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Physical Review A

Non-Markovian behavior for spontaneous decay of a V-type three-level atom with quantum interference

Wen-ju Gu, Gao‐xiang Li

Published Jan 30, 2012• 20 citations
Publisher

Abstract

The non-Markovian behavior of a V-type three-level atom coupled to a zero-temperature bosonic Lorentzian reservoir is investigated. The two decay channels from two upper states to the ground one are connected due to the spontaneously generated interference. When the two upper states are degenerate, the two channels can be decoupled, and an analytical lower bound of the non-Markovian behavior can be obtained by the optimal choice of a pair of initial states. The non-Markovian behavior can be enhanced by the interference.

DOI
10.1103/physreva.85.014101

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The non-Markovian behavior of a V-type three-level atom coupled to a zero-temperature bosonic Lorentzian reservoir is investigated. The two decay channels from two upper states to the ground one are connected due to the spontaneously generated interference. When the two upper states are degenerate, the two channels can be decoupled, and an analytical lower bound of the non-Markovian behavior can be obtained by the optimal choice of a pair of initial states. The non-Markovian behavior can be enhanced by the interference.
We present a paradigmatic method for exactly studying non-Markovian dynamics of a multi-level V-type atom interacting with a zero-temperature bosonic bath. Special attention is paid to the entanglement evolution and the dynamical non-Markovianity of a three-level V-type atom. We find that the entanglement negativity decays faster and non-Markovianity is smaller in the resonance regions than those in the non-resonance regions. More importantly, the quantum interference between the dynamical non-Markovianities induced by different transition channels is manifested, and the frequency domains for constructive and destructive interferences are found.
Studying the spontaneous emission of a V-type three-level atom embedded in a photonic crystal (PC) by fractional calculus, we found that the atomic excited states in the anisotropic PC can be expressed as a superposition of four dressed states analytically. Through detuning two allowed atomic transition energies with respect to the photonic band edge, the coupling between these two transitions leads to three dynamic regimes, namely non-Markovian decay, damped quantum interference and quantum interference, classified by the numbers of contributed bounded dressed states. From the degree of quantum interference of two atomic transitions, we found the energy exchange between the atom and PC reservoir is the lowest as the excited states become degenerate but with maximum quantum interference when the atom is prepared at one of the excited states. The results also show that excited states prefer to stay out of phase at all detuning energy except for near degenerate. Therefore, we can control the spontaneous emission rate not only by the amount of detuning frequencies but also the relative phase of initial states.
Considering a three-level $\ensuremath{\Lambda}$-type atom with both transitions coupled to a single photonic-band-gap reservoir, we investigate the upper-state population and spontaneous emission spectra by using the resolvent operator for the isotropic dispersion model, and give their analytical solutions. For the case of two transitions coupled to the same reservoir, the upper-state population always displays an oscillatory behavior and finally reaches a steady-state value. For atomic transition frequencies in the vicinity of the band-gap edge or inside the gap, the spontaneous emission spectra become strongly non-Lorentzian.
We study the influence of quantum interference on the spontaneous emission from an excited two-level atom when either the atomic upper or lower level is coupled by a coherent field to a third, usually higher-lying, state. In the case of the upper level coupling, destructive quantum interference between two competing decay amplitudes produces a dark line in the emission spectrum, a phenomenon that should not be confused with the well known population trapping, and a narrowing of one of the two side lobes that make up the spectral profile. Quantum interference is absent, instead, in the case of the lower level coupling, and the spectrum modified by the external driving field is just the incoherent superposition of two Lorentzian lines. We suggest a physical interpretation of these results. In addition, we compare the analytic predictions of the simplest nontrivial versions of these models with more realistic but nonanalytic descriptions and show, numerically, that the interference effects persist in the upper level case even when additional complications are taken into account.
A two-level atom coupled to a reservoir with Lorentzian spectral response function is considered. It is shown that if the free oscillations of the atomic dipole are suitably modulated by an external field, then the dynamics of the spontaneous decay can be strongly modified. As a result, the probability of finding the atom in an excited state can be large even for very long times. This is because the frequency modulation may lead to both effective detuning of the atom from the resonance with reservoir modes and to effective cancellation of the coupling between the atom and the reservoir. Non-Markovian features of the reservoir are found to be essential for this effect to be observable. Conditions of experimental verifications are provided.
The dynamics of a three-level Λ-atom coupled to a structured reservoir has been investigated. Comparing the Lorentzian time-dependent decay rate and population dynamics for the weak coupling regime with those for the strong coupling regime, we note that non-Markovian features exist in both regimes, but population dynamics shows fairly different behaviors. Moreover, the different positions of the two transition frequencies with respect to the structured reservoir reduces the influence of non-Markovian effects on population dynamics. Based on the non-Markovianity, we give an intuitive interpretation of the result that the non-Markovian effects have little influence on population dynamics in the weak coupling regime, but have an obvious influence in the strong coupling regime.