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arXiv:1901.00096

Controllable spin-Hall and related effects of light in an atomic medium via coupling fields

Jinze Wu, Junxiang Zhang, Shi‐Yao Zhu, G. S. Agarwal

Published Jan 1, 2019• 0 citations
arXivHTMLPDF

Abstract

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 $2.5\times10^{17}\,\mathrm{m}^{-3}$, 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.

DOI
10.48550/arxiv.1901.00096

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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.
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.
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A precise, accurate, and relatively straightforward in situ method to measure and control the ellipticity of light resonantly interacting with an atomic vapor is described. The technique can be used to minimize vector light shifts. The method involves measurement of ellipticity-induced resonances in the magnetic-field dependence of nonlinear magneto-optical rotation of frequency-modulated light. The light propagation direction is orthogonal to the applied magnetic field B\mathbf{B}B and the major axis of the light polarization ellipse is along B\mathbf{B}B. When the light modulation frequency matches the Larmor frequency, elliptically polarized light produces a precessing atomic spin orientation transverse to B\mathbf{B}B via synchronous optical pumping. The precessing spin orientation causes optical rotation oscillating at the Larmor frequency by modulating the atomic vapor's circular birefringence. Based on this technique's precision, in situ nature (which avoids systematic errors arising from optical interfaces) and independent control of the most important systematic errors, it is shown that the accuracy of light ellipticity measurements achievable with this technique can exceed that of existing methods by orders of magnitude.
In the photonic spin Hall effect (SHE), also known as the transverse shift, incident light photons with opposite spins are spatially separated in the transverse direction due to the spin-orbit interaction of light. Here, we propose a gain-assisted model to control the SHE in the reflected probe light. In this model, a probe light is incident on a cavity containing a three-level dilute gaseous atomic medium, where the interaction between the atom and the control field follows two-photon Raman transitions. We show that the direction of photonic spin accumulations can be switched between positive and negative values across the Brewster angle in both the anomalous and normal dispersion regimes. For the same magnitude of control fields, the peak value of the photonic SHE is higher in the anomalous dispersion region compared to the normal dispersion regime. Additionally, the angular range around the Brewster angle is wider in the normal dispersion regime than in the anomalous dispersion region. Furthermore, the peak value of the photonic SHE and the angular range can be controlled by changing the Rabi frequencies of the control fields and the probe field detuning. The measurement of photonic SHE based on gain assistance may enable spin-related applications such as optical sensing.
We demonstrate all-optical control of birefringence in a cold atomic cloud of ytterbium. By optically dressing the excited 3P1^{3}\mathrm{P}_13P1​ state via an off-resonant coupling to the 3D1^{3}\mathrm{D}_13D1​ level, we induce polarization-dependent light shifts of the Zeeman sublevels, resulting in a tunable polarization-dependent refractive index. For a circularly polarized dressing beam, we observe a rotation of the probe linear polarization, characteristic of the Faraday effect, in the absence of any magnetic field. In addition, for a linearly polarized dressing beam, the probe acquires ellipticity without rotation, corresponding to linear birefringence. More generally, the polarization of the dressing beam controls the axis of rotation of the probe polarization on the Poincaré sphere. Our results establish cold atoms as a versatile platform for engineering and controlling light-induced birefringence and open new perspectives for the fast and reconfigurable control of optical response of resonant media.