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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical switching property of electromagnetically induced transparency in a Λ system

Lianshui Zhang, Jian Wang, Xiaomin Feng, Lijun Yang, Xiaoli Li, Min Zhao

Published Dec 11, 2008• 1 citation

Abstract

In this paper we study the coherent transient property of a Λ-three-level system (Ωd = 0) and a quasi- Λ -four-level system (Ωd>0). Optical switching of the probe field can be achieved by applying a pulsed coupling field or rf field. In Λ -shaped three-level system, when the coupling field was switched on, there is a almost total transparency of the probe field and the time required for the absorption changing from 90% to 10% of the maximum absorption is 2.9Γ0 (Γ0 is spontaneous emission lifetime). When the coupling field was switched off, there is an initial increase of the probe field absorption and then gradually evolves to the maximum of absorption of the two-level absorption, the time required for the absorption of the system changing from 10% to 90% is 4.2Γ0. In four-level system, where rf driving field is used as switching field, to achieve the same depth of the optical switching, the time of the optical switching is 2.5Γ0 and 6.1Γ0, respectively. The results show that with the same depth of the optical switching, the switch-on time of the four-level system is shorter than that of the three-level system, while the switch-off time of the four-level system is longer. The depth of the optical switching of the four-level system was much larger than that of the three-level system, where the depth of the optical switching of the latter is merely 14.8% of that of the former. The speed of optical switching of the two systems can be increased by the increase of Rabi frequency of coupling field or rf field.

DOI: 10.1117/12.824653

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A quasi-lambda four-level system shows both electromagnetically induced absorption (EIA) and electromagnetically induced transparency (EIT). In addition to an optical coupling field and a probing field, there is a radio field which interacts with two excited state hyperfine levels of the quasi-lambda four-level system consisting of two excited state hyperfine levels and two ground state hyperfine levels. If a driving field which interacts with two ground state hyperfine levels is introduced, the quasi-lambda four-level system is modified to a closed-lambda four-level system. The behaviors of the driving field and radio field are studied in this paper and it is seen that the occurence of EIA or EIT and the whole probing properties are controlled by the Rabi frequencies of both driving field and radio field.

Electromagnetically induced transparency (EIT) resonance is obtained in a well-studied lambda three level system where an optical coupling field and a probing field interact with two optical transitions. However, both electromagnetically induced absorption (EIA) and EIT can be obtained in a modified quasi-lambda four level system consisting of an optical-radio two-photon coupling field and a probing field. By solving the density matrix equation of motion, a physical account of EIA and EIT is given in terms of a dressed state picture. It can be seen that the optical coupling field in this quasi-lambda four level system has a crucial effect on the forming of EIA and EIT. An EIA is observed under a resonant optical coupling and it evolves into an EIT when there is a detuning. Furthermore, the width of EIA or EIT increases as the optical coupling Rabi frequency increases.

In this paper we present a theoretical study of the nonlinear effect in the quasi-lambda type four-level system. The system consists of an excited state level and three ground state hyperfine levels. Probing and coupling field are coupled to between the excited state and two higher ground states, and the microwave field drives the two lower ground states which are associated with probing field. By solving the precision solutions of the equations of motion of density matrix, the absorption properties as a function of Rabi frequencies of the probing field and microwave field are given. As a result, the switch from double EIT to single EIA is found due to the power broadening of probing field. However, the splitting frequency of double EIT has some connection with the Rabi frequency of microwave field.

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.

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 transparency and absorption of the Λ-type three-level scheme driven by two coupling fields were investigated.Mollow profile was obtained in a two-level scheme where a strong coupling field and a probing field were applied on the same optical transition between excited state and ground state.There was another coupling field which drived excited state to another ground states hyperfine level in this paper.The Λ-type three-level scheme driven by two coupling fields was introduced,and some new quantum coherent phenomena were given.It can be seen that there is superposition of Mollow profile and electromagnetically induced transparency(EIT) or electromagnetically induced absorption(EIA).The dependence of the position of EIT or EIA on Rabi frequencies and frequency detunings of two coupling fields is investigated.The results can be explained by dressed-state formalism.