Anomalous light-induced broadening of the spin-noise resonance in cesium vapor
A. A. Fomin, M. Yu. Petrov, G. G. Kozlov, A. K. Vershovskii, M. M. Glazov, V. S. Zapasskii
AAnomalous light-induced broadening of the spin-noise resonance in cesium vapor
A. A. Fomin, M. Yu. Petrov, G. G. Kozlov, A. K. Vershovskii, M. M. Glazov, and V. S. Zapasskii Spin Optics Laboratory, Saint Petersburg State University, 198504 St. Peterbsurg, Russia Ioffe Institute, 194021 St. Petersburg, Russia
We uncover a highly non-trivial dependence of the spin-noise (SN) resonance broadening inducedby the intense probe beam. The measurements were performed by probing the cell with cesiumvapor at the wavelengths of the transition S / ↔ P / ( D line) with unresolved hyperfinestructure of the excited state. The light-induced broadening of the SN resonance was found to bestrongly different at different slopes of the D line and, generally, varied nonmonotonically with thelight power. We discuss the effect in terms of the phenomenological Bloch equations for the spinfluctuations and demonstrate that the SN broadening behavior strongly depends on the relationbetween the pumping and excited level decay rates, the spin precession and decoherence rates. Toreconcile the puzzling experimental results, we propose that the degree of optical perturbation ofthe spin-system is controlled by the route of the excited-state relaxation of the atom or, in otherwords, that the act of optical excitation of the atom does not necessarily breaks down completely itsground-state coherence and continuity of the spin precession. Spectral asymmetry of the effect, inthis case, is provided by position of the ‘closed’ transition F = 4 ↔ F = 5 at the short-wavelengthside of the line. This hypothesis, however, remains to be proven by microscopic calculations. I. INTRODUCTION
Spin noise spectroscopy (SNS) is a developing methodof magnetic resonance research that is aimed to detectspontaneous (rather than induced) precession of elec-tron spins. Spontaneous or incoherent precession ofthe spin-system in its equilibrium state is revealed inthe form of fluctuating magnetization which may be de-tected as fluctuations of magneto-optical effects (Fara-day or Kerr rotation). Viability of this effect was firstdemonstrated in 1981 [1], by detecting magnetic reso-nance in the Faraday-rotation noise spectrum of sodiumatoms. The main stream of research in the field ofSNS has arisen in our century after successful detec-tion of spin-noise resonances in semiconductors [2, 3].Nowadays, the SNS is widely used not only for study-ing magnetic resonance and spin dynamics of diverseparamagnets, as a specific method of electron para-magnetic resonance (EPR) spectroscopy, but also forstudying properties of optical transitions [4, 5], spa-tial spin distribution [6, 7], nuclear spin dynamics insemiconductor structures [8–10], spin alignment noise inatomic systems [11, 12], etc., see Refs. [13–17] for re-view.An important feature of the SNS, which was pri-marily considered as the most valuable property ofthis technique, is that the probe laser beam, provid-ing information about spin-system fluctuations, prop-agates through the medium in the spectral regionof its transparency, does not induce any real transi-tions, and, therefore, does not perturb the spin sys-tem. In the last decade, however, it was shown thatthe SNS with resonant or high-power probing, whenthe probe beam may noticeably affect properties ofthe material, realizes the resonant or nonlinear ver-sion of this technique with much broader capabili-ties. Under these conditions, the SNS becomes essen-tially perturbative, with characteristics of this pertur- bation being the subject of investigation, see, e.g., [18–22].While various aspects of perturbations in the SNSof semiconductors and semiconductor nanosystems arewidely studied, see, e.g., Refs. [19–25], much less is knownabout these effects in atomic systems. In Refs. [19, 26],the non-linearities related to the coherent and collectiveeffects in the spin system in alkali atoms have been stud-ied. Work [27] studied the effects of the probe beam in-duced renormalizations of the spin system’s energy spec-trum in a strong optical field. Significant prospects arerelated to the realization of the spin correlations by theperturbative SNS [28].This paper is devoted to studying what may seem to beone of the simplest nonlinear effects of SNS, namely, tothe light-induced broadening of the spin-noise (SN) res-onance in the field of resonant probe beam. Our interestto this problem was initiated by a curious spectral andintensity-related behavior of this effect in cesium vaporprobed in the region of the transition S / ↔ P / ( D line). The broadening was found to be essentially dif-ferent at different sides of the transition, varying stronglynonmonotonously with the light power at one of them. Inaddition, the effect showed unusual dependence on den-sity/temperature of the atomic system.Phenomenological analysis of the experimental datahas shown that the observed anomalous behavior of theSN resonance broadening could be unambiguously ex-plained under assumption that the ground-state spin pre-cession was more efficiently perturbed in the region of the‘unclosed’ optical transitions, when the atom, after theexcitation cycle, did not necessarily return back to itsinitial state.The paper is organized as follows. Section II describesexperimental setup and Cs vapor sample. Section IIIsummarizes all the experimental observations that at-tracted our attention and discuss these results in Sec. IV.A brief conclusion is presented in Sec. V. a r X i v : . [ phy s i c s . op ti c s ] F e b P S F' = 5432 F = 43
251 MHz201 MHz151 MHz9193 MHz ≈≈≈
Figure 1. The energy-level diagram of D line of cesium atom.The ‘closed’ transitions are indicated by red arrow. II. EXPERIMENTAL SETUP AND SAMPLE
The measurements were performed at the wavelengthof D line of cesium atom corresponding to the tran-sitions S / ( F = 3 , ) ↔ P / ( F = 2 , . . . , ), λ ≈ . nm. The relevant energy-level diagram ofcesium atom is presented in Fig. 1.In our experiments, the Doppler width of the D lineis comparable with the hyperfine (HF) splitting of theexcited state, so that, in the absorption spectrum of thisline, one can observe only two spectral components, cor-responding to transitions from two HF components of theground state (Fig. 1) [29]. In accordance with the selec-tion rules, the allowed transitions from the states F = 3 and F = 4 may occur to the excited states with the totalspin F = 2 , , and F = 3 , , , respectively.The SN spectra were detected in the conventional Voigtgeometry with the probe beam tuned in resonance withthe transition from the upper HF component of theground state ( F = 4 ). We also confirmed that similar re-sults were obtained when the lower HF component of theground state with F = 3 was probed. As a light source,we used the ring-cavity tunable Ti:sapphire laser withFabry-Perot-based frequency stabilization. This laser al-lowed us to scan the laser frequency with a step of 100MHz and thus to study wavelength dependence of the SNspectra with spectral resolution substantially exceedingDoppler width of the D line. Fluctuations of the po- Frequency (MHz) N o i s e po w e r Shot-noise powerHWHMSN resonance
Figure 2. A typical experimental SN spectrum of cesium un-der our experimental conditions. A slight tilt of the shot-noisepower spectrum is related to frequency response characteristicof the detection channel. larization plane azimuth of the transmitted laser beamwere detected with a balanced polarimetric detector andprocessed with a Fourier-transform spectrum analyzer,providing at the output the SN power spectrum of thesystem. The power of the laser beam, ∼ mm in diame-ter, was varied from tens of µ W to several mW. The cellwith small amount of metal cesium and Torr of buffergas (Ne), (cid:31) × mm in size, was placed into a heaterthat provided its temperature stabilization at the levelof ± ◦ C . The magnetic field of around . mT, with ahomogeneity of ∼ % within the cell, was created by apair of Helmholtz-type coils.A typical SN spectrum of Cs atoms obtained underthese experimental conditions is shown in Fig 2. TheSN power, in most cases, exceeded the shot-noise levelby more than %. The line shape was usually ap-proximated by a Lorentzian (see Sec. III C where theshape is discussed in more detail), with the half-widthat half-maximum (HWHM) taken for the measure of itswidth.Note that experimental conditions of the present in-vestigation substantially differ from those of our previouswork [27], devoted to studying the light-induced energysplitting of the cesium ground-state spin-system. Thesetwo experimental works are indeed close methodologi-cally, but in the previous study [27], the measurementswere performed at the long-wavelength slope of the line,where, despite even higher power densities of the probebeam, as will be shown below, the light-induced broad-ening is almost absent. It is also noteworthy that theeffects of the SN resonance broadening described in thispaper, did not show any pronounced dependence on theazimuth of the light-beam polarization plane with respectto magnetic field. Light power density (mW/cm ) H W H M ( M H z ) B = 1.6 mT T = 63.4 °C −1 −0.5 0 0.5 100.511.522.5 Detuning, Δ v (GHz) O p ti ca l d e n s it y Figure 3. Experimental dependence of the light-inducedbroadening of the SN resonance in cesium vapor. Here andin the following experimental figures, points show the dataand solid lines are guides for the eye. The absorption spec-trum of the D line is shown in the inset, with vertical arrowindicating spectral position of the probe light. III. EXPERIMENTAL OBSERVATIONS
In this section, we report on the puzzling variationof the light-induced broadening of the SN resonance as afunction of intensity (Sec. III A) and detuning (Sec. III B)of the probe laser beam and versus the cell temperature,Sec. III D. The shape of the SN resonance is discussed inSec. III C.
A. Intensity-related variations of the SN resonancewidth
The first experimental observation that attracted ourattention to this issue was a nonmonotonous dependenceof the SN resonance width on light intensity for the probebeam tuned to the long-wavelength slope of the transition F = 4 ↔ F = 3 , , (Fig. 3). The SN resonance profile,in these experiments, was fitted with a single Lorentzian,though, more accurately, as will be seen below, it shouldbe considered as comprised of two components, with thewidth of one of them being intensity-independent. Atlow light-power densities, i.e., at the left part of theplot in Fig. 3, the SN linewidth increased monotonously,which seemed quite natural. Indeed, the increasing ex-citation rate strengthened perturbation of the cesiumspin-system, shortened the spin dephasing time in theground state of cesium atom, and, thus, broadened itsspin resonance peak. However, further nonmonotonousbehavior of the SN resonance width looked paradoxical:at sufficiently high light-power densities (of around 20mW/cm ), the width of the SN resonance became, towithin the experimental error, equal to that of the unper- Light power density (mW/cm ) H W H M ( M H z ) −0.7 GHz (1)−0.5 GHz (2)−0.3 GHz (3) −0.1 GHz (4)0.1 GHz (5)0.3 GHz (6)0.5 GHz (7)0.7 GHZ (8)234 5 6 7 81 Cs (Ne, 2 Torr) T = 64 °C B = 1.6 mT Figure 4. Dependence of the SN resonance width on the probebeam intensity at different detunings of the probe light fre-quency from the center of the Doppler-broadened transition F = 4 ↔ F = 3 , , of cesium. turbed spin-system observed either at lowest intensitiesof the resonant probe beam or at strongly nonresonantprobing. B. Spectral characteristics of the effect
To get additional information about this non-monotonous, anomalous intensity dependence of the SNresonance width, we examined how this dependence var-ied with the wavelength of the probe light within the D line width. Results of these measurements are shown inFig. 4. As seen from the figure, the effects of the light-induced SN resonance broadening are strongly differentat different sides of the D line. The effect of opticalperturbation at the short-wavelength (positive detuning)side of the line appeared to be much weaker and prac-tically monotonous with the light intensity, while theanomalous behavior was most pronounced at the long-wavelength side of the resonance (negative detuning).These dependencies look even more spectacular asfunctions of the optical frequency (for fixed probe beamintensities). Figure 5 shows, in the same scale along theabscissa axis, optical spectra of the SN resonance broad-ening at different light intensities (a) and optical spec-trum of the SN power of Cs vapor in the regime of linearprobing reported in [29] (b). The spectra of the SN res-onance broadening, as seen from Fig. 5(a), are clearlyseparated into two unequal parts, with the larger (long-wavelength) part being (at low intensities) much moresusceptible to optical perturbation. Curiously, due toessentially different behavior of the SN resonance broad-ening at different wings of the line, there exists a point(indicated by asterisk in Fig. 5), where the SN resonancewidth appears to be virtually independent on the probe −1.2 −0.8 −0.4 0 0.4 0.8 1.200.10.20.30.40.50.60.70.8 H W H M ( M H z ) (1)6.4 mW/cm (2)14.4 mW/cm (3)17.6 mW/cm (4)30.4 mW/cm (5)36.8 mW/cm (6)56 mW/cm (7) −1.2 −0.8 −0.4 0 0.4 0.8 1.200.511.522.5 Detuning, Δ v (GHz) S N po w e r Fitting W = 18·10 −2 mW/cm F = 5 F = 4 F = 31 23 45 6 7 (a)(b) * Figure 5. (a) Spectral dependence of the SN resonance widthof cesium vapor at different intensities of the probe beam.Arrows above the curves indicate positions of the excited-state HF components. Spectral point where the SN resonancewidth practically does not depend on the light intensity is in-dicated by asterisk. (b) shows, for comparison, optical spec-trum of the SN power of cesium atoms under conditions ofweak (linear) probing (taken from our earlier publication [29]).This spectrum shows that, in the linear regime, optical spec-trum of the SN does not reveal any hidden HF structure ofthe transition, see also inset in Fig. 3. beam intensity in a wide range of its variation.It is important to note that the other HF componentof the D line, corresponding to transition from the lowersublevel ( F = 3 ), exhibits qualitatively the same behav-ior with inversion of the short- and long-wavelength sidesof the absorption line, as shown in Fig. 6. In this case theshort-wavelength part is more susceptible for the opticalperturbation than the long-wavelength one. C. Shape of the SN resonance
In all the measurements presented above, the SN res-onance was approximated by a single Lorentzian. Moreaccurate analysis has shown, however, that the profile ofthe SN resonance, practically in all cases, can be pre-sented as a sum of two Lorentzians with different widths.A typical example of such a decomposition is shown inFig. 7. We have found that the width of the narrowcomponent of the SN resonance, within the experimental
Light power density (mW/cm ) H W H M ( M H z ) Δ ν = −0.2 GHz Δ ν = −0.2 GHz B = 1.6 mT T = 67.0 °C Figure 6. Example of the same dependence as in Fig. 4, butobtained on the transition from the lower HF component ofthe ground state ( F = 3 ). The sides of the transition withhigher and lower sensitivity to optical perturbation of theground-state spin-system are interchanged. −17 −17 −17 −17 −17 −17 −17 Frequency (MHz) P o w e r s p ec t r a l d e n s it y ( W ) P = 17.6 mW/cm Δ ν = −0.28 GHz B = 1.6 mT T = 64 °C Figure 7. A typical shape of the Faraday rotation noise (SN)spectrum of cesium vapor and its decomposition into twoLorentzians. error, did not depend on the light intensity. Based onthis fact, we ascribed this component to SN of the lowerHF sublevel of the ground state ( F = 3 ). Large detuningfrom the resonant transition provides, in this case, weakperturbation of the fluctuating spins. This suppositionwas confirmed by the measurements of the SN spectraat frequencies detuned by ≈ . GHz above the transi-tion from the component F = 3 . The SN line, underthese conditions could be easily detected, and its widthdid not noticeably depend on the probe beam power.In most cases, this contribution (from the lower HFsublevel of the ground state) did not affect essentially Light power density (mW/cm ) H W H M ( M H z ) T = 71 °C (1) T = 66.7 °C (2) T = 62.1 °C (3) T = 52.8 °C (4) Cs (Ne, 2 Torr) Δ ν = −0.28 GHz B = 1.6 mT Figure 8. The width of the ‘wide’ component of the SN res-onance as functions of the probe light intensity at differenttemperatures. results of the measurements, and all the dependenciespresented above in Figs. 3, 4, 5 remained qualitativelythe same for the ‘wide’ component of the SN resonancerelated, as we believe, to SN of the resonantly probedstate with F = 4 . D. Temperature variations of the effect
Additional unexpected results were obtained from themeasurements of temperature-related variations of thelight-induced SN resonance broadening. Figure 8 showsthe light-intensity dependence of the SN peak width atdifferent temperatures of the cesium cell. For this fig-ure, only the width of the ‘wide’ component of the SNresonance was used. This made the dependence noisier,but allowed us to separate the SN contribution of the F = 4 state in a pure form and to make sure that ad-mixture of spin fluctuations in the state F = 3 does notqualitatively affect the observed characteristics of the SNresonance broadening.Note that increasing the temperature mainly resultsin increasing density of the Cs atoms in the cell, be-cause changes in kinetic characteristics of atomic mo-tion, in this temperature range, are evidently insignifi-cant. Meanwhile, as we see from the figure, the increas-ing temperature generally strengthens the light-inducedbroadening of the SN resonance. This behavior of theSN linewidth under so low densities of cesium atoms, (0 . . . . · cm − , also looks unusual and cannot beexplained in a straightforward way. IV. DISCUSSION
In this section, we discuss the key experimental resultsrelated to the probe-intensity variations of the SN res-onance width and possible model interpretation of theobservations.
A. Model considerations
Let us consider the effect of the light-induced broad-ening of the SN resonance in a more rigorous way. Notethat, in the low probe-power regime, when the probe-induced perturbation of the spin noise may be neglected,the SN resonance width is determined by spontaneous re-laxation processes in the system and, what is more impor-tant in our experimental conditions, by inhomogeneity ofthe applied magnetic field in the vapor cell [11, 27, 29].The perturbations induced by the probe beam can beroughly separated into two classes: (i) the effects relatedto the renormalization of the energies of the spin states(mainly caused by the virtual transitions between theground and excited spin multiplets and important for thedetuned from the optical transition probe) and (ii) theeffects of real transitions of the atom between the groundand excited states (which are particularly prominent forthe resonant probing). Generally, both effects coexistand should be taken into account simultaneously, but,for the sake of qualitative discussion, we address themseparately.The effects of the renormalization of the spin statesin the presence of the intense probe beam have beenanalyzed in our previous papers [23, 27]. As shown inRef. [27], linearly polarized probe results in the light-induced fine structure splittings of the ground HF state F = 3 and F = 4 . The magnitudes of the splittings de-pend on the probe intensity and orientation of the probepolarization plane with respect to the magnetic field. Ad-ditionally, if the probe beam is elliptically polarized, itproduces the effective magnetic field controlled by theprobe ellipticity [23, 30, 31]. Taking into account thatthe intensity of the probe beam can be inhomogeneousinside the cell (e.g., due to the Gaussian beam profileor due to absorption processes), the probe-induced en-ergy renormalizations may result in an effective inhomo-geneous broadening of the SN spectrum similarly to theeffect of inhomogeneous magnetic field. While this kindof effects cannot be fully ruled out, but we can note that,as was confirmed by our special measurements, the over-all shifts of the SN peak induced by the probe were, inour experiments, smaller than the variation of the SNlinewidth.Also, and importantly, these renormalizations canhardly explain the non-monotonous dependence of theSN linewidth as a function of the probe beam intensity.Thus, it seems natural to relate the observed behav-ior of the SN resonance with the real transitions betweenthe ground and excited states of the Cs atom induced bythe intense probe beam. The role of the real transitionsbetween the spin states can be illustrated in the frame-work of the simple phenomenological model that consid-ers dynamics of the spin fluctuations in the ground, δ F g ,and excited, δ F e , multiplets and the coupling betweenthe multiplets via probe-induced optical transitions. Wepresent the Bloch equations for the fluctuations in theform: δ ˙ F g + δ F g × Ω g + (cid:18) G + 1 τ s,g (cid:19) δ F g − Rδ F e = ξ g , (1a) δ ˙ F e + δ F e × Ω e + (cid:18) R + 1 τ s,e (cid:19) δ F e − Gδ F g = ξ e . (1b)Here, the dot on top denotes the time-derivative, Ω g and Ω e are the spin precession frequencies in the ground andexcited multiplets (these frequencies can, generally, in-clude the contributions from the renormalization of theenergy spectra), τ s,g and τ s,e are the spin relaxation timesunrelated to the optical processes , G and R are the op-tical excitation (pumping) and excited-state decay rates,respectively, and ξ g,e are the random Langevin forces in-troduced in the theory of fluctuations [16, 33, 34]. In oursimplest model, we assume that the spins of the groundand excited multiplets are the same ( F g = F e ) and op-tical processes are spin-conserving, with G and R beingscalars , and set R = G + 1 /τ , where τ is the sponta-neous transition time. At relatively weak probe intensity I , the optical pumping rate G ∼ (cid:36) R T / (1 + ∆ T ) ∝ I ,where (cid:36) R is the Rabi frequency, ∆ is the detuning be-tween the probe beam frequency and the resonance fre-quency and T is the optical coherence time. With in-crease in I , the G and R saturate. Equations similar tothe set (1) have been used previously to describe the spinfluctuations in semiconductor quantum wells and quan-tum dots [16, 20–22, 36], color centers [37] and also thespin fluctuations and dynamics under electron hoppingbetween the localization sites [38–40]. Note that the pa-rameters in Eqs. (1) should be considered as effectivephenomenological parameters which depend, in particu-lar, on the particular optical transition we study.The complex eigenfrequencies ω i = ω (cid:48) i + i ω (cid:48)(cid:48) i of theequation set (1) (at ξ g,e ≡ ) describe the positions of thepeaks, ω (cid:48) i , and their widths, − ω (cid:48)(cid:48) i , in the SN spectrum.For the spin fluctuations transversal to the direction ofthe magnetic field, they can be found from solution ofthe equation det K = 0 , where the matrix K describing The spin relaxation can be caused by interatomic collisions [32]or scattering on the cell walls. The times τ s,g and τ s,e can phe-nomenologically include the contribution from the magnetic fieldinhomogeneity, and, in the case of the excited state, the contri-butions to the transitions to another ground-state HF multiplet. The effects of spin relaxation and pumping in the course of op-tical transitions are disregarded, see, e.g., [35, 36] for details ofthese processes.
Figure 9. SNS linewidth (main panel) and peak position(inset) calculated after Eq. (3) as functions of the satura-tion parameter Gτ . The parameters of the calculations are Ω g τ = 10 , ω e τ = 5 , τ /τ s,g = 0 . , and τ /τ s,e = 0 . . kinetics of the system reads K = (cid:18) − i ω + iΩ g + G + τ − s,g − R − G − i ω + iΩ e + R + τ − s,e (cid:19) . (2)Such form of K immediately follows from the two cou-pled equations for the δF + g = δF g,z + i δF g,y and δF + e = δF e,z + i δF e,y , where we assumed that the magnetic fieldis applied along the x -axis, i.e., Ω e (cid:107) Ω g (cid:107) x . It followsthen that ω ± = Ω g + Ω e − i( τ − s,g + τ − s,e )2 − i2 τ − i G ± i 12 (cid:115)(cid:20) τ + 1 τ s,e − τ s,g + i(Ω e − Ω g ) (cid:21) + 4 G (cid:18) G + 1 τ (cid:19) . (3)Let us analyze in detail the frequency ω + which corre-sponds, at G = 0 , to the ground-state spin fluctuations.The dependence of the imaginary part of the frequency(i.e., the SN peak width) on G for an arbitrary set ofparameters is plotted in Fig. 9. The inset shows the realpart of the frequency (i.e., SN peak position) as a func-tion of the pumping rate G . At a weak probe, Gτ (cid:28) , ω + ≈ Ω g − i τ s,g − i G (cid:18) −
11 + τ /τ s,e − τ /τ s,g + i τ (Ω e − Ω g ) (cid:19) , (4a)and both the spin precession frequency and the linewidthacquire linear in G contributions resulting from the ad-mixture of the excited-state dynamics. Depending onthe relation between the system parameters, the SN res-onance can be broader or narrower than at G = 0 . Forthe particular set chosen for Fig. 9 the | Ω e − Ω g | τ (cid:29) ,and the SN resonance broadens ∝ G . At the strong probe( Gτ (cid:29) ), the dynamics of the fluctuations in the ex-cited and ground state effectively averages, and ω + ≈ Ω g + Ω e − i2 τ s,g − i2 τ s,e . (4b)Thus, for sufficiently long τ s,e the SN resonance widthcan decrease for sufficiently large pumping rates and,eventually, become comparable (or even smaller) thanthe SN linewidth measured at a weak probe.This feature can be explained as follows. At sufficientlyhigh values of the probe beam intensity, the processes ofstimulated emission begin to prevail over the processesof spontaneous relaxation. As a result, the polarizationproperties of the photons absorbed and emitted by theatom become identical, and the atom returns to its initialstate at the end of the optical excitation cycle. Thiseffect is similar to the averaging of the spin precessionfrequencies due to the exchange interaction [41, 42] orhopping [38, 39].While the model consideration presented above allowedus, at least for a particular choice of the parameters, toobtain the dependence of the SN resonance width simi-lar to that observed experimentally, the quantitative de-scription of the data, including strongly pronounced spec-tral asymmetry of the effect across the optical transition,leave beyond the scope of the suggested simplified model.Still, general pattern of the spectral and temperature be-havior of the effect allows us to make certain assumptionsabout basic reasons underlying the observed anomalies. B. Hypothetical assumption
Experimental results of this work clearly show thatspectra of optical perturbation of a spin system (as itis often the case in nonlinear optics) may provide infor-mation about light-matter interaction hidden in linearoptical spectra of the medium. As seen from Fig. 4, theoptical transition F = 4 ↔ F = 3 , , , revealed itselfin the linear SNS as a single homogeneously broadenedspectral line [29], under conditions of strong optical per-turbation breaks down to two spectral regions with qual-itatively different characteristics and fairly sharp bound-ary between them. As seen from this figure, the short-wavelength region of the transition, characterized bylower sensitivity of the SN resonance width to optical per-turbation, occupies a smaller part of the line. We recallthat the spectrum of the SN resonance broadening at theother HF component of the D line ( F = 3 ↔ F = 2 , , )exhibits similar behavior with inverted short- and long-wavelength regions, Fig. 6. This fact offers a clue to un-derstanding of such a structure of the SN perturbationspectrum. Referring to the energy diagram of Cs atom,Fig. 1, we can see that the short- and long-wavelength re-gions of the transitions from sublevels F = 4 and F = 3 ( F = 4 ↔ F = 5 and F = 3 ↔ F = 2 , respectively)correspond to the so-called ‘closed’ transitions, when the excited atom can be radiatively de-activated only by re-turning back to the same state. When excited into otherHF components of the upper state, the atom acquires theroute of radiative relaxation to the other HF sublevel ofthe ground state. This process, which is known to bethe reason of HF pumping [43], plays crucial role, as webelieve, in the effect of the light-induced SN resonancebroadening.To ascribe to ‘unclosed’ transitions a higher sensitivityto optical perturbation of the ground-state spin-system,we have to accept that the process of optical excitation ofthe atom perturbs its ground-state spin system to a lesserdegree when the atom returns back to its initial state. Inother words, we have to accept that there exists certainprobability that the act of optical excitation does notchange phase relations of the ground-state wavefunctionof the atom. In the frame of the model presented above,it means, that, for the ‘closed’ transitions, the τ and τ s,e are significantly shorter than those of the ‘unclosed’transitions, which makes the ground-state spin fluctu-ation dynamics much less sensitive to the excited-statedynamics for the case of the ‘closed’ transitions. In thiscase, the escape from the excited optical transition (pos-sible for the ‘unclosed’ transitions) will inevitably breakthe ground-state precession phase and will broaden theSN resonance. This is really a strong assumption, andwe did not manage to justify it theoretically, but our ex-perimental results provide a convincing evidence in favorof this hypothesis.The nonmonotonous behavior of the SN resonancebroadening, as has been shown above, can be interpretedqualitatively with allowance for light-power dependentdynamic characteristics of the excited state. Still, formore accurate description of this dependence, we alsohave to take into account the effects of HF pumping andhole-burning (disregarded in the model above) that be-come essential at the elevated light-power densities usedin our study. It is noteworthy that these two latter effectsof bleaching of the cesium cell affect differently on the SNresonance broadening. With increasing the spectral holedepth, the number of resonance atoms decreases, the SNsignal decreases also, but the main contribution to theSN signal is made by nonresonant and, therefore, unper-turbed atoms, and the SN resonance is getting narrower.The HF pumping only decreases the SN signal amplitude.A specific feature of temperature dependence of the ef-fect, as shown in Fig. 8, is the growth of the light-inducedcontribution to the SN resonance width with temperaturethat is with density of cesium atoms. Since the laser fieldacting upon the atoms does not increase with increasingtemperature, this behavior cannot be explained withouttaking into account interatomic interactions which maychange either dynamic parameters of the excited state ofcesium, or the effective optical field due to effects of ra-diation trapping. We plan to investigate these effects inmore detail elsewhere. V. CONCLUSION
In this paper, we applied the method of nonlinear SNSfor studying sensitivity of the ground-state spin-systemof cesium atoms to resonant optical perturbations. Wehave discovered and studied anomalous behavior of theSN resonance broadening of cesium under condition ofresonant probing and advanced a hypothesis about effectof the excited-state relaxation route upon efficiency ofthe spin-system optical perturbation. We have found, inparticular, that optical perturbation of the spin-systemthrough ‘closed’ transitions proves to be less perturba-tive for the ground-state spin-system. We show also thatthe effects of the light-induced SN resonance broadeningmay be sensitive to hidden HF structure of the excitedstate of the atom, as well as to interatomic interactions in the atomic medium. These findings, including nar-rowing of the magnetic resonance line under conditionsof strong resonant probing, may be of interest both foratomic physics and for applications in magnetometry andmetrology.
ACKNOWLEDGMENTS
The work was supported by the RFBR Grant No. 19-52-12054 which is highly appreciated. The authors ac-knowledge Saint-Petersburg State University for a re-search grant 73031758. M.M.G. acknowledges partialsupport of theoretical research by the RFBR Grant No.19-52-12038. [1] E. Aleksandrov and V. Zapasskii, Magnetic resonance inthe Faraday-rotation noise spectrum, Sov. Phys. JETP , 64 (1981).[2] M. Oestreich, M. Römer, R. J. Haug, and D. Hägele, Spinnoise spectroscopy in GaAs, Phys. Rev. Lett. , 216603(2005).[3] S. A. Crooker, L. Cheng, and D. L. Smith, Spin noise ofconduction electrons in n -type bulk GaAs, Phys. Rev. B , 035208 (2009).[4] V. S. Zapasskii, A. Greilich, S. A. Crooker, Y. Li, G. G.Kozlov, D. R. Yakovlev, D. Reuter, A. D. Wieck, andM. Bayer, Optical spectroscopy of spin noise, Phys. Rev.Lett. , 176601 (2013).[5] L. Yang, P. Glasenapp, A. Greilich, D. Reuter, A. D.Wieck, D. R. Yakovlev, M. Bayer, and S. A. 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