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Chinese Physics

Phase-dependent inversionless gain in a four-level atomic system with a closed interaction loop

Weihua Xu, Jin‐Hui Wu, Jin-Yue Gao

Published Jan 24, 2007• 5 citations
Publisher

Abstract

A four-level atomic system with a closed interaction loop connected by two coherent driving fields and a microwave field is investigated. The results show that inversionless gain can be achieved on a higher frequency transition outside the closed interaction loop, and the gain behaviour can be modulated by the phase of the closed loop as well as the amplitude of the microwave field. The phase sensitivity property in such a scheme is similar to that in an analogous configuration with spontaneously generated coherence, but it is beyond the rigorous condition of near-degenerate levels with non-orthogonal dipole moments. Therefore this scheme is much more convenient in experimental realization.

DOI
10.1088/1009-1963/16/2/026

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A four-level atomic system with a closed interaction loop connected by two coherent driving fields and a microwave field is investigated. The results show that inversionless gain can be achieved on a higher frequency transition outside the closed interaction loop, and the gain behaviour can be modulated by the phase of the closed loop as well as the amplitude of the microwave field. The phase sensitivity property in such a scheme is similar to that in an analogous configuration with spontaneously generated coherence, but it is beyond the rigorous condition of near-degenerate levels with non-orthogonal dipole moments. Therefore this scheme is much more convenient in experimental realization.
We study a four-level atomic system controlled by a three-level closed loop subsystem in order to obtain the phase-sensitive probe gain without population inversion. In the case of three-photon resonance, a large steady-state inversionless probe gain can be obtained. Due to the quantum interference effect, the inversionless gain is sensitive to the relative phase of the three-level closed loop subsystem. Further, the field intensity of the three-level closed loop subsystem is also an important parameter that can affect gain characteristic of the probe field.
We have studied the probe gain via a double-Λ atomic system with a pair of closely lying lower levels in the presence of two probe and two coherent pump fields. The inversionless gain can be realized by using nondegenerate four-wave mixing under the condition of spontaneously generated coherence (SGC) owing to near-degenerate lower levels. Note that by using SGC, two probe fields can be amplified with more remarkable amplitudes, and the gain spectra of an extremely narrow linewidth can be obtained. Last but not least, our results show that the probe gain is quite sensitive to relative phases due to the SGC presence which allows one to modulate the gain spectra periodically by phase modulation, and can also be influenced by all laser field intensities and frequencies, and the angles between dipole elements.
We examine the gain property of a probe field interacting with two different three-level Lambda-type atomic systems with an open loop or a close loop. In the atomic system with an open loop, there exists quantum interference resulting from spontaneous emissions to two near-degenerate lower levels from a common upper level, and the weak probe field can be greatly amplified due to the spontaneously generated coherence. Moreover, the probe gain becomes sensitive to the relative phase between the probe and coupling fields, so we can realize phase control of the probe gain in principle. In the atomic system with a close loop, we use a microwave field to couple the two well-spaced lower levels so that quantum coherence similar to SGC can be generated. In this atomic system, we also can achieve the phase-sensitive probe gain due to the quantum interference between two different absorption channels for the probe field. Note, only in the case of three-photon resonance, this close-loop atomic system can reach a steady state. While in the case of three-photon off-resonance, the probe gain without inversion always oscillates periodically versus time, thus no steady-state probe gain can be achieved.
In order to achieve the phase-sensitive probe gain without population inversion, we investigate a four-level atomic system, where the probe field is controlled by a three-level closed loop subsystem. In the case of three-photon resonance, large steady-state inversionless probe gain can be obtained. Owing to the quantum interference, the probe gain is sensitive to the relative phase of the three-level closed loop subsystem. The intensities of the fields of the three-level closed loop subsystem are also important factors that can result in different gain behaviors of the probe field.
Phase Dependence of the Inversionless Gain in a Λ\LambdaΛ System with Near-Degenerate Levels
We propose a new scheme for achieving inversionless gain that depends on both an internal interference effect and external coherent fields. We have found that, owing to the quantum interference effect that originates from spontaneous emissions from two closely lying levels, large inversionless gains can be achieved under appropriate conditions. In particular, in addition to the amplitudes, the phases of the applied fields also affect inversionless gain remarkably. That is to say, we can use the relative phase between two intense fields to control probe gain without inversion.