Nonlocal Nonlinear Control of Photonic Spin Hall Effect in Strongly Interacting Rydberg Media

TL;DR

The paper addresses the challenge of achieving active, real-time control over the photonic spin Hall effect (PSHE). It develops a theoretical framework for a glass–Rydberg–glass trilayer in ladder-type EIT, where strong Rydberg–Rydberg interactions create a nonlocal third-order susceptibility $\chi^{(3)}_{\rm nonlocal}$ that spatially modulates the refractive index and amplifies spin-dependent light deflection. A combined angular-spectrum and transfer-matrix approach, together with a perturbative Bloch-equation treatment, reveals that the nonlocal nonlinearity yields large, detuning- and density-tunable PSHE shifts up to $\sim$ $20\mu$m near the Brewster angle, with controllable sign reversals via $\Delta_2$ and $\Delta_c$. This mechanism provides a robust, all-optical pathway to reconfigurable spin-sensitive photonic components for beam steering and precision metrology, outperforming fixed nanostructures or local Kerr media. The results set the stage for real-time, spin-resolved photonic processing in quantum-optical devices.

Abstract

We present a theoretical study demonstrating enhanced tunability of the photonic spin Hall effect (PSHE) using a strongly interacting Rydberg atomic medium under electromagnetically induced transparency (EIT) conditions. In contrast to conventional approaches that rely on static refractiveindex profiles or metamaterials, here the PSHE is controlled via a nonlocal third-order nonlinear susceptibility arising from long range Rydberg-Rydberg interactions. We show that this nonlocal nonlinearity enables dynamic modulation of spin-dependent light trajectories, amplifying the normally weak PSHE into a readily observable and adjustable effect. These results pave the way for new capabilities in photonic information processing and sensing. In particular, an adjustable PSHE may enable beam steering based on photon spin, improve the sensitivity of precision measurements, and support photonic devices whose functionality can be reconfigured in real time.

Figures (6)

• Figure 1: (a) Schematic of the planar three-layer (glass–Rydberg–glass) optical model. In experiment, the two “glass” layers correspond to the ultra-high-vacuum (UHV) cell windows, and the central layer is the laser-cooled $^{87}$Rb cloud (magneto-optical trap (MOT), optionally a weak dipole trap) inside the evacuated cell. The “layer thickness” $d_2$ denotes the axial extent of the probed atomic cloud inside the UHV cell. (b) Ladder-type EIT diagram defining the probe detuning $\Delta_{2}$ and two-photon detuning $\Delta_{3}=\Delta_{2}+\Delta_{c}$.
• Figure 2: (a) The graphical representation of $\text{Re}[\chi]$ (red solid line) along with $\text{Im}[\chi]$ (blue dashed line) against the probe detuning $\Delta_2$. (b) Corresponding magnitudes of the Fresnel reflection coefficients for s- and p-polarizations, $|r_s|$ (blue solid line) and $|r_p|$ (orange solid line). (c) Ratio $|r_{s}|/|r_{p}|$ versus probe incident angle $\theta_i$. (d) The PSHE shifts $\delta_{y}^{\pm}$ versus probe incident angle $\theta_i$ for left(red solid line) and right(blue solid line) circular polarized reflected beams. Other parameters used in calculation: $\Omega_c/2\pi=4.0$MHz, $\Omega_p/2\pi=0.75$MHz, $N_a=4\times10^7$mm$^{-3}$, $\lambda_p=780$nm.
• Figure 3: The PSHE shift for left circular polarized beam $\delta_y^{+}$.(a)Shift versus probe detuning $\Delta_{2}/2\pi$ for three incident angles around the Brewster value $\theta_{i}=33.80^\circ$(blue), $\theta_{i}=33.87^\circ$(red) and $\theta_{i}=33.97^\circ$(green). (b)Shift versus incident angle $\theta_i$ for three representative detunings $\Delta_{2}/2\pi=-2.5$MHz(blue), $\Delta_{2}/2\pi=1.1$MHz(red) and $\Delta_{2}/2\pi=3.3$MHz(green). Other parameters used in calculation: $\Omega_c/2\pi=4.0$MHz, $\Omega_p/2\pi=0.75$MHz, $N_a=4\times10^7$mm$^{-3}$, $\lambda_p=780$nm.
• Figure 4: The distribution of normalized transverse intensity for (a)incident Gaussian beam (b) reflected left-circular polarized field and (c) reflected right-circular polarized field. The first row corresponds to probe detuning $\Delta_2 / 2 \pi= 3.5$MHz and the second row corresponds to probe detuning $\Delta_2 / 2 \pi= -3$MHz. Other parameters are the same in Fig. \ref{['fig:PSHE_shift']}.
• Figure 5: Density plot of PSHE shift $\delta_{y}^+$ versus incident angle $\theta_i$ and probe detuning $\Delta_2$ at different atomic density (a)$N_a=4 \times 10^{7}\text{mm}^{-3}$, (b)$N_a=8 \times 10^{7}\text{mm}^{-3}$. Other parameters are the same in Fig. \ref{['fig:PSHE_shift']}.