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arXiv:1706.02545 · Physical Review A

Phase-induced transparency-mediated structured-beam generation in a closed-loop tripod configuration

Sandeep Sharma, Tarak Nath Dey

Published Sep 7, 2017• 64 citations
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Abstract

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.

DOI
10.1103/physreva.96.033811

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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.
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.
We investigate theoretically a scheme for all-optical generation of structured light beams with and without a microwave field in an electromagnetically induced transparency (EIT) medium composed of rubidium atoms. In a conventional EIT system, two optical fields (namely, a strong control field and a weak probe field) drive two electric-dipole-allowed transitions of an atom to form a three-level system in a $\mathrm{\ensuremath{\Lambda}}$ configuration. At EIT resonance, we found that a Laguerre-Gaussian (LG) control beam induces a radial modulation of probe's absorption profile in such way that a Gaussian probe beam is reshaped into a hollow-Gaussian beam following the position-selective absorption. The transmitted probe beam has a doughnut-shaped intensity structure similar to that LG beam whereas the phase profile is still a spherical wave. Moreover, the presence of a microwave field between two ground states of three-level system leads to a closed-loop system, and probe response is modified with an additional term proportional to the amplitudes of Rabi frequencies of control and microwave fields, and relative phase of three fields. This term acts as driving field which is responsible for the generation of a vortex probe beam having a helical phase profile. We have further shown that the amplitude and helical phase of generated vortex beam can be manipulated by changing the relative phase of applied fields and temperature of the vapor cell. The present study may provide a useful tool for creation of structured light beams with and without orbital angular momentum.
We conduct theoretical investigations into a fundamental closed-loop Λ-type atomic system using 87 Rb atoms, aiming to efficiently generate and manipulate structured light beams. A phase-singular microwave (MW) beam with a topological charge l μ and a phase-singular optical probe beam with a topological charge l p collectively induce phase-dependent atomic coherence, resulting in periodic oscillations of probe absorption in the transverse plane. The number of absorption or transparency windows in the transverse plane is determined by the resultant topological charge of the system, denoted as l = l μ − l p . We investigate the propagation of a paraxial doughnut-shaped probe beam through the phase-dependent atomic medium and showcase the generation of petal-like structured beams for various combinations of l μ and l p . We provide a detailed theoretical explanation of these results using the analytical expression of probe susceptibility. We outline how this scheme effectively serves as a sensor adept at discerning particular OAM modes. This selective detection capability is valuable in scenarios where only certain OAM states carry relevant information. The relative phase between the interacting fields can be used to rotate the structured probe beam by 360 deg in the clockwise or counterclockwise direction. This manipulation of spatial position of different OAM modes can be employed in implementing OAM-based logical operations.
We study the interaction of a weak probe field, having two orthogonally polarized components, with an optically dense medium of four-level atoms in a tripod configuration. In the presence of a coherent driving laser, electromagnetically induced transparency is attained in the medium, dramatically enhancing its linear as well as nonlinear dispersion while simultaneously suppressing the probe field absorption. We present the semiclassical and fully quantum analysis of the system. We propose an experimentally feasible setup that can induce large Faraday rotation of the probe field polarization and therefore be used for ultrasensitive optical magnetometry. We then study the Kerr nonlinear coupling between the two components of the probe, demonstrating a novel regime of symmetric, extremely efficient cross-phase modulation, capable of fully entangling two single-photon pulses. This scheme may thus pave the way to photon-based quantum information applications, such as deterministic all-optical quantum computation, dense coding, and teleportation.
Recent years have seen vast progress in the generation and detection of structured light, with potential applications in high capacity optical data storage and continuous variable quantum technologies. Here we measure the transmission of structured light through cold rubidium atoms and observe regions of electromagnetically induced transparency (EIT), using the phase profile as control parameter for the atomic opacity. With q plates we generate a probe beam with azimuthally varying phase and polarization structure, and its right and left circular polarization components provide the probe and control of an EIT transition. We observe an azimuthal modulation of the absorption profile that is dictated by the phase and polarization structure of the probe laser. Conventional EIT systems do not exhibit phase sensitivity. We show, however, that a weak transverse magnetic field closes the EIT transitions, thereby generating phase-dependent dark states which in turn lead to phase-dependent transparency, in agreement with our measurements.
We investigate the propagation of an optical vector vortex beam in an atomic medium featuring four-level tripod transitions, where ground-state coherence is mediated by a transverse magnetic field. The vector beam consists of left- and right-circularly polarized components, each carrying an optical vortex with opposite orbital angular momentum (OAM). We study the linear response of the medium to the vector beam in order to determine the evolution of the beam's intensity and polarization profile. We find that the beam structure undergoes significant transformations as it propagates: the transverse intensity evolves from a ring-shaped profile to a petal-like structure, while the polarization transitions between left-circular, linear, and right-circular polarizations. Furthermore, when only the right-circular polarization component (a scalar vortex) enters the medium, it parametrically generates a left-circular polarization component, transferring its OAM to the generated field. This process converts the initial vortex beam into a superposition of left- and right-circular components, forming a scalar vortex beam where both polarization components carry the same OAM.