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Physical Review A

Electromagnetically induced transparency and controlled group velocity in a multilevel system

Emmanuel Paspalakis, P. L. Knight

Published Jul 24, 2002• 186 citations
Publisher

Abstract

We analyze the interaction of N laser fields with a $(N+1)$-level quantum system. A general analytic expression for the steady-state linear susceptibility for a probe-laser field is obtained and we show that the system can exhibit multiple electromagnetically induced transparency, with at most $N\ensuremath{-}1$ transparency windows occurring in the system. The group velocity of the probe-laser pulse can also be controlled.

DOI
10.1103/physreva.66.015802

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We analyze the interaction of N laser fields with a (N+1)(N+1)(N+1)-level quantum system. A general analytic expression for the steady-state linear susceptibility for a probe-laser field is obtained and we show that the system can exhibit multiple electromagnetically induced transparency, with at most N\ensuremath−1N\ensuremath{-}1N\ensuremath−1 transparency windows occurring in the system. The group velocity of the probe-laser pulse can also be controlled.
We analyze the interaction of a triple quantum dot molecules controlled by the tunneling coupling instead of coupling laser. A general analytic expression for the steady-state linear susceptibility for a probe-laser field is obtained and we show that the system can exhibit two transparency windows. The group velocity of the probe-laser pulse is also analyzed. By changing the tunneling couplings, two laser pulses with different central frequency can propagate with the same group velocity. And the group velocity can be as low as 300 m/s in our system. We extend our analysis to the case of multiple quantum dot molecules (the number of the quantum dots is N) and show that the system can exhibit at most N-1 transparency windows. And at most N-1 laser pulses with different central frequencies can be slowed down.
The interaction of a weak probe laser with an inverted Y-type four-level atomic system driven by two additional coherent fields is investigated theoretically. Under the influence of the coherent coupling fields, the steady-state linear susceptibility of the probe laser shows that the system can have single or double electromagnetically induced transparency windows depending on the amplitude and the detuning of the coupling lasers. The corresponding index of refraction associated with the group velocity of the probe laser can be controlled at both transparency windows by the coupling fields. The propagation of the probe field can be switched from superluminal near the resonance to subluminal on resonance within the single transparency window when two coupling lasers are on resonance. We propose an atomic 87Rb system for experimental observation.
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.
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.
We investigate the interaction of an open (N + 1)-level extended V-type atomic system (i.e. a closed (N + 2)-level atomic system) with N coherent laser fields and one incoherent pumping field through both analytical and numerical calculations. Our results show that the system can exhibit multiple resonant gain suppressions via perfect quantum destructive interference, which is usually believed to be absent in closed three-level V system and its extended versions involving more atomic levels, with at most N - 1 transparency windows associated with very steep anomalous dispersions occurring in the system. The superluminal group velocity of the probe-laser pulse with at most N - 1 negative values can also be generated and controlled with little gain or absorption.