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Acta Physica Sinica

Selective reflection spectrum in a quasi-lambda four-level atomic system

Tengfei Meng, Jianfeng Tian, Yaoyao Zhou

Published Jan 1, 2020• 0 citations
Publisher

Abstract

Selective reflection (SR) from the interface between transparent medium and dilute vapour is caused by the atomic vapor near the interface. The sub-Doppler structure in SR is due to the deexcitation caused by the collision between atomic vapor and the wall. Beacuse the interaction region between atomic vapor and incident light is on the order of a few hundred nanometers, SR has low optical loss and high spatial resolution. The experimental device of SR is simple. Because of the above characteristics, the SR has been widely studied and applied. The nonlinear SR spectrum of quasi lambda-type four-level system at gas-solid interface is studied theoretically in this paper. By sloving the density matrix equations, the approximate analytic solution of the matrix element associated with the probe field is obtained at normal incidence when the intensity of the probe field is very weak. The effect of the Rabi frequency, the detuning of the signal field and the detuning of the coupling field on the lineshape are analyzed by numerical simulation, respectively. Three peaks and two transparent windows appear in SR spectrum when the detuning of coupling field and signal field are both zero. The middle peak is generated due to the participation of signal field, and the other two peaks are caused by the other two fields. The linewidth and the amplitude of the middle peak can be changed by varying the Rabi frequency of signal field, and the other two peaks have little effect on the Rabi frequency of signal field. The signal generated due to the participation of signal field can be transformed from peak to transparent window when the detuning value of the signal field is equal to the Rabi frequency of coupling field. When the detuning value of the signal field is not equal to the Rabi frequency of coupling field, a dispersion-like signal between reflection peak and transparent window is generated due to the participation of signal field. The position of peak and transparent window can be manipulated by controlling the detuning value of the coupling field. When the detuning value of coupling field decreases from zero, three peaks all shift to red detuning direction. When the detuning value of coupling field is blue-detuned and increases, three peaks all shift to blue detuning direction. The numerical results can be explained by using the various electric transition pathways and dressed state theory. This study is helpful in investigating quantum coherence and dynamic process of atoms at gas-solid interface.

DOI
10.7498/aps.69.20191099

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Selective reflection (SR) from the interface between transparent medium and dilute vapour is caused by the atomic vapor near the interface. The sub-Doppler structure in SR is due to the deexcitation caused by the collision between atomic vapor and the wall. Beacuse the interaction region between atomic vapor and incident light is on the order of a few hundred nanometers, SR has low optical loss and high spatial resolution. The experimental device of SR is simple. Because of the above characteristics, the SR has been widely studied and applied. The nonlinear SR spectrum of quasi lambda-type four-level system at gas-solid interface is studied theoretically in this paper. By sloving the density matrix equations, the approximate analytic solution of the matrix element associated with the probe field is obtained at normal incidence when the intensity of the probe field is very weak. The effect of the Rabi frequency, the detuning of the signal field and the detuning of the coupling field on the lineshape are analyzed by numerical simulation, respectively. Three peaks and two transparent windows appear in SR spectrum when the detuning of coupling field and signal field are both zero. The middle peak is generated due to the participation of signal field, and the other two peaks are caused by the other two fields. The linewidth and the amplitude of the middle peak can be changed by varying the Rabi frequency of signal field, and the other two peaks have little effect on the Rabi frequency of signal field. The signal generated due to the participation of signal field can be transformed from peak to transparent window when the detuning value of the signal field is equal to the Rabi frequency of coupling field. When the detuning value of the signal field is not equal to the Rabi frequency of coupling field, a dispersion-like signal between reflection peak and transparent window is generated due to the participation of signal field. The position of peak and transparent window can be manipulated by controlling the detuning value of the coupling field. When the detuning value of coupling field decreases from zero, three peaks all shift to red detuning direction. When the detuning value of coupling field is blue-detuned and increases, three peaks all shift to blue detuning direction. The numerical results can be explained by using the various electric transition pathways and dressed state theory. This study is helpful in investigating quantum coherence and dynamic process of atoms at gas-solid interface.
Using density matrix eqution, the absorption and dispersion properties of a A-type four-level system driven by coherent fields are investigated. The result obtained by means of numerical method indicates that by adjusting the intensity of Rabi frequencies of the coherent field in the steady state, three, double or single electromagnetically induced transparency (EIT) can appear explicitly in this system. And the explanations of these phenomena are given by using the dressed states. In the three EIT, the location of transparent windows can be manipulated by controlling the detuning of the driving field. What's more, it is also found that the medium shows a large refractive index at each transparency window, and the group velocity of the probe laser can be enhanced.
The Electromagnetically Induced Transparency (EIT) is associated with a Λ three-level system and the spectral position of EIT window can be changed by varying the frequency of the coupling field, however, at large detuning the EIT will evolve into a dispersion-like feature and transparency property of EIT become less obvious. In this paper, it is shown that we can perform EIT frequency tuning by a radio-frequency (rf) field. In the cascade quasic-Λ four-level system, the absorption profile of probe field is calculated by solving the equations of motion of the density matrix. It is shown that the Autler-Townes doublet originates from the rf-field induced dynamic Stark effect and the spectral position of EIT window is determined by the frequency detuning of the coupling field. When the frequency detuning of the coupling field is half of the rf Rabi frequency, the EIT feature remain its absorptive profile. The frequency tuning rang of EIT is determined by the rf Rabi frequency, and can be explained using a dressed-state analysis. Therefore, frequency tuning range of EIT can be controlled by the rf Rabi frequency.
Atomic coherence and interference play an important role in the study of the atom-photon interactions. Electromagnetically induced transparency (EIT) is an extensively studied two-photon coherence phenomenon theoretically as well as experimentally. EIT is mainly observed in three-level atomic systems which causes transparency by quenching absorption of the medium. In this paper, based on the lambda type three-level system including energy level |1>, |2> and |3>, a microwave driving field is introduced between the excited-state energy level |3> and another excited-state energy level |4> to form an inverted Y-type four-level system. We theoretically study the two- and three-photon coherence in this system. The results show that the coupling field makes the probing absorption intensity at the resonant frequency have a very narrow line-width depression, i.e., EIT. The microwave field causes a dynamic Stark splitting of the energy level |3> and induces the Aulter-Townes double peaks. Their frequency interval is exactly equal to the Rabi frequency of the microwave field. The presence of all three fields induces wide window of EIT at the line center owing to the enhanced depression results. The transient evolution is also discussed to understand the optical switching process in the system. Our theoretical study will be helpful to get a deeper insight into the three-photon effects in multilevel systems.
We study the cascade three-level selective-reflection spectroscopy for normal incidence at a dielectric--atomic-vapor interface in a pump-probe scheme. Taking into account the effects of spatial dispersion arising from deexcitation by collisions with the interface and the transient response of atoms leaving the surface, we evaluate the modification of the probe-field reflection induced by the presence of the pump field in terms of a nonlocal nonlinear susceptibility. The dependence of this susceptibility on the probe frequency for various given pump frequencies is calculated. Sub-Doppler structures in the selective reflection spectrum are obtained and analyzed. Potential applications to the study of the interaction of highly excited atomic states with the surface are indicated.
We theoretically present the nonlinear selective reflection spectroscopy of V‐type atomic system at gas‐solid interface in a pump‐probe scheme. The saturation and coherence effects are distinguished by solving Liouville equation in the absence and presence of reduced density matrix element between the two excited levels. When the coherence effect exists, two peaks appear in reflection spectroscopy with asymmetry lineshape. We investigate the dependence of reflection spectroscopy on pump field intensity, frequency detuning and coherent decay rate induced by collision between atoms. The lineshape can be explained based on reflection spectroscopy contributed from atoms with negative (before collision) and positive (after collision) velocities, single‐photon and two‐photon processes. This study is helpful for investigating quantum coherence and dynamic processes of atoms at gas‐solid interface.
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.