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Acta Physica Sinica

Evolution of entanglement between a two-level atom and spontaneous emission field in structured reservoir

Haozhen Li, Xie Shuang-Yuan, Xu Jing-Ping, Yang Ya-Ping

Published Jan 1, 2014• 0 citations
Publisher

Abstract

The time evolutions of the entanglement between a two-level atom and its spontaneous emission field in free space, cavity, isotropic and anisotropic photonic crystal are studied by using quantum entropy. It is found that the evolution properties of the atom-field entanglement are directly related to the nature of the structured reservoir,specifically, to the distribution of the density of modes. In free space and cavity, as the density of the modes varies smoothly with frequency, the atom-field entanglement decays to zero in a finite time. However in an isotropic and anisotropic photonic crystal, the atom-field entanglement can keep steady due to the existence of a photonic band gap in the density of the modes. Thus, we can control the time evolution of the entanglement between the atom and its spontaneous emission field by changing the density of the modes of the structured reservoirs.

DOI
10.7498/aps.63.124201

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The time evolutions of the entanglement between a two-level atom and its spontaneous emission field in free space, cavity, isotropic and anisotropic photonic crystal are studied by using quantum entropy. It is found that the evolution properties of the atom-field entanglement are directly related to the nature of the structured reservoir,specifically, to the distribution of the density of modes. In free space and cavity, as the density of the modes varies smoothly with frequency, the atom-field entanglement decays to zero in a finite time. However in an isotropic and anisotropic photonic crystal, the atom-field entanglement can keep steady due to the existence of a photonic band gap in the density of the modes. Thus, we can control the time evolution of the entanglement between the atom and its spontaneous emission field by changing the density of the modes of the structured reservoirs.
By means of Von Neumann entropy and Schmidt number K, we study the time evolution properties of the entanglement between a two-level atom and spontaneous emission field in anisotropic photonic crystal. The evolution properties of the atom-field entanglement are directly related to the relative position of the upper level from the band edge. The atom-field entanglement can keep steady when the atomic upper level is within the band gap. The atom-field entanglement increases to the maximum value firstly and then decay to zero when the atomic upper level is within the transmitting band. The atom-field entanglement also depends on the initial state of the atom. We can control the time evolution properties of the atom-field entanglement by choosing special atomic initial state and the relative position of the upper level from the band edge.
We have studied the properties of the spontaneous emission from a two-level atom embedded in two-band photonic crystals. Due to the anisotropic two-band dispersion relation, the localized and propagating fields cannot coexist, this leads to the non-quasi-oscillation behaviour of the upper level population. Thus the upper level population will tend to a constant as time goes to infinity, or decay with time in a power law, or decay with time exponentially, different from that in the isotropic one-band dispersion relation case. These properties are directly related to the relative position of the upper level from the band edge and the width of the gap.
We theoretically investigate the spontaneous emission light of an excited three-level atom embedded in an anisotropic photonic crystal with two asymmetric bands. The property of spontaneous emission relating to the atomic position in a unit cell of the crystal is described with a position-dependent phase difference. The atomic transition in free space can be manipulated by the other associated transition coupling to photonic crystal. The result shows that the spontaneous emission spectra are effectively shifted and tuned by the atomic position-dependent phase, which results in the asymmetric distribution of the photonic density of states between two bands, and the increasing band can push the emitted light towards the other band. The physical process can be further illuminated through analyzing the emitted field in photonic crystal. The result perhaps offers an interesting route towards tunable photonic devices.
Spontaneous emission from a two-level atom embedded in photonic crystals was investigated in this paper. Due to the photon localization and the quantum interference between the two dressed states, some changes in the radiation field take place: when the excited level moves from the gap to the band, the energy of the localized field is transferred to the propagating field through the diffusion field. If the localized field and the propagating field could coexist, the population evolution in the excited level would exhibit quasi-oscillation behavior. If they could not coexist, there would be no quasi-oscillation. The steady-state trapped atom population in the excited level is changed also. All these characteristics depend not only on the relative position δ of the excited level ω _1 with respect to the band-edge ω _c but also on the photon density of states ρ(ω_k) (or the band-edge smoothing parameter e ) near the band edge.
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.
[[abstract]]We study the spontaneous emission (SE) spectra of a three-level A-type atom in photonic crystals. The air-band, the dielectric-band and the free-space vacuum reservoirs coupled with the atom are considered. With the consideration of the phase difference between the air-band and the dielectric-band fields, two band reservoirs become coherent and can interfere with each other. This interference effect depends on the embedded position of the atom and the band-gap width and can affect the SE spectrum. The effect of this interference on the SE spectrum is shown.