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 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.
This study presents an innovative scheme for detecting the orbital angular momentum (OAM) of vortex beams within an atomic ensemble. Leveraging a homogeneously broadened four-level atomic system driven by two orthogonal polarization probe beams, we demonstrate the selective generation of structured beams without the need for magnetic fields between the two ground states. Through detailed theoretical analysis and numerical simulations, we elucidate the phase-dependent behavior of atomic coherences induced by an OAM-carrying Laguerre–Gaussian optical probe beam. These findings enable the creation of petal-like structures within the probe beam, with the number of petals directly correlated to the OAM value. Our investigation underscores the potential of this OAM detection scheme as a highly sensitive and precise sensor, applicable across diverse domains such as telecommunication, microscopy, and optical metrology.
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.
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 Spatially structured optical reflection and phase modulation in cavity quantum electrodynamics present a pathway to programmable control of structured light and topological photonic states. This study examines the spatial response of a three-level atom–assisted single-sided cavity, driven by a composite vortex control field, by analyzing the transverse distributions of the reflection coefficient and reflected-phase shift as influenced by variations in cavity decay rate, external coupling strength, and the orbital angular momentum (OAM) content of the driving fields. The control Rabi frequency Ω l ( r , ϕ ) , which inherits the doughnut-shaped amplitude and helical phase of vortex beams, results in position-dependent atomic coherence and effective cavity susceptibility, imprinting ring-like or petal-like textures onto both reflectivity and phase. For symmetric counter-rotating vortices with l 1 = − l 2 = 1 − 4 , the reflection forms 2 l -petal patterns, and the phase exhibits complementary 2 l -fold lobes with sharp phase-gradient boundaries dictated by cos ( 2 l ϕ ) interference, while central singular features intensify with OAM order. In the case of asymmetric OAM pairs, rotational symmetry is disrupted, and the spatial spectra are primarily determined by Δ l = 3 and 5, respectively, resulting in distorted threefold and fivefold modulations with localized singular defects and star-like phase topology.
We propose an efficient scheme to manipulate spontaneous emission spectra using optical vortices carrying orbital angular momentum (OAM) in a coherently driven cold five-level atomic system assisted by a radio frequency (RF) or microwave field. Using experimentally achievable parameters, we find that the spontaneous emission is strongly influenced by quantum destructive interference. And we show that the structured light profile of the probe field can be transferred to the spontaneous emission spectrum via spontaneously generated coherence (SGC). With the aid of SGC, the intensities and detunings of the control and RF fields can be used to tailor the vortex-induced spontaneous emission spectra. When the control and RF fields are configured as vortex beams, it is demonstrated that the spontaneous emission can be coherently controlled through quantum interference by adjusting their topological charges (TCs). Furthermore, we explore intriguing optical properties of the vortex-induced spontaneous emission by varying the TCs of the probe and control fields. This coherently driven atomic system features three closely spaced levels, giving rise to multiple vortex-induced SGC pathways. Our scheme opens avenues for applications in structured light, ranging from optical storage to optical communication.
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.