teixeira, Aurélien Eloy, Dilleys Ferreira da Silva, Robin Kaiser, Romain Bachelard, Mathilde Fouché
aa r X i v : . [ phy s i c s . a t o m - ph ] J a n Mollow triplet in cold atoms
Luis Ortiz-Guti´errez , , Raul Celistrino Teixeira , Aur´elien Eloy , DilleysFerreira da Silva , , Robin Kaiser , Romain Bachelard , , and Mathilde Fouch´e ∗ Universit´e Cˆote d’Azur, CNRS, INPHYNI, France CAPES Foundation, Ministry of Education of Brazil,Caixa Postal 250, Bras´ılia – DF 70040-020, Brazil and Departamento de F´ısica, Universidade Federal de S˜ao Carlos,Rodovia Washington Lu´ıs, km 235 - SP-310, 13565-905 S˜ao Carlos, SP, Brazil (Dated: January 24, 2019)In this paper, we measure the spectrum of light scattered by a cold atomic cloud driven by astrong laser beam. The experimental technique is based on heterodyne spectroscopy coupled tosingle-photon detectors and intensity correlations. At resonance, we observe the Mollow triplet.This spectrum is quantitatively compared to the theoretical one, emphasizing the influence of thetemperature of the cloud and the finite-size of the laser beam. Off resonance measurements are alsodone showing a very good agreement with theory.
I. INTRODUCTION
The Mollow triplet, described theoretically by B. R.Mollow in 1969 [1], corresponds to the three peaks of in-elastically scattered light in the fluorescence spectrumof a two-level system driven by a strong and resonantincident field. Besides its importance in describing theatom fluorescence, it can also be viewed as a fundamen-tal signature of quantum optics, highlighted by photoncorrelations between the peaks of the spectrum and an-tibunching in some particular cases. These correlationswere first observed by A. Aspect et al. in 1980 [2] andquantitatively characterized by C. A. Schrama et al. in1992 [3] which had remained the state of the art until re-cently. Indeed, this topic has attracted a renewed inter-est [4], mainly in solid state physics where, for example,Mollow triplet in a quantum dot appears as a promisingcandidate of heralded single-photon sources [5].This power spectrum was theoretically investigated inthe 60’s and it was first established by B. R. Mollow [1]. Itcan be decomposed in an elastic component, representedby a delta function in frequency space, and an inelasticcomponent. The latter, in the specific case of resonantand strong enough driving field, is commonly known asthe Mollow triplet: the spectrum is made of a carrierand two spectrally symmetric sidebands. It can be inter-preted as the signature of spontaneous emission down aladder of paired states that corresponds to the new eigen-states of the two-level system dressed by a strong drivingfield [6].The Mollow triplet was first observed in atomicbeams [3, 7–10], with a configuration that allowed toavoid as much as possible the inhomogeneous broadeningdue to temperature. The spectrum was usually measuredusing a Fabry-Perot cavity. Several improvements havebeen made, especially regarding the polarization of thedriving field, to be as close as possible to a two-level ∗ [email protected] system. This led to a first quantitative agreement withtheory in 1977 [9], despite the presence of unaccountedeffects such as the inhomogeneous broadening due to thenonuniformity of the laser field. Since then, the Mol-low triplet has been observed in many different systems:ions [11], single molecules [12], or quantum dots [4, 13–15].Surprisingly, the Mollow triplet was rarely studied incold atomic clouds despite its specific advantages. Thelow temperature makes its impact on the fluorescencespectrum minimal. Under certain conditions, atomicbeam experiments gave unexpected asymmetric spec-tra [9, 10]. This effect, due to position dependent atomicrecoil [16], is inherent to the specific configuration imple-mented to minimize the Doppler contribution of theseatomic beams. Compared to single-particle systems,a multi-atom source increases the signal available forthe detection. On the other hand, solid state quan-tum emitters often exhibit significant deviations from theideal two-level system, for example through phonon cou-pling [17, 18]. And finally, cold atomic clouds can reachhomogeneous optical densities of up to about 1000 [19]which makes them suitable to go beyond the single scat-tering approximation and identify fundamental effects ofmultiple scattering in the Mollow triplet, including asym-metries and additional resonances [20, 21]. One of thefirst attempts using cold atoms was done by K. Nakayama et al. [22] on optical molasses. However, the Mollow spec-trum was characterized out of resonance, where the spec-trum is composed mainly of the Doppler-broadened elas-tic part plus two sidebands of inelastically scattered light.At resonance, the Mollow triplet was hardly visible anda quantitative comparison with the theoretical spectrumis still lacking. In 2016, K. M. Shafi et al. [23] also pub-lished some data that could be interpreted in terms ofMollow spectrum. However, the experiment was doneon a magneto-optical trap (MOT), thus with an atomiccloud illuminated by six different off-resonant laser beamsand in the presence of a magnetic field gradient, whichmakes the interpretation of the data and its quantitativeanalysis much more challenging.In this paper, we present the measurement of the spec-trum of light scattered by a cold atomic cloud and drivenby a strong laser field. We detect this optical spectrumusing a beat note (BN) technique, coupled with an inten-sity correlation measurement setup [24]. This allows usto take advantage of the good sensitivity provided by theheterodyne spectroscopy and of photon counting devicessuited for extremely low signal [25]. We report on bothresonant and off-resonant excitation. In the first case,the Mollow triplet is clearly visible. We will show thatthe experimental data are in quantitative agreement withthe expected spectra if one takes into account some in-homogeneous broadening. For off-resonance excitation,the amount of elastic and inelastic scattering is quan-tified and presents a very good agreement with theory.Finally, we investigate the effect of light polarization andintensity modulation to show the importance of being asclose as possible to a two-level system with homogeneousexcitation to observe a clear and reliable signal. II. EXPERIMENTAL SETUPA. Cold atomic cloud
The experimental setup is described in Refs. [24, 26].A cold atomic cloud is provided by loading Rb atomsin a MOT. A compression stage is added to increase itsdensity and to obtain a smooth density profile. For thisspecific experiment, the cloud is made of typically 5 × atoms with a longitudinal rms radius σ z = 0 . ± . σ r = 0 . ± . µ K beforeapplying the strong laser beams to detect the Mollowspectrum.
B. Laser beams
To observe the Mollow triplet, the atomic cloud is illu-minated by two counter-propagating laser beams A andB, as depicted in Fig. 1, applied along the longitudinalcloud axis z . Their power can be adjusted independentlywhich allows, for instance, to avoid pushing the atomsdue to imbalanced radiation pressure forces. The twobeams come from the same distributed-feedback laseramplified by a tapered amplifier, and their frequency islocked close to the F = 3 → F ′ = 4 hyperfine transitionof the Rb D line, with linewidth Γ = 2 π × .
07 MHz.The locking system uses a master-slave configurationwith an offset locking scheme [27], allowing us to adjustthe laser frequency without changing the beam directionand power.We adjust the laser beam polarization, measured witha polarimeter just before the vacuum cell, with a λ/ λ/ APD
FIG. 1. Experimental setup. Two counter-propagating laserbeams (beams A and B) illuminate a cold atomic cloud. Thespectrum of the scattered light is measured thanks to a beatnote technique and its intensity autocorrelation. The scat-tered light is collected by a polarization maintaining (PM)single-mode fiber, after passing through a λ/ we use the same circular polarization for the two beams.For a σ + polarization, the atoms are quickly pumpedin ( F = 3, m F = 3) and we probe the F = 3 ( m F =3) → F ′ = 4 ( m ′ F = 4) transition. Since both beamshave the same polarization, if applied simultaneously,they would interfere and create a standing wave, lead-ing to a strong spatial modulation of the intensity [28]with a corresponding convolution of the expected Mollowtriplet. To avoid such a convolution, one need to apply asingle laser beam with a well defined homogeneous Rabifrequency. We therefore illuminate the atoms alternat-ing successively beam A and beam B, the switching onand off being done using two acousto-optic modulators(AOMs).On the one hand, achieving a homogeneous Rabi fre-quency in the transverse direction would require a uni-form intensity distribution, i.e., a plane-wave. On theother hand, the maximum available laser power imposesto decrease the beam waist to get a Rabi frequency ashigh as possible and thus well-resolved Mollow sidebands.As a compromise between the laser intensity and its non-uniformity over the cloud, we have used a beam waist of w = 2 . λ/ s , max = I/I sat ≃ I sat = 1 .
67 mW/cm for the transition consid-ered in this experiment, and a maximum Rabi frequencyof Ω max = Γ p s / ≃ C. Measurement of the first order correlationfunction
Our goal is to measure the spectrum ˜ g sc(1) ( ω ) of thelight scattered by the atomic cloud, or its Fourier trans-form which corresponds to the first order temporal corre-lation function g sc(1) ( τ ). The latter quantity is obtainedby recording the beat note between the scattered lightand a local oscillator (LO). The light scattered while il-luminating the atomic cloud with beam A or B is col-lected by a polarization-maintaining (PM) single-modefiber. This allows us to select only one spatial mode. A λ/ ◦ . As the polarization of beams Aand B are circular, once the atoms are pumped into thestretched m F = +3 Zeeman sublevel, the polarization ofthe fluorescence in the direction of the fiber will be mostlylinear. The λ/ ω BN = 2 π ×
120 MHz.The local oscillator is then injected in another PM single-mode fiber, with a polarization selected by a PBS parallelto the fluorescence one.The two fibers that collect the local oscillator and thelight scattered by the atoms are then connected to a fiberbeam splitter (FBS). We compute the | g sc(1) ( τ ) | func-tion via the measurement of the intensity autocorrela-tion of the beat note g BN(2) ( τ ), given by the followingformula [25]: g BN(2) ( τ ) = h I BN ( t ) I BN ( t + τ ) ih I BN ( t ) i , (1)= 1 + 2 h I sc ( t ) ih I LO ( t ) i ( h I sc ( t ) i + h I LO ( t ) i ) | g sc(1) ( τ ) | cos( ω BN τ ) h I sc ( t ) i ( h I sc ( t ) i + h I LO ( t ) i ) (cid:16) g sc(2) ( τ ) − (cid:17) , (2)with I BN , I sc , I LO the intensity of the beat note, thecollected scattered light and the local oscillator respec- tively, g sc(2) ( τ ) the temporal intensity correlation of thescattered light, and with h . i corresponding to averagingover time t . It is important to note that this signal isnot sensitive to the field correlation of the laser itself.This is due to the fact that the local oscillator and laserbeams A and B are derived from the same laser, a wellknown technique used to get rid of the laser linewidth, atleast at the first order. This is an advantage compared toother kind of techniques often used to measure the spec-trum, such as Fabry-Perot interferometers, which requirea laser with a low spectral width as well as a high reso-lution spectrometer [9, 10, 13].Experimentally, we have a local oscillator intensitymore than 10 times higher than the scattered intensity.In this case, one can neglect the last term in Eq. (2).In addition, it is shifted in frequency by ω BN from the g sc(1) term under investigation. We are left with a sig-nal oscillating at the frequency ω BN and with an ampli-tude proportional to | g sc(1) ( τ ) | . We then take the Fouriertransform of g BN(2) ( τ ) − ω BN .The experimental setup to measure intensity correla-tions has been described in Ref. [24]. As shown in Fig. 1,the two outputs of the FBS are sent to two single-photonavalanche photodiodes (APDs). This scheme allows toovercome the photodiode dead time and afterpulsing.The counts of the two APDs are time-tagged thanks to atime-to-digital converter (TDC). The corresponding fileis finally sent to Matlab to calculate the histogram of thecoincidences. D. Temporal experimental sequence
To measure the Mollow triplet, the following time se-quence is used. We first turn off the trapping laserbeams and the magnetic field. The atoms are releasedfrom the MOT and a TOF of 2 ms is applied to ensurethat the MOT magnetic field gradient is completely offwhile keeping a small cloud radius compared to the waistof the incident laser beam. Then, we apply the laserbeams. To avoid any interference effect, the counter-propagating beams A and B are switched on successivelyduring t pulse = 20 µ s for each pulse, with a waiting timeof 20 µ s between two consecutive pulses. We use for eachrun a train of 10 pulses, i.e. 5 pulses from beam A and5 pulses from beam B. These parameters were chosento minimize the effect of pushing and heating the atomswhile keeping a reasonable pulse duration to perform ameasurement.The APDs are gated on the beam pulses. We calcu-late the histogram of the temporal coincidences for eachpulse and after the first µ s of the pulse once the laser in-tensity is stable. This also ensures that the stationarystate is reached, as assumed in the calculations of theMollow triplet [1, 29]. We then analyse the data comingfrom beams A and B separately. We first check that thehistograms are the same for all the pulses, allowing tosum the 5 histograms corresponding to each beam. Be-cause of the finite time-window of the measurement, thehistogram needs to be normalized to get the intensitycorrelation function, as explained in Ref. [24]. III. RESULTS AND DISCUSSIONA. Theoretical spectrum
The spectrum ˜ g sc(1) ( ω ) of light scattered by a two-level system driven by a strong incident field close toresonance is commonly known as the Mollow triplet. Itsderivation can be found in Ref. [1] assuming a quantumtwo-level system driven by a classical field, or in Ref. [29]with a fully quantum-mechanical approach. It can bedecomposed in two parts:˜ g sc(1) ( ω ) = ˜ g el(1) ( ω ) + ˜ g inel(1) ( ω ) , (3)with ˜ g el(1) ( ω ) the elastic part and ˜ g inel(1) ( ω ) the inelasticpart given by the following formula:˜ g el(1) ( ω ) = s s ) δ ( ω ) , (4)˜ g inel(1) ( ω ) = s π Γ s s × s + (cid:0) ∆Γ (cid:1) h + s + (cid:0) ∆Γ (cid:1) − (cid:0) ω Γ (cid:1) i + (cid:0) ω Γ (cid:1) h + s + (cid:0) ∆Γ (cid:1) − (cid:0) ω Γ (cid:1) i , (5)where ω denotes the frequency relative to the atomictransition. The laser detuning is denoted by ∆, and thesaturation parameter depends on the laser detuning asfollows: s (∆) = II sat (cid:0) ∆Γ (cid:1) = s (cid:0) ∆Γ (cid:1) . (6)One can show that the ratio of the intensity of the in-elastic part to the elastic part, obtained by integratingEqs.(4-5) over the emitted spectrum, is given by: I inel I el = s / (1 + s ) s/ (1 + s ) = s. (7)For Ω ≫ Γ and Ω ≫ ∆, the inelastic part can be ap-proximated by three Lorentzians, the carrier at the laserfrequency and the sidebands separated from the carrierby the generalized Rabi frequency:Ω G = p Ω + ∆ , (8)with Ω the Rabi frequency given by:Ω = Γ vuut s " (cid:18) ∆Γ (cid:19) = Γ r s . (9)At resonance, the height ratio is 1:3:1 ans the width is3Γ / B. First order correlation function and spectrum
A typical experimental intensity correlation is plottedin the inset of Fig. 2. The laser frequency was set to res-onance and with a saturation parameter of the order of80. We first observe a fast oscillation at the frequency ω BN corresponding to the frequency beat note betweenthe local oscillator and the light scattered by the atomiccloud. These oscillations decay on a time scale of theorder of 1 / Γ ≃
26 ns. Finally, we can identify the beatnote between different frequency components, namely be-tween the Mollow sidebands and its carrier, giving rise toa revival of the amplitude of the oscillations.In our experimental conditions, g BN(2) ( τ ) − | g sc(1) ( τ ) | cos( ω BN τ ). The Fouriertransform, plotted in blue in Fig. 2, will thus directly givethe spectrum of the scattered light. The height of thisspectrum has been arbitrarily normalized to unity. TheMollow triplet is clearly visible with its carrier and thetwo sidebands. C. Fitting procedure
When s ≫
1, the inelastic part is dominant and wethus neglect, at first, the elastic part. To extract s fromthe experimental spectrum, and the corresponding Rabifrequency, we first fit the data using Eq. (5). The resultis plotted in dashed black line in Fig. 2. The first obser-vation is that the full width at half maximum (FWHM) -15 -10 -5 0 5 10 1500.20.40.60.81 -0.1 0 0.1 ( s) -0.200.2 FIG. 2. Resonant Mollow triplet of the light scattered by thecold atomic cloud, with no detuning and s ≃
80. Blue curve:experimental data; dashed black curve: fit by Eq. (5); dash-dotted red curve: fit including the inhomogeneous broadeningdue to temperature and laser finite size. Inset: temporal in-tensity autocorrelation of the beat note. of the carrier is underestimated: the experimental datayields a FWHM of 1 . ν L =3 MHz. As said before, this linewidth has no effect onthe carrier because we use the same laser for the localoscillator and the laser beams A and B. On the otherhand, different frequencies on the atoms lead to differ-ent generalized Rabi frequencies, and consequently to abroadening of the sidebands. However, if ∆ ν L ≪ Ω, thechange in the generalized Rabi frequency is of the orderof ∆ ν / . The minimum Rabi frequency used on thisexperiment is higher than 4 Γ, corresponding to a changein Ω G of less than 1 % which can thus be neglected. Thesame argument holds if one considers the temperature ofthe cloud T . The distribution of the effective detunings,in the atomic rest frame, corresponds to a Gaussian withan rms width of k p k B T /M , where k is the wave vec-tor, k B is the Boltzmann constant and M is the atomicmass. We will see in the next section that, when thelaser beams A and B are applied, T increases to a fewtens of mK. This corresponds to a rms width of a fewMHz, thus still with almost no effect on the generalizedRabi frequency and the sidebands broadening. The lastcontribution, which actually fully explains the sidebandsbroadening, comes from the finite waist of the laser beam.This results in a Rabi frequency not being the same forall the atoms. This does not affect the carrier width butleads to an inhomogeneous broadening of the sidebands:their height is thus decreased and their width increased.Finally, the increase in the carrier width is due to tem-perature. In the previous paragraph, we have evaluatedthe impact of the frequency detuning of the incident pho-ton in the atomic rest frame, but one also needs to take account the frequency shift of the scattered photon. Thiseffect has been characterized quantitatively in one of ourprevious experiments on the elastic spectrum [24], show-ing that the theoretical spectrum, given for the inelasticpart by Eq. (5) for atoms at rest, should be convolutedby the Doppler-broadened spectrum. This spectrum isGaussian with a rms width ∆ ω D that depends on thetemperature as well as the angle θ between the incidentphoton and the scattered direction:∆ ω D = k p − cos θ ) k B T /M . (10)To take into account these two contributions, namelytemperature and finite waist of the laser beam, we haveimplemented a new fitting procedure. First, the laserbeam is considered homogeneous in the propagation di-rection z since the Rayleigh length is of several meters.Then, we model the cloud as a continuous Gaussian dis-tribution which, after integration over the longitudinalaxis z , reads ρ ( r ⊥ ) = N exp( − r ⊥ / σ r ) / (2 πσ r ). Thespectrum radiated by the cloud in the finite-waist beam,with Rabi frequency Ω r ⊥ = Ω exp( − r ⊥ /w ), is given by:˜ g cloud(1) = 2 π Z ∞ ρ ( r ⊥ )˜ g Ω r ⊥ (1) ( ω ) r ⊥ dr ⊥ , (11)where the single-atom spectrum ˜ g Ω r ⊥ (1) is given byEq.(5) for a Rabi frequency Ω r ⊥ . Finally, to take into ac-count the effect of the temperature, the spectrum is con-voluted with the following Gaussian: exp( − ω / ω D )and the final height is renormalized to unity. The freeparameters are the frequency beat note ω BN (which isalways in agreement with the experimental value, withinfluctuations of ∼ w /σ r , and the tem-perature T . D. Results
1. Resonant Mollow triplet
This fitting procedure is first applied on the data ofFig. 2. The result is plotted in dash-dotted red and is invery good agreement with the experimental data. Thefitted ratio w /σ r gives a radial atomic cloud radius of σ r = 950 ± µ m, comparable to the radius measuredby absorption imaging and when the laser beams are ap-plied. The fitted broadening of the carrier width due totemperature is of the order of 0 . µ K to a few tens of mK during the intensity correla-tions measurements, corresponding to the same order ofmagnitude extracted from the fit and thus validating thehypothesis that temperature is the main contribution tothe carrier broadening.We repeated the same kind of measurements, still atresonance, but with different powers. For each spectrum,we checked that the temperature and w /σ r correspondto what is experimentally extracted by absorption imag-ing. We finally plot the Rabi frequencies measured inthe spectrum as a function of the powers measured justbefore the vacuum cell (see Fig. 3). The vertical errorbars are given by the fit, and the horizontal ones bythe power fluctuations estimated during each experimen-tal run. The theoretical Rabi frequency can be deducedfrom Eqs. (6) and (9), as well as the laser waist and peakpower. This theoretical value corresponds to the curve inFig. 3, and is in very good agreement with our measure-ments, the only free parameters being those of the fittingprocedure. P [mW]0246810 / FIG. 3. Dots: Rabi frequency extracted from the experimen-tal spectra as a function of the laser power. The vertical errorbars are given by the fit of the Mollow triplet spectra and thehorizontal error bars come from the power fluctuations duringone experimental run. Full curve: Rabi frequency calculatedfrom Eqs. (6) and (9), and from the measured laser power andwaist.
2. Off-resonance spectrum
We now turn to the analysis of the Mollow spectrumwhen the laser frequency is shifted from the atomic tran-sition by a detuning ∆ of a few linewidths. A typi-cal spectrum is shown in Fig. 4, for ∆ = 3 Γ and with s = 140. Two sidebands due to the inelastic scat-tering are still observed. The sharp central part nowcorresponds to the inelastic contribution plus a signifi-cant elastic component. Because of the lower saturationparameter for a nonzero detuning, the elastic part canno longer be neglected in our analysis. We thus includeEq. (4) in the computation of the total spectrum given by (11) where, as before, the finite size of the laser waistand the temperature are accounted for. In particular,the temperature not only broadens the carrier of the in-elastic spectrum, but also turns the homogeneous elas-tic component into a Doppler-broadened Gaussian peak.The resulting fit is plotted in Fig. 4 in dashed red, show-ing a good agreement with the experimental data. Thetemperature and the ratio w /σ r are comparable to thevalues obtained at resonance, as expected from the largesaturation parameters that are used. -10 -5 0 5 10 1500.51 -10 0 1000.5 FIG. 4. Off-resonant Mollow spectrum of the light scatteredby the cold atomic cloud with ∆ = 3Γ and s = 140. Bluecurve: experimental spectrum. The fitting is shown in dashedred, taking into account the elastic and the inelastic contri-butions. Inset: Green curve: elastic part obtained from thefit; black dashed curve: inelastic part. The amplitudes of the elastic component A el and ofthe inelastic component A inel are fitted independently asfollows:˜ g sc(1) ( ω ) = A el × ˜ g el(1) ( ω ) + A inel × ˜ g inel(1) ( ω ) . (12)The resulting ratio I inel /I el , corresponding to the ratioof the integral of the inelastic spectrum and the integralof the elastic one, is computed. It is theoretically equalto the saturation parameter, as shown in Eq. (7). Thismeasurement has been done for different laser detuningsand two different powers. On the other hand, the satu-ration parameter is calculated using the Rabi frequencyΩ of the inelastic component, also extracted from the fit,thanks to Eq. (9). As shown in Fig. 5, the ratio I inel /I el is in good agreement with the computed saturation pa-rameter.
3. Simultaneous pulses & Non-circular polarization
So far, we have paid attention to have the system asclose as possible to an ideal two-level system, with a welldefined Rabi frequency. To illustrate the importance ofthese points, we have performed two more tests. Wefirst measured the spectrum of light scattered by the coldatomic cloud when it is illuminated by a laser beam witha linear polarization, at resonance and with s ≃
80. Theresult is plotted in Fig. 6 (red dashed curve) where we s I i n e l / I e l FIG. 5. Intensity ratio of the inelastic and elastic part asa function of the saturation parameter. These two quanti-ties are extracted independently from the fit. The intensityratio is calculated from the integral of the fitted elastic andinelastic spectra, the fitting being done using two differentfree parameters for the amplitudes of the elastic and inelas-tic components. The saturation parameter is calculated usingthe Rabi frequency, also extracted from the fit, and the de-tuning. Dots: experimental data. Error bars come from thefit. Line: expected behavior given by Eq. (7). compare the circular and linear polarization. As said be-fore, for a left-handed or right-handed circular polariza-tion, we only excite the transition F = 3 ( m F = ± → F ′ = 4 ( m ′ F = ± F = 3 ( m F = ± → F ′ = 4 ( m ′ F = ± -15 -10 -5 0 5 10 15 ( ω − ω BN ) / Γ ˜ g ( ) s c ( ω ) [ a . u .] FIG. 6. Spectrum of the scattered light when the atomiccloud is illuminated by laser beams A and B one at a time,or both together, in a plane wave or standing wave config-uration. Blue continuous curve: laser beam A with circularpolarization. Red dashed curve: laser beam A with linearpolarization. Green dash-dotted curve: laser beams A andB shined simultaneously and with the same circular polariza-tion. nite waist, which is responsible for a weaker modulationof the driving amplitude.
IV. CONCLUSION
In summary, we have performed the first clear exper-imental observation of the resonant Mollow triplet oncold atoms. On resonance, our fluorescence spectrumis completely dominated by inelastically scattered light.The difference between the measurement and theory isfully understood taking into account the finite tempera-ture of our cloud and the finite size of the exciting laserbeam. As far as we know, this is the first time thatall these effects are integrated in the analysis. Off reso-nance, the two Mollow sidebands were observed as well,yet in this case the central peak mainly corresponds toDoppler-broadened elastic scattering. The measured ra-tio of inelastically to elastically scattered light, a quantitythat is surprisingly rarely reported in the literature, is invery good agreement with the theoretical one.Throughout this work, our cloud was assumed to be-have as a large set of independent emitters, thanks tothe low ratio between the optical thickness (between 1and 5 on this experiment) and the saturation parame-ter. An optically denser cloud, for example achieved byincreasing the atom number, could actually allow us toinvestigate the effects of the dipole-dipole coupling onthe cloud fluorescence, and in particular the emergenceof new resonances. While few-atom physics requires sub-wavelength distances to correlate efficiently the dipolefluctuations [30–32], large dilute atomic clouds with alarge optical thickness have recently been predicted topresent an asymmetric Mollow triplet [20] as well ashigher-order Mollow sidebands [21].Furthermore, the fluorescence of single emitters isknown to present photon correlations [2, 33–35], a featurethat was used to produce heralded photons [4, 36]. In thiscontext, a promising idea is to use the dipole-dipole in-teraction to manipulate the cloud optical coherence, andthus generate higher-order photon correlations.
AKNOWLEDGEMENTS
A. E. was supported by a grant from the DGA. R. B.and R. C. T. benefited from Grants from S˜ao Paulo Re- search Foundation (FAPESP) (Grant Nos. 2015/50422-4and 2014/01491-0). L. O. G., D. F. S., R. B., M. F., R.K. and R. C. T. received support from project CAPES-COFECUB (Ph879-17/CAPES 88887.130197/2017-01).This experiment was supported by grants from the Excel-lence Initiative UCA-JEDI from University Cˆote d’Azur.Part of this work was performed in the framework of theEuropean Training network ColOpt, which is funded bythe European Union Horizon 2020 program under theMarie Skodowska-Curie action, grant agreement 72146.The Titan X Pascal used for this research was donatedby the NVIDIA Corporation. [1] B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. , 1969–1975 (1969).[2] A. Aspect, G. Roger, S. Reynaud, J. Dalibard, andC. Cohen-Tannoudji, “Time correlations between thetwo sidebands of the resonance fluorescence triplet,”Phys. Rev. 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