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Journal of Nonlinear Optical Physics & Materials

A comparative study of electromagnetically induced transparency (EIT) in Λ-, V-, and Ξ-type systems using Laguerre–Gaussian (LG) laser beams

Samim Akhtar, Jayanta K. Saha, Md. Mabud Hossain

Published Aug 20, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1142/s0218863523500820

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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.
The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields, namely, the control field and the coupling field. An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium. The most striking result is the conversion of electromagnetically induced transparency (EIT) into electromagnetically induced absorption (EIA) as we start switching from weak probe regime to strong probe regime. The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.
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We investigate the steady-state optical response of a Laguerre-Gaussian vortex cavity system integrated with cold atoms featuring a double-ΛΛΛ energy level structure. Within this hybrid system, the atoms are driven by cavity mode and three coherent vortex beams, each carrying independent orbital angular momentum (OAM). We first check the steady-state output spectrum of the hybrid system in the passive/active case (without/with external cavity driving). Our findings reveal that the optomechanically induced transparency (OMIT) spectrum is modulated by the OAM difference (Δℓℏ)(Δ\ell\hbar)(Δℓℏ) from the atomic component throughout the four-wave mixing (FWM) process. The resulting loop phase (ΔℓθΔ\ellθΔℓθ) can achieve a switching effect on the absorption and gain behavior of the hybrid system for the probe beam. Additionally, the group delay, indicative of fast/slow light phenomena, is also tuned by ΔℓΔ\ellΔℓ. We further display how the atomic OAM modulates the periodicity of the output spot pattern in the hybrid system. This research provides valuable insights into the modulation of optical responses in Laguerre-Gaussian vortex cavity systems.
Abstract We have theoretically studied the multi-window electromagnetically induced transparency (EIT) and the related dispersive signals in multi-level V-type systems which are formed by the co-propagating circularly polarized pump ( σ − ) and probe ( σ + ) laser fields in the Zeeman sublevels of hyperfine states of 87 Rb-D 2 line. The optical Bloch equations (OBEs) are derived and numerically solved under the steady-state condition to obtain the probe absorption and dispersion spectra. We present the study of a single-window EIT for the three-level, double-window EIT for the four-level and triple-window EIT for the five-level V-type systems under both Doppler-free and Doppler-broadened conditions. The dispersive signals corresponding to the multi EIT windows for each system are also observed separately. From the knowledge of the slopes of the probe dispersion signals, we have calculated group index ( n g ) of the medium considering three different V-type schemes. The effect of temperature on the EIT, dispersion and group index profiles is also studied in detail. It is found that the amplitudes of EIT and dispersion signals and also the positive and negative values of n g are decreased as the temperature of the medium increases. To understand the Doppler-broadening effect on the group index profiles, we have considered three different velocity groups of atoms in the calculation of group index profiles. Moreover, the effects of probe intensity variation on the Doppler-broadened EIT and dispersive signals are studied extensively, and the conversions of EIT to EIA and dispersive positive slope to negative slope are observed under strong probe regime. Also, we have investigated the variation of dispersive slope and group index with the variation of probe intensity and probe frequency, respectively, at the multi-frequency position of the multi-window EIT. Finally, the switching between subluminal (slow light) to superluminal (fast light) propagation of light with the variation of both probe intensity and probe frequency is discussed in detail.
Abstract The dispersive properties of 87 Rb atomic medium in electromagnetically induced transparency (EIT) have been studied experimentally as well as theoretically. To measure the dispersion signal, a balanced homodyne detection technique was used by forming a Mach–Zehnder interferometer. We studied the system in a Λ-type configuration. From the slope of the dispersive EIT signal, the group index ( n g ) of the atomic medium, the group velocity ( ) and the time delay ( ) of the light wave through the atomic medium were calculated. We measured the group index of the atomic medium from the dispersion signal and observed that it non-linearly depends on the pump power. This non-linearity signifies that to achieve the maximum reduced group velocity, optimization of the pump power is needed. We got the maximum reduction in the group velocity of the probe beam as m s −1 . The corresponding time delay was ns. To support our experimental observation, we have performed a theoretical simulation by taking the semi-classical approach of density matrix formalism of a Λ-type three level system. To get the probe response we solved the optical Bloch equation analytically assuming the Lorentzian velocity distribution of the atom. We have observed that our analytical solution matched exactly with the numerical solution. Our experimental observation of non-linear variation of the group index with the pump Rabi frequency matched quite well with both of our numerical and analytical simulations.
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.