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Physical Review A

Spontaneously generated coherence and dark states

P. R. Berman

Published Sep 16, 2005• 31 citations
Publisher

Abstract

It is shown that the response of a three-level atom interacting with an optical field in a ''dark state geometry'' (single field, degenerate ground states) depends critically on whether or not spontaneously generated coherence (SGC) is present. In the absence of SGC, the system evolves to a dark state. With SGC present, the dark state population is a constant of the motion and the steady-state values for density-matrix elements depend on their initial values at the time the field is applied.

DOI
10.1103/physreva.72.035801

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Journal of Physics B Atomic Molecular and Optical Physics•Oct 20, 2006•15 citations
It is shown that the response of a three-level atom interacting with an optical field in a ''dark state geometry'' (single field, degenerate ground states) depends critically on whether or not spontaneously generated coherence (SGC) is present. In the absence of SGC, the system evolves to a dark state. With SGC present, the dark state population is a constant of the motion and the steady-state values for density-matrix elements depend on their initial values at the time the field is applied.
The effect of a dark state on the entanglement properties of the two-mode field from a laser-driven Λ-type three-level atomic system is investigated by taking into account the spontaneously generated coherence (SGC). When the dark state is present, it is found that the entanglement between the two cavity modes can be significantly enhanced compared to the case without the dark state. When the value of SGC is maximal, the dark state population depending on the initial values of the system can affect the entanglement dramatically. Moreover, the effects of a squeezed parameter and Rabi frequency on entanglement evolution are also presented in the presence of a dark state.
The entanglement between a ?-type three-level atom and its spontaneous emission fields is investigated. The effect of spontaneously generated coherence (SGC) on entanglement between the atom and its spontaneous emission fields is then discussed. We find that in the presence of SGC the entanglement between the atom and its spontaneous emission fields is completely phase dependent, while in absence of this coherence the phase dependence of the entanglement disappears. Moreover, the degree of entanglement dramatically changes by the coherent superposition of the atomic states.
The effect of spontaneously generated coherence (SGC) on spontaneous emission and dynamical evolution of a microwave-driven four-level atomic system is studied. Interesting phenomena due to SGC, such as spectral-line narrowing, spectra-line enhancement, spectral-line suppression, and fluorescence quenching, are shown in the spontaneous emission spectra, which can be effectively modulated by amplitude and phase of the microwave field. Due to SGC, the total populations are partly, even completely, trapped in upper levels in steady state, the decay time of which is sensitive to the phase of the microwave field. In the dressed state picture, multiple SGC arise during the process of three close-lying states decaying to the same state. The corresponding experiment to observe the expected phenomena related to SGC can be more conveniently realized in atoms, since no rigorous conditions are required and the amplitude and phase of the microwave field can be conveniently controlled.
Abstract Owing to interference induced by spontaneous emission, the density-matrix equations in a three-level Λ-type system have an additional coherence term, which plays a critical role in modulating the inversionless gain and electromagnetically induced transparency effect. In addition, it is shown that spontaneously generated coherence (SGC) has an effect on the entanglement between an atom and a photon of the coupling laser field by calculating the degree of entanglement (DEM) of the atomic system. In this paper, we investigate the influence of the SGC effect on atom-photon entanglement in a Λ-type system, which generally remains a high entangled state. When an incoherent pump source is introduced, we find that the SGC effect could exert considerable influence on the atom reduced entropy under certain conditions for both transient and steady states. More interestingly, such an incoherent pump field could actively affect the short-time dynamic behaviors of the transient quantum entangled state at a certain range of pump rate as a typical coherent case.
In a three-level closed Λ system with incoherent pumping, both the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role in inducing different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). These two coherences can interfere destructively and constructively giving rise to different nonlinear processes (EIT, EIA, AWI) when the strength of these two coherences is comparable. Therefore the system can switch over from one nonlinear process to the other and the desired response of the system can be achieved by controlling the system parameters. It has been shown that this switching can occur by changing the relative strength of Rabi frequencies for the coherent and probe fields and the mode of incoherent pumping (unidirectional and bidirectional) for a chosen SGC parameter. Further control over the response can be achieved by changing the phase between two radiation fields. But the dependence on phase is different when both the coherences contribute than that obtained only from SGC. Exact analytical expressions for the coherences and populations in the steady state limit have been derived (keeping all orders of system parameters) to generalize the analysis and any restrictions over the system parameters (e.g. spontaneous decay widths on probe and coherent transitions are equal) have been avoided to make it applicable to various atomic and molecular systems. However the approximate expressions can be derived from these exact values. Numerical values obtained by solving the density matrix equations agreed well with these exact analytical values.