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Annalen der Physik

Nonlinear Dynamics of the Photonic Spin Hall Effect in Rydberg Atoms

Muqaddar Abbas, Wenzhang Liu, Pei Zhang, Hamid Reza Hamedi

Published Aug 30, 2025• 1 citation
Publisher

Abstract

Abstract The photonic spin Hall effect (SHE) is explored in a highly tunable Rydberg‐based atomic system by leveraging the distinctive properties of Rydberg superatoms. These superatoms arise from strong dipole–dipole interactions and extended radiative lifetimes, resulting in collective excitations governed by the dipole blockade mechanism. An ensemble of three‐level atoms in a cascade configuration models a medium in which each superatom acts as a coherent quantum entity. The photonic SHE shows strong dependence on the probe field Rabi frequency and atomic number density. At high Rabi frequencies, the blockade effect suppresses the photonic SHE, confining its occurrence to specific resonant conditions. In contrast, under weak probe excitation, the blockade influence diminishes, enabling an amplified photonic SHE response at resonant detuning due to increased light‐matter interaction sensitivity. Reducing atomic number density further broadens the detuning range over which the photonic SHE occurs, indicating a transition toward a more sensitive, less resonance‐constrained optical behavior. The effect of van der Waals interactions on the photonic SHE shift is also characterized. This expanded operational bandwidth demonstrates the potential of Rydberg‐based systems for robust spin‐optical control, particularly in scenarios where precise stabilization of the probe field frequency is experimentally challenging.

DOI
10.1002/andp.202500194

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Abstract The photonic spin Hall effect (SHE) is explored in a highly tunable Rydberg‐based atomic system by leveraging the distinctive properties of Rydberg superatoms. These superatoms arise from strong dipole–dipole interactions and extended radiative lifetimes, resulting in collective excitations governed by the dipole blockade mechanism. An ensemble of three‐level atoms in a cascade configuration models a medium in which each superatom acts as a coherent quantum entity. The photonic SHE shows strong dependence on the probe field Rabi frequency and atomic number density. At high Rabi frequencies, the blockade effect suppresses the photonic SHE, confining its occurrence to specific resonant conditions. In contrast, under weak probe excitation, the blockade influence diminishes, enabling an amplified photonic SHE response at resonant detuning due to increased light‐matter interaction sensitivity. Reducing atomic number density further broadens the detuning range over which the photonic SHE occurs, indicating a transition toward a more sensitive, less resonance‐constrained optical behavior. The effect of van der Waals interactions on the photonic SHE shift is also characterized. This expanded operational bandwidth demonstrates the potential of Rydberg‐based systems for robust spin‐optical control, particularly in scenarios where precise stabilization of the probe field frequency is experimentally challenging.
We discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our calculations reproduce and interpret the results of recent experiments.
Abstract We present a theoretical study demonstrating that the photonic spin Hall effect (PSHE) can be both actively tuned and greatly amplified by exploiting the nonlocal, nonlinear optical response of a strongly interacting Rydberg gas operating under electromagnetically induced transparency. Rather than relying on fixed phase metasurfaces or conventional Kerr materials, long range interactions between Rydberg atoms create a spatially extended, intensity dependent refractive index profile that enables dynamic spin resolved beam deflection. In a glass–Rydberg–glass trilayer model, we show that the PSHE displacement can be varied smoothly in magnitude and even reversed in sign by adjusting atomic density, probe intensity, laser detunings, and interaction strength. This nonlocal nonlinearity transforms the typically weak PSHE into a macroscopically observable and dynamically controllable effect. Our results establish a versatile platform for reconfigurable spin-dependent photonic control, with potential applications in high-sensitivity optical metrology, spin-based beam steering, and tunable quantum-optical information processing.
Transmission properties of a weak probe field traveling through a sample of interacting cold 87Rb atoms driven into the three-level ladder configuration, which is a typical Rydberg electromagnetically induced transparency (EIT) system, are investigated. Rydberg atoms are considered to be a perfect platform in the research fields of quantum optics and quantum information processing due to some exaggerated properties of Rydberg atoms with high principal quantum number, especially, the dipole-dipole interaction between Rydberg atoms leads to the so-called dipole blockade effect accommodating at most one Rydberg excitation within a mesoscopic volume. The dipole blockade effect may be mapped onto the spectrum of EIT, and the EIT exhibits the cooperative optical nonlinearity which is usually characterized by two indicators, i.e., the probe intensity and the photonic correlation. The cooperative optical nonlinearity is also found here in the phase of transmission spectrum, and the phase can be regarded as the third indicator of nonlinearity in Rydberg EIT. However, there are tremendous differences between the phase and probe transmission (photonic correlation) though they both originate from the conditional polarization. Specifically, the phase is not sensitive to neither the incident probe intensity nor the initial photonic correlation at the resonant probe frequency under the condition of the Autler-Townes (AT) splitting where two other indicators exhibit significant cooperative nonlinearity. The nonlinearity in phase spectrum occurs only in the regime between the resonant probe frequency and the AT splitting and especially is remarkable at the frequency where the probe field is classical. Finally, influence of the principal quantum number and the atomic density on the transmitted phase are examined. In the nonlinear regime, the absolute value of the phase becomes smaller and smaller as the principal quantum number and the atomic density are raised. This indicates that the nonlinearity is strengthened by increasing them. The probe phase provides an attractive supplement to study in depth the cooperative optical nonlinearity in Rydberg EIT and offers us the considerable flexibility to manipulate the propagation and evolution of a quantum light field.
We predict a resonant enhancement of the nonlinear optical response of an interacting Rydberg gas under conditions of electromagnetically induced transparency. The enhancement originates from a two-photon process which resonantly couples electronic states of a pair of atoms dressed by a strong control field. We calculate the optical response for the three-level system by explicitly including the dynamics of the intermediate state. We find an analytical expression for the third-order susceptibility for a weak classical probe field. The nonlinear absorption displays the strongest resonant behavior on two-photon resonance where the detuning of the probe field equals the Rabi frequency of the control field. The nonlinear dispersion of the medium exhibits various spatial shapes depending on the interaction strength. Based on the developed model, we propose a realistic experimental scenario to observe the resonance by performing transmission measurements.
High optical nonlinearities can be achieved at the single photon level by coupling the photon states to strongly interacting Rydberg excitations under the conditions of electromagnetically induced transparency. The nonlinear response in Rydberg quantum optics comes as a direct result of the long range dipole-dipole interactions via Rydberg blockade and interaction induced dephasing. In this thesis, Rydberg quantum optics experiments are performed with two spatially separated mediums with a nonlinear response at the single photon level. Two ultracold rubidium atomic clouds are tightly confined by a pair of in-vacuo aspheric lenses such that only a few Rydberg excitations can exist in each one of the clouds simultaneously. The long range character of the dipole-dipole interactions leads to the generation of quantum states of light. The effective photon-photon interactions are directly observed as an anti-correlation in the simultaneous photon retrieval as a result of the non resonant van der Waals interactions. The collective Rydberg excitations, stored in the non-overlapping mediums, experience an additional spatial non-uniform phase. In addition, we experimentally characterize the cooperative optical response of a cold atomic medium at a single photon level. This aims to exploit the enhancement of the spontaneous emissions decay rate (superradiance) as a dependence of the number of atoms involved in the ensemble. The observed atomic response in two different regimes gives a further understanding of the system dynamics and unlocks a promising potential route towards the implementation in scalable, multichannel quantum optical devices.
Interaction between Rydberg atoms can significantly modify Rydberg excitation dynamics. Under a resonant driving field the Rydberg-Rydberg interaction in high-lying states can induce shifts in the atomic resonance such that a secondary Rydberg excitation becomes unlikely leading to the Rydberg blockade effect. In a related effect, off-resonant coupling of light to Rydberg states of atoms contributes to the Rydberg anti-blockade effect where the Rydberg interaction creates a resonant condition that promotes a secondary excitation in a Rydberg atomic gas. Here, we study the light-matter interaction and dynamics of off-resonant two-photon excitations and include two- and three-atom Rydberg interactions and their effect on excited state dynamics in an ensemble of cold atoms. In an experimentally-motivated regime, we find the optimal physical parameters such as Rabi frequencies, two-photon detuning, and pump duration to achieve significant enhancement in the probability of generating doubly-excited collective atomic states. This results in large auto-correlation values due to the Rydberg anti-blockade effect and makes this system a potential candidate for a high-purity two-photon Fock state source.