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Journal of Physics B Atomic Molecular and Optical Physics

Revisiting the four-level inverted-Y system under both Doppler-free and Doppler-broadened conditions: an analytical approach

Arindam Ghosh, Khairul Islam, Dipankar Bhattacharyya, Amitava Bandyopadhyay

Published Sep 22, 2016• 15 citations
Publisher

Abstract

Abstract We report the occurrence of electromagnetically induced transparency (EIT) in the simulated probe response signal for a four-level inverted-Y type system that is being acted upon by a weak coherent probe field, a strong coherent pump field and a coherent repump field. There are two ground energy levels, one intermediate energy level and one uppermost energy level. The weak probe field couples the lowest ground level to the intermediate level whereas the repump field connects the other ground level with the intermediate level. The strong control field couples the intermediate level with the uppermost energy level, thereby forming an inverted-Y type system. The density matrix based theoretical model has been developed and solved analytically for this four-level system and the probe response signal has been simulated at different values of the control and repump Rabi frequencies, control and repump frequency detunings and under both Doppler-free and Doppler-broadened conditions using the parameters of 87 Rb D 2 transition. Extremely low line width (few tens of kHz) for the EIT signal has been noticed under thermal averaging for copropagating probe, control and repump field configuration. The EIT signal is found to be immune to the variation in the control Rabi frequency.

DOI
10.1088/0953-4075/49/19/195401

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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.

AIP conference proceedings•Jan 1, 2019•0 citations
Abstract We report the occurrence of electromagnetically induced transparency (EIT) in the simulated probe response signal for a four-level inverted-Y type system that is being acted upon by a weak coherent probe field, a strong coherent pump field and a coherent repump field. There are two ground energy levels, one intermediate energy level and one uppermost energy level. The weak probe field couples the lowest ground level to the intermediate level whereas the repump field connects the other ground level with the intermediate level. The strong control field couples the intermediate level with the uppermost energy level, thereby forming an inverted-Y type system. The density matrix based theoretical model has been developed and solved analytically for this four-level system and the probe response signal has been simulated at different values of the control and repump Rabi frequencies, control and repump frequency detunings and under both Doppler-free and Doppler-broadened conditions using the parameters of 87 Rb D 2 transition. Extremely low line width (few tens of kHz) for the EIT signal has been noticed under thermal averaging for copropagating probe, control and repump field configuration. The EIT signal is found to be immune to the variation in the control Rabi frequency.
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 four-level inverted Y-type atomic system is subjected to three coherent laser fields simultaneously. The system has two closely spaced ground energy levels, one intermediate energy level and an uppermost energy level. Transition from the two ground levels to the intermediate level as well as from the intermediate level to the uppermost level are dipole allowed. Transition from the two ground energy levels to the uppermost level is dipole forbidden. A weak laser beam, known as the probe beam, acts between one of the ground levels and the intermediate level. A strong laser field, known as the control or pump field, couples the intermediate level with the uppermost level. A repump filed of intensity usually higher than the probe field acts between the other ground level and the intermediate level. The probe transmission through such a medium is investigated at different values of the control and repump Rabi frequencies under Doppler free condition as well as with thermal averaging. The nonradiative population transfer rates between the ground energy levels have been incorporated.
In this paper, we present the theoretical study of double electromagnetically induced transparency (EIT) in a four-level V-type system which is formed by two co-propagating laser fields and the Zeeman sublevels of hyperfine transitions of 87Rb D2 line. The density matrix equations for the four-level V-type system are derived from the Liouville’s equation of motion and numerically solved under steady state condition to get the EIT signals. We consider both the probe and pump transmission spectra for the observation of double EIT signals under both Doppler free and Doppler broadened conditions. In case of Doppler free medium, two EIT peaks are formed in the two Lorentzian shape dips present in the both Doppler free probe and pump transmission spectra. When the medium becomes Doppler broadened, the two EIT peaks are formed in the probe transmission spectrum having Doppler broadened background, but the pump transmission spectrum gives two EIT peaks in the Doppler free background. The effect of probe intensity variation on the two EIT peaks is studied in case of Doppler broadened probe transmission spectrum. It is found that the heights of the EIT peaks decrease as the probe intensity increases, and interestingly one EIT peak converts into EIA (electromagnetically induced absorption) dip at some strong probe intensity value. The depth of the EIA dip is significantly increased as the intensity of the probe field increases. We also present the effect of probe intensity variation on the EIT peaks in the pump transmission spectrum and found that the EIT peak heights are increased as the probe intensity increases.
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.
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.