Detection of long-range coherence in driven hot atomic vapors by spin noise spectroscopy

TL;DR

The paper investigates long-range coherence between ground Zeeman states in driven hot atomic vapors and detects it with spin noise spectroscopy. By mapping the driven cascaded-Lambda system to an effective non-Hermitian Floquet tight-binding lattice with imaginary hopping $iJ_o$, where $J_o = \Omega^2/\gamma$, the authors explain how multi-photon pathways generate higher-harmonic peaks at multiples of $\delta\omega_s$ in the spin-noise spectrum. The peak amplitudes reveal an exponential decay of coherence with ground-state separation, $\rho^R_{l,l+2n} \propto (J_o/\gamma')^n$ in the weak-coupling limit, a signature corroborated by experiments on $^{85}$Rb with 3-, 5-, and 7-level cascaded-Lambda configurations. The work demonstrates a minimally perturbative method to probe coherence in unpolarized spin ensembles and highlights anti-PT like dynamical features with potential implications for precision magnetometry and quantum sensing.

Abstract

We study intriguing dynamical features of hot Rubidium atoms driven by two light fields. The fields resonantly drive multiple Zeeman states within two hyperfine levels, yielding a cascaded-$Λ$ like structure in the frequency space. A non-Hermitian Floquet tight-binding lattice with imaginary hopping between the nearest states effectively describes the coherence dynamics between Zeeman states within the ground hyperfine manifold. By performing spin noise spectroscopy, we observe higher harmonic peaks in the noise spectrum that capture multi-photon transitions in the ground manifold. Moreover, the peak amplitudes reveal an exponential decay of long-range coherence with increasing separation between the ground states.

Figures (2)

• Figure 1: (a) Energy level schematics. Hyperfine levels, $|5\,^{2}\text{S}_{1/2}, \text{F}=3 \rangle$ and $|5\,^{2}\text{P}_{3/2}, \text{F}'=4 \rangle$ of Rb atoms coupled by two Raman fields. They drive $\pi^{0},\sigma^{+}$ transitions, which generate a C$\Lambda$ structure in the frequency space. Here, we have shown a $7$-LC$\Lambda$S. (b) The coherence between the Zeeman states in the ground hyperfine manifold is governed by an effective non-Hermitian (Floquet) tight-binding lattice with imaginary hopping $i J_o$ between the states. Such non-Hermitian dynamics generate long-range coherence between distant ground states. (c) Variation of the height-ratio $H_{2,1}$ with detuning $\Delta$ in a $5$-LC$\Lambda$S; and (d) variation of the height-ratios $H_{3,1},H_{2,1}$ in a $7$-LC$\Lambda$S with the Rabi frequency $\Omega$. We use $\Delta_1=\Delta_2=0$ in (d) and $\gamma=1.9$ GHz in (c-d). The solid and dashed lines are obtained numerically using the steady state of C$\Lambda$ systems; the black dots are obtained from the effective non-Hermitian description.
• Figure 2: (a) The schematics for the Faraday rotation fluctuation measurements in the experiment. A linearly polarized probe beam is focused at the center of the vapor cell. A pair of Raman beams having polarizations $(\sigma^+)_x$ and $(\pi^0)_x$ is merged using a non-PBS (NPBS) and made to pass through the vapor cell in the opposite direction to the probe propagation. The frequency and intensity of the Raman fields are tuned by the AOMs. We use the saturation absorption spectroscopy (SAS) setup to determine the frequency of all laser beams. A uniform magnetic field is created along the z-axis. The probe beam falls on the polarimetric detection setup comprising a PBS and a balanced detector. (b) The experiment yields the power spectral density represented by the green-dotted line. The plot indicates five spin noise peaks in our driven system. The blue-diamond (magenta-square) points represent the corresponding theoretical comparison for the height ratios in the coherence spectrum using the full simulation of the system (using simulation of a $13$-LC$\Lambda$S). The parameters used for the simulation in the plots are: $\Delta_1=\Delta_2=0$, $\Omega=8\times 10^{-3}\gamma$, $\gamma=1.9$ GHz, and $\gamma\,'=200$ kHz.