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Chinese Physics B

Electromagnetically induced transparency and electromagnetically induced absorption in Y-type system

Kalan Mal, Khairul Islam, Suman Mondal, Dipankar Bhattacharyya, Amitava Bandyopadhyay

Published Mar 11, 2020• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ab7ea0

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AIP conference proceedings•Jan 1, 2019•0 citations
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.
Abstract Probe field propagation through a four-level Y-type system is studied analytically under steady state condition by using density matrix formulation. The probe field scans the intermediate state from the ground state whereas two other coherent radiation fields, namely the control field and the coupling field, are set to couple two different excited states from the intermediate energy level. Under Doppler free condition, simulated probe absorption shows single or twin EIT windows depending on whether the control and the coupling field are on-resonant or detuned. Under Doppler broadened condition, the residual Doppler averaging due to wavelength mismatch between the probe field and the control field as well as that between the probe field and the coupling field plays significant role in the formation of transparency window.
We study electromagnetically induced transparency (EIT) of a probe field in a four-level Y-type atomic system driven by two strong laser (coupling) fields. Both homogeneously (radiative) and Doppler broadened systems are considered. The effect of residual Doppler broadening on EIT is demonstrated for various wave-vector mismatches occurring when the frequency of coupling fields is equal (kc{k}_{c}kc​ === kp{k}_{p}kp​), higher (kc>kp{k}_{c}>{k}_{p}kc​>kp​), or lesser (kc<kp{k}_{c}<{k}_{p}kc​<kp​) than that of the probe field frequency. Contrary to usual belief it is found that for the kc>kp{k}_{c}>{k}_{p}kc​>kp​ wave-vector mismatch case, the probe absorption profile displays very wide and almost complete single or double EIT windows whose width, depth, and location depend upon the wave-vector mismatch, Rabi frequencies, and atom field detuning of the coupling fields. Analytical results are also obtained to explain these interesting features.
Abstract Coherent probe field (L A ) propagation through an eight-level inverted Y-type atomic system, in the presence of two additional coherent radiation fields termed the field L C (control or pump field) and the field L B (repump field), is investigated by using the parameters of 87 Rb 5 S 1 / 2 → 5 P 3 / 2 → 7 S 1 / 2 transitions. The system has two ground energy levels, four intermediate energy levels, and two uppermost energy levels. A theoretical model based on the density matrix method is used for numerical simulation of the probe response under different conditions. Simulated probe absorption spectra under a Doppler-free condition as well as under thermal averaging exhibit electromagnetically induced transparency (EIT). The position and line shape of this EIT profile change with different detunings of the control and repump fields. When the three coherent fields share a common level, a funnel-like EIT window appears in the simulated probe absorption curve. Velocity selective optically pumped absorption peaks are seen in the simulated probe response at room temperature.
A density matrix based analytical model is developed to study the coherent probe field propagation through a four-level V type system in presence of a coherent control field. The model allows coupling of the probe field from the upper ground level to both of the excited levels keeping the control field locked to a particular transition. The addition of an extra ground level to a conventional three-level V type system creates extra decay paths to the ground levels for the upper level population. A set of sixteen density matrix based equations are formed and then solved analytically under rotating wave approximation to study the probe response under steady state condition. The simulated probe absorption spectra shows absorption dip at the centre of a transparency window only under Doppler broadened condition although the conventional EIT window appears under Doppler free condition. The dependence of the field induced absorption signal on the Rabi frequency of the control field, population transfer rate among the ground levels and temperature of the vapour medium has been studied in details.
The absorption features of a probe field propagating through a six-level inverted-Y type atomic system in presence of two additional coherent fields are investigated under both Doppler-free and Doppler-broadened conditions resembling the 87Rb 5S1⁄2 → 5P3⁄2 → 44D5⁄2 (Tr-I) through numerical simulation. A comparative study in the probe absorption is also made with the 87Rb 5S1⁄2 → 5P3⁄2 → 7S1⁄2 transition (Tr-II). Under thermal averaging five velocity selective optically pumped absorption peaks (VSOPAP) appear for both the transitions (Tr-I and Tr-II). An interesting feature noticed in the simulated absorption profile is that under thermal averaging we get two extra electromagnetically induced transparency (EIT) dips for Tr-I compared to Tr-II where only two EIT dips are noticed.
We investigate the effect of the residual Doppler averaging on the susceptibility and optical switching of a weak probe field propagating through a four-level inverted-Y type atomic system driven by two strong coherent fields, namely the pump field (control field) and the repump field. A theoretical model of the inverted-Y type system is developed by using density matrix method and a set of sixteen optical Bloch equations (OBEs) are solved analytically under steady state condition to determine the probe coherence term. The imaginary part of susceptibility shows electromagnetically induced transparency (EIT) under Doppler free condition as well as under Doppler broadening. The line parameters of 5S1/2 → 5P3/2 → 5D5/2 and 5S1/2 → 5P3/2 → 7S1/2 transitions executed by 87Rb atoms are used to simulate the susceptibility and group index related to probe field propagation in order to show the effect of residual Doppler broadening due to wavelength mismatch between the pump field and the probe field. Under Doppler free condition the probe field propagation is subluminal on resonance while that under Doppler broadened condition is superluminal on resonance for both the transitions.