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Journal of Physics B Atomic Molecular and Optical Physics

Study of coherence effects in a four-level Ξ−Λ type system

Kavita Yadav, Ajay Wasan

Published Apr 5, 2018• 3 citations
Publisher

Abstract

Abstract We theoretically study the two- and three-photon coherence in a Ξ−Λ type four-level system for stationary as well moving atoms at the room temperature using density matrix formalism. We discuss the role of dressed states to elucidate the electromagnetically induced transparency and electromagnetically induced absorption phenomena. The presence of the third field induces absorption at the line centre. A negative dispersion slope owing to the enhanced absorption results in super-luminal light propagation and the group index variation with the coupling field is switched from sub- to super-luminal. Group index with probe detuning shows super-luminal light propagation behaviour at the dressed state positions. The three optical fields trigger four-wave mixing as a result of the third order nonlinearity. The transient evolution is also discussed for optimum strengths of the coupling and drive fields to realize the optical switching in the system.

DOI
10.1088/1361-6455/aabc01

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Abstract We theoretically study the two- and three-photon coherence in a Ξ−Λ type four-level system for stationary as well moving atoms at the room temperature using density matrix formalism. We discuss the role of dressed states to elucidate the electromagnetically induced transparency and electromagnetically induced absorption phenomena. The presence of the third field induces absorption at the line centre. A negative dispersion slope owing to the enhanced absorption results in super-luminal light propagation and the group index variation with the coupling field is switched from sub- to super-luminal. Group index with probe detuning shows super-luminal light propagation behaviour at the dressed state positions. The three optical fields trigger four-wave mixing as a result of the third order nonlinearity. The transient evolution is also discussed for optimum strengths of the coupling and drive fields to realize the optical switching in the system.
Abstract A comparative theoretical study of two-photon electromagnetically induced transparency (EIT), absorption (EIA) and three-photon electromagnetically induced transparency (TPEIT), absorption (TPEIA) and their associated dispersion and group index profiles are presented by using a four-level ladder-type system of both stationary and moving 85 Rb Rydberg atoms. We have observed EIT, EIA and their respective positive and negative dispersive slopes under two-photon conditions, while the TPEIT, TPEIA signals and the respective multiple positive and negative dispersive slopes at around zero detuning of the probe field are observed under the three-photon conditions. It is found that the control and manipulation of the coherent optical responses under three-photon conditions are much richer than the two-photon conditions. The group index profiles related to the dispersion of the medium have been studied under both two- and three-photon conditions to compare and explain the optical switching between the subluminal and superluminal modes of propagation for both stationary and moving atomic medium. The influence of the ‘pump’ Rabi frequency on the group index has also been investigated to illustrate the action of optical switching. Finally, the existence of the four-wave mixing (FWM) process due to the action of three optical fields in the EIT medium is also discussed.
Abstract In this paper, we present a theoretical study of Autler-Townes (AT) splitting, electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) phenomena in a four-level ladder (Ξ)-type configuration formed by two coupling and one probe laser fields using density matrix formalism in dressed state representation (DSR). The DSR is followed by the analytical solution of the optical Bloch equations (OBEs) under density matrix formalism in bare state representation (BSR). The density matrix elements are presented in both linear and non-linear interaction regimes under DSR. The concept of transfer of population (TOP) mechanism has been shown by calculating the different transition probabilities in DSR. It has been found that the population in a particular dressed state is greatly enhanced by increasing the strength of coupling field and played a key role to manipulate the induced coherence between different energy levels. The present theoretical model of DSR offers an excellent interpretation of the formation of EIT, EIA and conversion from EIT to EIA in both linear and third order non-linear probe absorption profiles. Besides, the dispersion profiles in both linear and non-linear interaction regimes have also been studied and the conversion of normal to anomalous dispersion profile which drastically modifies the optical responses of the medium has been discussed. We have found that the amplitudes of the coherent signals are more sensitive to the third order non-linear interaction compared to first order linear interaction.
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.
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.
Using matrix theory,the absorption and dispersion properties of a lamda-type four-level system driven by two 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,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 double electromagnetically induced transparency,the location of transparent windows can be manipulated by controlling the detuning of the driving field.Additionally,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.
Abstract We report a theoretical investigation of the dispersion resulting from electromagnetically induced transparency (EIT) and the associated group refractive index profiles n g of a four-level inverted Y-type system formed by the interaction of three optical fields (probe, pump and control) with 87Rb atoms. The density matrix equations are derived from the semi-classical Liouville’s equation and solved both numerically and analytically to study the coherent nonlinear optical properties of the medium. We first present the EIT, dispersion and corresponding group index profiles n g under the switch-on/off and on/off-resonance conditions of the pump and control lasers. In presence of both pump and control lasers, an enhancement of the EIT window, a sharp EIT spike and related steeper dispersion slopes are obtained at the line centre of the probe frequency detuning. The group index profiles with the variation of the strengths of individual applied optical fields are studied. The effect of the ground state decoherence rates on the group index profile is examined in detail. It is found that the manipulation of n g values and the corresponding group velocities ν g of the probe light can be easily controlled from subluminal to superluminal values or vice versa by changing the strengths of the applied fields and the ground state decoherence rates. Besides, the EIT-based ‘optical switching’ phenomenon in the medium is explained by studying the variation of the group index with the pump and control Rabi frequencies.