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Quantum Information Review

Non-Markovian Dynamics of Entanglement of three-level atom embedded in a 3D photonic band gap structure

M. S. Ateto

Published Jul 1, 2013• 4 citations
Publisher

Abstract

Entanglement evolution for a classically pumped three-level atom interacting with an anisotropic structured reservoir is studied. We demonstrate that entanglement decay is much slower in the reservoir with the memory effects. This point is beneficial for the implementation of quantum computation in the non-Markovian environments. Unlike the free-space case, the unusual reservoir stimulates stationary entanglement with amplitude depends strongly on the relative phase between the control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in a coherent superposition of the two upper levels. An optimal stationary degree of entanglement is achieved for negative relative phase, where both detunings - from the upper band gap and driving laser - are the same. Moreover, a significant stationary degre e of entanglement is reached, for high detuned upper levels with the pump laser pulse, on resonant frequency near the edge of the PBG. For entanglement in stationary regime, the Rabi frequency of the control laser field exceeds the rate of entanglement degradation or e nhancement for tuned or detuned frequency from the band gap, depending on the relative phase value.

DOI
10.12785/qir/010201

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Entanglement evolution for a classically pumped three-level atom interacting with an anisotropic structured reservoir is studied. We demonstrate that entanglement decay is much slower in the reservoir with the memory effects. This point is beneficial for the implementation of quantum computation in the non-Markovian environments. Unlike the free-space case, the unusual reservoir stimulates stationary entanglement with amplitude depends strongly on the relative phase between the control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in a coherent superposition of the two upper levels. An optimal stationary degree of entanglement is achieved for negative relative phase, where both detunings - from the upper band gap and driving laser - are the same. Moreover, a significant stationary degre e of entanglement is reached, for high detuned upper levels with the pump laser pulse, on resonant frequency near the edge of the PBG. For entanglement in stationary regime, the Rabi frequency of the control laser field exceeds the rate of entanglement degradation or e nhancement for tuned or detuned frequency from the band gap, depending on the relative phase value.
The coherent control of the entanglement between a three-level atom located within a three-dimensional (3D) anisotropic photonic band gap (PBG) material, with one transition frequency near the edge of the PBG, and its radiation field is demonstrated. As a result of quantum interference and photon localization, the entanglement can be decreased or increased depending on the relative phase between the control laser coupling, the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state entanglement is strongly dependent on the externally prescribed initial conditions. This non-zero steady-state entanglement is achieved by virtue of the localization of light in the vicinity of the emitting atom.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band gap (PBG) material, with one resonant frequency near the edge of the PBG. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This non-zero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive optical memory device on the atomic scale. The protected electric dipole within the PBG provides a basis for a qubit to encode information for quantum computations. A detailed literature survey on the nature, fabrication and applications of PBG materials is presented to provide context for this research.
A comparative study of a qutrit (three-level atomic system) coupled to a classical field in a typical Markovian reservoir (free space) and in a photonic-band-gap (PBG) crystal is carried out. The aim of the study is to assess the collective impact of a structured environment and classical control of the system on the dynamics of quantum coherence, non-Markovianity, and estimation of parameters that are initially encoded in the atomic state. We show that the constructive interplay of PBG material as a medium and a classical driving field as a part of the system results in a significant enhancement of all the quantum traits of interest, compared to the case when the driven qutrit is in a Markovian environment. Our results supply insights for preserving and enhancing quantum features in qutrit systems, which are promising alternative candidates to be used in quantum processors instead of qubits.
We examine the impact of the non-Markovian environment on the dynamical behavior of the quantum coherence and entropy squeezing considering a two-level atomic system (qubit) immersed in a reservoir with zero-temperature for two types of non-Markovian environments. We consider a cavity little off-resonance with the transition frequency of the qubit and the case of a non-perfect photonic band gap (PBG). We show that the amount of coherence is dependent on the structure of the environment and influenced through the memory effects. We obtain that the delay and revival of the coherence loss might take place by controlling the detuning of the cavity-qubit system. Whereas, a partial coherence trapping occurs in non-ideal PBG and the decrease of the gap width will destroy the coherence. On the other hand, we show the situation for which the squeezing is occurring and enhanced with respect to the main parameters for the system. Finally, we display the monotonic dependence of the quantum coherence and squeezing on the main model parameters.
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.
ABSTRACT We study the time evolution of quantum Fisher information and atom–field entanglement for a V‐type three‐level atom embedded in an anisotropic photonic bandgap crystal. The structured reservoir strongly modifies the atomic decay near the photonic bandgap, giving rise to non‐Markovian memory effects. By employing the quantum Fisher information matrix, we determine the quantum Cramér‐Rao bound for both single‐parameter estimation and simultaneous two‐parameter estimation encoded in the atomic initial state. In parallel, we investigate the dynamics of atom‐field entanglement, quantified through the Von Neumann entropy, to characterize the correlations resulting from the interaction with the photonic bandgap. Our results show that both the detuning of the atomic transition frequency from the upper band edge frequency and the initial relative phase play a crucial role in the attainable precision and long‐lived entanglement. These findings demonstrate the potential of photonic bandgap materials as structured reservoirs for protecting quantum information, sustaining long‐time entanglement, and enhancing multiparameter quantum metrology.