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Annalen der Physik

All‐Optical Spin–Orbit Coupling of Light in Coherent Media Using Rotating Image

Lu Zhao

Published Dec 4, 2019• 4 citations
Publisher

Abstract

Abstract The possibility of all‐optical spin–orbit coupling (SOC) of light is investigated based on a rotating spinor image traveling through an electromagnetically induced transparency (EIT) medium. It is shown that the paraxial evolution of the spinor image composed of two Laguerre–Gaussian (LG) modes with different frequencies can be analogous with the quantum dynamics of a spin‐1/2 particle with strong and tunable SOC governed by the Pauli equation, where the spin‐up and ‐down states have different effective masses. Using realistic EIT parameters with cold atoms, both the radial inhomogeneity of the strong control field and the atomic density distribution with comparable size are considered. The results confirm that the large group refractive index varying in the radial dimension mimicking the central potential can greatly enhance the spin–orbit interaction, leading to visible spatial quantization of the oppositely oriented spin states, equivalent to the two LG modes.

DOI
10.1002/andp.201900371

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Journal of Nonlinear Optical Physics & Materials•Aug 20, 2023•5 citations
Abstract The possibility of all‐optical spin–orbit coupling (SOC) of light is investigated based on a rotating spinor image traveling through an electromagnetically induced transparency (EIT) medium. It is shown that the paraxial evolution of the spinor image composed of two Laguerre–Gaussian (LG) modes with different frequencies can be analogous with the quantum dynamics of a spin‐1/2 particle with strong and tunable SOC governed by the Pauli equation, where the spin‐up and ‐down states have different effective masses. Using realistic EIT parameters with cold atoms, both the radial inhomogeneity of the strong control field and the atomic density distribution with comparable size are considered. The results confirm that the large group refractive index varying in the radial dimension mimicking the central potential can greatly enhance the spin–orbit interaction, leading to visible spatial quantization of the oppositely oriented spin states, equivalent to the two LG modes.
Analysis indicates that tunable spin-orbit coupling (SOC) can be introduced into the paraxial Schr\"odinger-type equation for a spinor image traveling through a rotating electromagnetically induced transparency (EIT) medium. As a fundamental example, we show that, due to a radial gradient of large group refractive index, the SOC can lead to spatial separation of the oppositely oriented spinor states in the probe image, mimicking the fine-structure splitting of a spin-12\frac{1}{2}21​ quantum harmonic oscillator described by the Pauli equation. Such a result enables a direct manipulation and visualization of spin-orbit physics by all-optical means based on EIT slow-light media. Possible experimental implementations of our model with ultracold atoms are discussed.
We explore the underlying spin-orbit coupling (SOC) mechanism for the interactions between complex structured light fields in a four-level tripod electromagnetically induced transparency (EIT) system. Because one coupling field in the system is a Bessel beam, the susceptibility of the EIT medium can be modulated quasiperiodically in the radial dimension. The paraxial propagation and evolution of a rotating spinor image as the probe field in the medium can be described by a Pauli-like equation with the SOC term. We calculate the spatial distributions of the diffracted patterns of the image in the near field and clearly show the tunable SOC-induced radial splitting of the oppositely polarized pseudospin states. Our scheme may be useful for all-optical processing of spatial multimode signals in coherent media.
Abstract We explore the spin–orbit coupling (SOC) mechanism for structured light in coherent atomic media with low-light-level cross-Kerr nonlinearity. Using the five-level M-type electromagnetic induced transparency (EIT) system as a prototype, we show that spin–orbit splitting for a weak spinor image can be generated by a weak trigger field carrying orbital angular momentum (OAM) at low-light intensity. By quantum-optical analogy, the paraxial focusing and defocusing of the two pseudo-spin states in the spinor image can be governed by a Pauli-like equation. More importantly, by changing the EIT parameters, especially the topological charge of the weak trigger field, the SOC-induced radial quantization of the spinor image can be rather significant, giving rise to positive or negative OAM-OAM mode separation in free space. This suggests that the separation can be flexibly controlled due to strong image-vortex interaction based on few-photon cross-Kerr modulation. Our findings may have the potential for all-optical OAM multiplexing and demultiplexing of structured light fields toward few-photon quantum control and multimode communication.
Based on the electromagnetically induced transparency (EIT) model and the higher-order Poincaré sphere (HOPS) framework, we establish a general paradigm to investigate the paraxial evolution of a vector beam in a tripod EIT system. By quantum-optical analogy, we introduce a formalism with a generalized Pauli-like equation under rotational invariance, in which the pseudo-spin-orbit coupling (PSOC) and the spin-orbit nonseparability of light can coexist. More importantly, we find that both the PSOC-based real and imaginary potentials play a key role in controlling and modulating the nonseparable state of the vector beam to traverse the entire HOPS, where the orientation and ellipticity of the transmitted polarization can be modified by varying the PSOC coefficients. Therefore, an all-optical scheme can be proposed to improve the flexibility for tailoring the space-variant polarization of light in coherent media, where the tunable spatial-polarization multiplexing may be useful in conventional and quantum information processing.
Abstract We report a novel pump-probe laser spectroscopy technique to measure the spatial polarization of spin-orbit coupling (SOC) mode of the vector vortex beam (VVB) using electromagnetically induced transparency (EIT) protocol. An experiment is performed for observing the EIT signal in a five-level Λ-type configuration of 85 Rb-D 2 line coupled with the pump VVB and non-vortex probe beam. Interestingly, the sinusoidal modulation of the EIT amplitude is observed with spatial polarization rotation of the pump VVB for two different orbital angular momenta (OAM). This remarkable feature enables the extraction of information about the spatial polarization and azimuthal petal-like pattern of the SOC mode of the VVB. Furthermore, we propose that the experimental results may be considered as a hybrid quantum logic gate operation by employing the spatial polarization and EIT amplitude as the photonic qubits, which may offer promising applications in quantum information science.
In this paper, a theoretical investigation of electromagnetically induced transparency (EIT) using Laguerre–Gaussian (LG) beams has been carried out for the three canonical atom-laser coupled systems (e.g. [Formula: see text]-, V-, and [Formula: see text]-type) in [Formula: see text]Rb atom. The required optical Bloch equations (OBEs) are derived for each system. The OBEs are analytically solved in steady-state condition under the weak probe field approximation. We have used the iterative perturbative technique to obtain the probe coherence term. The probe response w.r.t. probe detuning for different orders of the orbital angular momentum (OAM) number of both the pump and probe LG beams has been studied. We have also studied the effect of the OAM number on probe response in both Doppler-free and Doppler-broadened mediums. It has been observed that the EIT signal is squeezed for nonzero OAM number of the pump beam with arbitrary OAM number of the probe beam. It is found that for higher-order OAM number, the EIT signal is further squeezed. The modification of the EIT signal is attributed because of the spatial-dependent Rabi frequency. Our study demonstrates that the dynamic of the probe field inside an atomic medium may be controlled by tuning the OAM number of the LG beam.