Bistability of optical properties of cesium vapor due to collective interaction of alignment and orientation under strong spin exchange conditions

TL;DR

This study demonstrates that in dense cesium vapor under spin-exchange relaxation-free (SERF) conditions, the quadrupole alignment and the dipole orientation can coexist and interact, leading to bistability and hysteresis in the optical response when elliptically polarized pumping is used. A phenomenological model describes the observed symmetric (alignment) and antisymmetric (orientation) signal contours and their dependence on ellipticity, magnetic fields, and pump power. The authors propose that nonuniform pumping may create spatially separated regions that couple via an effective field, yielding a collective SERF mechanism. The findings open avenues for long-lived optical switches and memory elements in atomic vapors, with potential two-input operation controlled by magnetic field and light ellipticity for quantum information and cryptography applications.

Abstract

Hydrogen-like alkali atoms with a single valence electron are the most common objects in quantum optics and, at the same time, serve as essential tools of the field. Under conditions of optical pumping, strong spin-exchange and ultra-weak magnetic field (spin-exchange relaxation free mode, SERF), ensembles of such atoms in the gas phase can demonstrate not only the absence of spin-exchange relaxation, but also nonlinear collective effects. We present experimental evidence that the alignment, i.e. the quadrupole momentum, can not only be preserved under SERF conditions, but also coexist and interact with the orientation, i.e. the dipole momentum. We also show that this interaction leads to bistability: a small change in conditions can cause the medium to transition to a different steady state, an effect characterized by hysteresis. The combination of properties of this effect opens up a wide range of applications as optical keys or memory elements with a storage time of hundreds of seconds in tasks of quantum information and cryptography.

Figures (5)

• Figure 1: (a) Energy diagram of the lower levels of Cs; (b) calculated absorption coefficient in a thin layer on the $D_1$ line of Cs in the presence of 300 Torr N$_2$: the profiles corresponding to individual lines are filled in color, the thick purple line is the overall absorption profile. Solid vertical lines are the centers of the profiles shifted by nitrogen pressure, dashed vertical lines are the centers of the undisturbed profiles. The red arrow indicates the laser radiation frequency in our experiment; (c),(d) schemes of pumping with linearly polarized light resonant to the $F = 3 \rightarrow F' = 3$ transition: (c) the external field $\bf{B}$ is parallel to the electric vector $\bf{E}$ of the light wave, the alignment is negative, (d) the field $\bf{B}$ is perpendicular to $\bf{E}$, the alignment is positive; (e) spatial distribution of moments during pumping with linearly polarized light: negative alignment ("donut") and positive ("dumbbell"); (f) calculation of alignment signals in the presence of a small $B_y$ field according to Eqs.\ref{['eq:eq1']},\ref{['eq:eq2']}: $S_T$ is the absorption signal, $S_B$ is the polarization rotation signal, $S_{BL}$ is the result of lock-in amplification of the modulated $S_B$ signal.
• Figure 2: (a) Block diagram of the setup: MS - magnetic shield, LP - linear polarizer (Glan prism), QWP - quarter-wave plate, HC - Helmholtz coils system, C - cell, PBS - polarization cube, PHD1, PHD2 - photodiodes; (b) example of an experimental recording demonstrating the effects of bistability (dashed lines) and hysteresis (solid lines); a digital low-pass filter is applied to the data to eliminate high-frequency interference. (c) model used to explain the results. $\text{A}$ - antisymmetric contour, $\text{S}$ - symmetric contour, $\text{H}$ - hysteresis, $\text{A-S}$ and $\text{A+S}$ - resulting envelopes. Solid lines - experimental data (the same recording as in (b); (d) schematic representation of the moments $\bf{M}^{(1)}$ (orientation) and $\bf{M}^{(2)}$ (alignment) created by weakly elliptical spatially non-uniform optical pumping, and the dynamics of $\bf{M}^{(1)}$ in the presence of an external field $\bf{B}||\bf{x}$.
• Figure 3: Examples of recordings (a) of absorption signals; (b-d) of demodulated polarization rotation signals. In fragments (a-b), the pump ellipticity is varied, (c) the $B_z$ field component is varied at three ellipticity values, (d) the $B_y$ field component is varied at an ellipticity close to zero. In fragment (b), the simulation results are shown as large dots. Fragments (a, b, d) show the original recordings (dots) and the result of digital low-pass filtering (lines). In fragment (c), only the result of digital filtering is shown to avoid overloading the figure.
• Figure 4: Results of fitting the data in Fig. \ref{['fig3']}(b) to the "antisymmetric $\pm$ symmetric contour" model: (a) widths of both contours. Solid lines are the linear approximation; (b) amplitudes of both contours. Solid lines are the linear approximation and Lorentzian contour approximation, (c) hysteresis in magnetic field units. Solid line is the hyperbolic approximation; (d) maximum values of the slope $dS_B/dB_x$ of the transient process, that is, the change in the $dS_B$ signal during scanning $dB_x$. Solid line is the arctangent approximation; (e) value of the effective field that could lead to a reversal of the alignment moment by $\pi$ during the time corresponding to the duration of the transient process. Solid line is the arctangent approximation.
• Figure 5: (a) Examples of recordings of transient processes (signal $S_T$) for different values of the longitudinal field $B_z$ and the ellipticity angle $\chi$ = +0.$5^\circ$; (b) the results of their processing -- hysteresis and the magnitude of the effective field, dependences of signal amplitudes and the corresponding relaxation times (inverse resonance widths) on the longitudinal field $B_z$; (c) amplitudes of the symmetric and antisymmetric resonance contours in Fig. \ref{['fig3']}(c). Solid lines are approximations by Lorentz contours; (d) resonance amplitudes Fig. \ref{['fig3']}(d). Solid lines are approximations by polynomials.