Anomalous light-induced broadening of the spin-noise resonance in cesium vapor

We uncover a highly nontrivial dependence of the spin-noise (SN) resonance broadening induced by the intense probe beam. The measurements were performed by probing the cell with cesium vapor at the wavelengths of the transition $6{}^{2}S_{1/2}\leftrightarrow 6{}^{2}P_{3/2}$ ($D_2$ line) with the unresolved hyperfine structure of the excited state. The light-induced broadening of the SN resonance was found to differ strongly at different slopes of the $D_2$ line and, generally, varied nonmonotonically with light power. We discuss the effect in terms of the phenomenological Bloch equations for the spin fluctuations and demonstrate that the SN broadening behavior strongly depends on the relation between the pumping and excited-level decay rates, the spin precession, and decoherence rates. To reconcile the puzzling experimental results, we propose that the degree of optical perturbation of the spin system is controlled by the route of the excited-state relaxation of the atom or, in other words, that the act of optical excitation of the atom does not necessarily break down completely its ground-state coherence and continuity of the spin precession. Spectral asymmetry of the effect, in this case, is provided by the position of the “closed” transition $F=4\leftrightarrow F^{\prime }=5$ at the short-wavelength side of the line. This hypothesis, however, remains to be proven by microscopic calculations.

Figure 1

The energy-level diagram of the $D_2$ line of the cesium atom. The “closed” transitions are indicated in red.

Figure 2

(a) Schematic of the experimental setup. Here, $\lambda /2$ and $\lambda /4$ are the half- and quarter-wave plates, PBS is the polarizing beamsplitter, LP is the linear polarizer, PD1 and PD2 are the photodiodes. The frequency of the strong linearly polarized laser light was scanned in the vicinity of the transitions $F=4\leftrightarrow F^{\prime }=3,4,5$ of the cesium $D_2$ line. (b) A typical experimental SN spectrum of cesium under our experimental conditions. A slight tilt of the shot-noise power spectrum is related to the frequency response characteristic of the detection channel.

Figure 3

Experimental dependence of the light-induced broadening of the SN resonance in cesium vapor. Here and in the following experimental figures, points show the data, and solid lines are guides for the eye. The spectrum of linear absorption of the $D_2$ line is shown in the inset, with the vertical arrow indicating the spectral position of the probe light. The optical spectrum of the SN power, under conditions of linear probing, is shown in Fig. 5.

Figure 4

Dependence of the SN resonance width on the probe beam intensity at different detunings of the probe light frequency from the center of the Doppler-broadened transition $F=4\leftrightarrow F^{\prime }=3,4,5$ of cesium.

Figure 5

(a) Spectral dependence of the SN resonance width of cesium vapor at different intensities of the probe beam. Arrows above the curves indicate positions of the excited-state HF components. A spectral point where the SN resonance width practically does not depend on the light intensity is indicated by the asterisk. Panel (b) shows, for comparison, the optical spectrum of the SN power of cesium atoms under conditions of weak (linear) probing (taken from our earlier publication [29]). This spectrum shows that, in the linear regime, the optical spectrum of the SN does not reveal any hidden HF structure of the transition, see also inset in Fig. 3.

Figure 6

Example of the same dependence as in Fig. 4, but obtained on the transition from the lower HF component of the ground state ($F=3$). The symbols represent the data measured at $+0.2$ GHz (circles) $-0.2$ GHz (squares) detunings. The solid lines are a guide to the eye. The sides of the transition with higher and lower sensitivity to optical perturbation of the ground-state spin system are interchanged.

Figure 7

A typical shape of the Faraday rotation noise (SN) spectrum of cesium vapor (red curve) and its decomposition into two Lorentzians: dashed and dash-dotted curves. The fitting sum is shown by the thin black line. Note that the contributions of the electronic and photon shot noise have been subtracted.

Figure 8

The width of the wide component of the SN resonance as a function of the probe light intensity at different temperatures: $T=71$ ${}^{\circ }\mathrm{C}$ (triangles), $T=66.7$ ${}^{\circ }\mathrm{C}$ (diamonds), $T=62.1$ ${}^{\circ }\mathrm{C}$ (squares), and $T=52.8$ ${}^{\circ }\mathrm{C}$ (circles). The solid lines are a guide to the eye.

Figure 9

SNS linewidth (main panel) and peak position (inset) calculated after Eq. (3) as a function of the saturation parameter $G{\tau }_0$. The parameters of the calculations are ${\mathrm{\Omega }}_g{\tau }_0=10$, ${\omega }_e{\tau }_0=5$, ${\tau }_0/{\tau }_{s,g}=0.1$, and ${\tau }_0/{\tau }_{s,e}=0.2$.