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arXiv:2103.06596 · Optics Express

Detecting the transverse spin density of light via electromagnetically induced transparency

Jinhong Liu, Jinze Wu

Published Jun 10, 2022• 5 citations
arXivHTMLPDF

Abstract

For light that is transversely confined, its field vector spins in a plane not orthogonal to the propagation direction, leading to the presence of transverse spin, which plays a fundamental role in the field of chiral quantum optics. Here, we theoretically propose a scheme to detect the transverse spin density (TSD) of light by utilizing a multilevel atomic medium. The scheme is based on the electromagnetically induced transparency effect, which enables the TSD-dependent modulation of the susceptibility of the atomic medium by using a coupling field whose TSD is to be detected. The modulated susceptibility results in a spin-dependent absorption for a probe beam passing through the atomic medium. We show that there exists a corresponding relationship between the TSD distribution of the coupling field and the polarization distribution of the transmitted probe beam through a theoretical study of two typical cases, in which the coupling field is provided by a tightly focused field and a two-beam interference field, respectively. Based on this relationship, the key features of the TSD of the coupling field, such as the spatial distribution, the symmetry property, and the spin-momentum locking, can be inferred from the transmitted probe beam. Benefiting from the fast response of the atomic medium to the variation of the coupling field, the present scheme is capable of detecting the TSD in real time, offering new possibilities for developing transverse-spin-based techniques.

DOI
10.1364/oe.463519

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For light that is transversely confined, its field vector spins in a plane not orthogonal to the propagation direction, leading to the presence of transverse spin, which plays a fundamental role in the field of chiral quantum optics. Here, we theoretically propose a scheme to detect the transverse spin density (TSD) of light by utilizing a multilevel atomic medium. The scheme is based on the electromagnetically induced transparency effect, which enables the TSD-dependent modulation of the susceptibility of the atomic medium by using a coupling field whose TSD is to be detected. The modulated susceptibility results in a spin-dependent absorption for a probe beam passing through the atomic medium. We show that there exists a corresponding relationship between the TSD distribution of the coupling field and the polarization distribution of the transmitted probe beam through a theoretical study of two typical cases, in which the coupling field is provided by a tightly focused field and a two-beam interference field, respectively. Based on this relationship, the key features of the TSD of the coupling field, such as the spatial distribution, the symmetry property, and the spin-momentum locking, can be inferred from the transmitted probe beam. Benefiting from the fast response of the atomic medium to the variation of the coupling field, the present scheme is capable of detecting the TSD in real time, offering new possibilities for developing transverse-spin-based techniques.
We show the existence of spin-Hall effect of light (SHEL) in an atomic medium which is made anisotropic via electromagnetically induced transparency. The medium is made birefringent by applying an additional linearly polarized coupling light beam. The refractive index and the orientation of the optics axis are controlled by the coupling beam. We show that after transmitting the atomic medium, a linearly polarized probe light beam splits into its two spin components by opposite transverse shifts. With proper choice of parameters and atomic density of about 2.5×1017 m−32.5\times10^{17}\,\mathrm{m}^{-3}2.5×1017m−3, the shifts are about the order of wavelength and can be larger than the wavelength by increasing the atomic density. We propose a novel measurement scheme based on a balanced homodyne detection (BHD). By properly choosing the polarization, phase, and transverse mode of the local oscillator of the BHD, one can independently measure (i) the SHEL shifts of the two spin components; (ii) the spatial and angular shifts; (iii) the transverse and longitudinal shifts. The measurement can reach the quantum limit of precision by detecting signals at the modulation frequency of the electro-optic modulator used to modulate the input probe beam. The precision is estimated to be at the nanometer level limited by the quantum noise.
The interaction between cylindrical vector beams and atoms under a weak magnetic field induces spatially dependent electromagnetically induced transparency (EIT). Based on this coherence effect, we investigated the relationship between the magnitude and orientation of the transverse magnetic field (TMF) and the spatial intensity distribution of cylindrical vector beams passing through a thermal atom ensemble, which is intuitively manifested in polarization selection absorption. The radially polarized beam exhibits a spatial axisymmetric polarization structure. When a TMF is applied, transparent regions in the transmitted beam strongly correlate with the beam’s polarization distribution. Variations in the TMF magnitude alter the absorption of specific polarization components by the atomic system, thereby affecting the local transmittance. This enables the TMF magnitude to be inferred from the single transmittance of the intensity pattern. The alignment of the TMF orientation is reflected in the rotation of the petal-shaped transmission patterns aligned with the mirror axis. Theoretical solutions using optical Bloch equations reveal this specific spatially dependent EIT is closely related to the transverse relaxation rate between the ground state energy levels. Experimental data align perfectly with the theoretical results, suggesting potential applications in light field manipulation and magnetic field measurement.
Recently a scheme has been proposed for detection of the structured light by measuring the transmission of a vortex beam through a cloud of cold rubidium atoms with energy levels of the Λ-type configuration [N. Radwell et al., Phys. Rev. Lett.114, 123603 (2015) ]. This enables observation of regions of spatially dependent electromagnetically induced transparency (EIT). Here we suggest another scenario for detection of the structured light by measuring the absorption profile of a weak nonvortex probe beam in a highly resonant five-level combined tripod and Λ (CTL) atom-light coupling setup. We demonstrate that due to the closed-loop structure of CTL scheme, the absorption of the probe beam depends on the azimuthal angle and orbital angular momentum (OAM) of the control vortex beams. This feature is missing in simple Λ or tripod schemes, as there is no loop in such atom-light couplings. One can identify different regions of spatially structured transparency through measuring the absorption of probe field under different configurations of structured control light.
Abstract In this article, Spin density and Torque of two interfering waves are controlled and manipulated by applying two interacting control fields and a probe field using a four-level N-type atomic configuration of Rubidium-87 isotope. The spin density of light can be controlled coherently in the atomic medium by electromagnetically induced transparency (EIT). When the strong interacting control fields and the weak probe field are applied to the atomic medium, the Rubidium atoms become transparent to the probe field. It is due to the control fields that "dress" the atoms, creating a new energy state that the weak probe field can interact with. As a result, the weak probe field can pass through the Rubidium atomic medium without being absorbed. Substantial variations can be seen in the electric SAM and Torque of two interfering waves with variations in the angle β\betaβ between the two interfering waves, the Rabi frequencies of the control fields, the detuning of the probe field, and the phase difference δϕ\delta \phiδϕ between waves. By introducing these changes of parameters in the atomic medium, the spin density of two interfering waves can be made to rotate in a specific direction or at a specific rate. The parameters of control fields and probe field detuning play an essential role in the modification of electric SAM and electric spin vector field distribution of the probe field. The modified work of this manuscript is useful for Quantum computing, Optical communication, Quantum information processing. Key Words: Dynamical properties of light, Electric spin density, Two-wave interference, coherent control, Four-level N-type atomic configuration
Abstract In this article, Spin density and Torque of two interfering waves are controlled and manipulated by applying two interacting control fields in which one is the Kerr field with Rabi frequency Ω2 and a probe field using a four-level N-type atomic configuration of Rubidium-87 isotope. The spin density of light can be controlled coherently in the atomic medium by electromagnetically induced transparency (EIT). When the strong interacting control fields and the weak probe field are applied to the atomic medium, the Rubidium atoms become transparent to the probe field. It is due to the control fields that ”dress” the atoms, creating a new energy state that the weak probe field can interact with. As a result, the weak probe field can pass through the Rubidium atomic medium without being absorbed. Substantial variations can be seen in the electric SAM and Torque of two interfering waves with variations in the angle β between the two interfering waves, the Rabi frequencies of the control fields, the detuning of the probe field, and the phase difference δϕ between waves. By introducing these changes of parameters in the atomic medium, the spin density of two interfering waves can be made to rotate in a specific direction or at a specific rate. The parameters of control fields and probe field detuning play an essential role in the modification of electric SAM and electric spin vector field distribution of the probe field. The modified work of this manuscript is useful for Quantum computing, Optical communication, Quantum information processing.
We present a phase-induced transparency-based scheme to generate structured-beam patterns in a closed four-level atomic system. We employ a phase-structured probe beam and a transverse magnetic field (TMF) to create phase-dependent medium susceptibility. We show that such phase-dependent modulation of absorption holds the key to formation of a structured beam. We use a full density matrix formalism to explain the experiments of Radwell et al. [Phys. Rev. Lett. 114, 123603 (2015)] at weak probe limits. Our numerical results on beam propagation confirms that the phase information present in the absorption profile gets encoded on the spatial probe envelope, which creates petal-like structures even in the strong field limit. The contrast of the formed structured beam can be enhanced by changing the strength of TMF as well as of the probe intensity. In weak field limits an absorption profile is solely responsible for creating a structured beam, whereas in the strong probe regime, both dispersion and absorption profiles facilitate the generation of a high-contrast structured beam. Furthermore, we find the rotation of structured beams owing to strong-field-induced nonlinear magneto-optical rotation.