Coherent polarization self-rotation

Abstract

We introduce and study coherent polarization self-rotation (CPSR), a two-photon light-matter interaction in dense alkali-metal vapors that enables both narrowband optical spectroscopy of magnetic transitions and coherent coupling between light and collective atomic spins. Unlike conventional polarization self-rotation, CPSR requires initial spin polarization and a predominantly linearly polarized probe. It operates efficiently even in optically thick vapors with high buffer-gas pressure, rapid spin-exchange collisions, and optically-unresolved hyperfine structure. We demonstrate CPSR with near-unity contrast in rubidium and achieve an exceptionally narrow two-photon linewidth of 10 Hz in potassium. CPSR realizes a coherent interface between one optical quadrature and the long-lived collective electronic spin, offering a robust and scalable spin-light coupling in optically thick platforms. This opens new opportunities for quantum optics, including quantum-enhanced metrology in the audio-frequency band and coherent transduction between light and ultra-long-lived noble-gas spins via alkali spins.

Figures (6)

• Figure 1: Mechanism and setup for coherent polarization self-rotation.a. In the high-temperature limit, where spin-exchange collisions are rapid, the alkali ensemble is reduced to an effective spin-1/2 system. The polarization-modulated optical probe decomposes into two photonic modes: a strong control (dashed, blue) and a weak signal (solid, green), which drive spin dynamics under the dispersive Faraday Hamiltonian. At the two-photon resonance ($\omega\approx\pm\omega_\mathrm{a}$), the spin-polarized ensemble (red circle) undergoes coherent transitions within the ground-state manifold. b. Coupled precession of (left) the atomic spin on the Bloch sphere and (right) the optical polarization on the Poincaré sphere. Both are predominantly oriented along the vertical axis. Circular polarization ($S_3$) of the probe induces a vector lightshift that tilts the atomic spin, while the transverse spin component ($F_x$) rotates the optical polarization via the Faraday interaction. For $\omega\approx\omega_\mathrm{a}$, this mutual coupling leads to destructive interference in the diagonal component ($S_2$), manifesting coherent two-photon absorption. c. Experimental setup. A warm vapor cell contains a dense alkali-metal spin ensemble (rubidium or potassium) and buffer gas. An optical-pumping beam (tan) polarizes the atoms, while a polarization-modulated probe, comprising strong control and weak signal modes, is sent through the cell. The coherent signal beam is generated by splitting light from the control beam using a polarizing beam splitter (PBS). Acousto-optical modulators (AOMs) adjust the amplitude, frequency, and relative phase of the two modes, introducing a kHz-scale frequency offset $\omega$. The outgoing $S_2$ component is measured using balanced polarization detection.
• Figure 2: A complex spectrum of coherent polarization self-rotation. Measured transmission (a) amplitude and (b) phase of the optical signal traversing a rubidium vapor cell. The signal exhibits absorption at positive detuning and amplification at negative detuning, consistent with the predicted response near $\omega=\pm\omega_\mathrm{a}$. These spectral features, with a contrast exceeding unity and a full width below 100 Hz, arise from the dispersive Faraday interaction between the polarized collective alkali-spin and the polarization-modulated probe. The numerical solution of the detailed theoretical model (dotted black line) and the simplified model from Eq. (\ref{['eq:spectrum']}) (solid purple line) both agree well with the experimental data (circles).
• Figure 3: Resistance of CPSR to spin-exchange relaxation.a. Transmission spectra of the optical signal for a range of Larmor frequencies $\omega_\mathrm{a}$. Dashed lines indicate the fitted linewidths (FWHM) of the absorption (blue) and amplification (red) peaks. The spectral narrowing at low $\omega_\mathrm{a}$ is a hallmark of the SERF regime, where Zeeman coherence is preserved despite frequent spin-exchange collisions. Black arrows indicate the data shown in Fig. \ref{['fig:spectrum']}. b. Dependence of the fitted FWHM on $\omega_\mathrm{a}$, along with the theoretical prediction (black dotted line), showing the expected quadratic dependence characteristic of the SERF mechanism. c. Contrast of the measured optical lines, extracted from the transmission extrema. Contrast exceeding unity is observed for the amplification peaks at low $\omega$. In panels (b) and (c), dotted black and solid purple lines are the predictions of the detailed numerical model and simplified model [Eq. (\ref{['eq:spectrum']})], respectively.
• Figure 4: CPSR in a spin-polarized potassium ensemble. The transmission spectrum demonstrates CPSR resonances at $\pm\omega_\mathrm{a}=\pm 29$ Hz with a full width of $2\gamma=9.7$ Hz and $\sim$20% contrast. The data (blue circles) deviates from the simplified model's prediction [Eq. (\ref{['eq:spectrum']}), solid purple lines] due to non-negligible optical pumping by the input $S_3$ component, which is captured by the numerical model (dotted black lines)
• Figure 5: Single-photon absorption spectrum of the rubidium vapor cell with natural isotopic abundance. The measured optical depths (blue circles) are extracted from the logarithm of the transmitted power. The numerical fit (solid red line) is a sum of absorption profiles corresponding to the various hyperfine levels (dotted lines), all assumed to share a common homogeneous linewidth $\Gamma$. From this fit, we extract $\Gamma=\unit[2.6]{GHz}$. Note that this measurement was performed at a reduced temperature relative to the main CPSR experiments.