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Quantum Information Review

Geometric phase as entanglement probe in a pumped three-level atom placed near a dielectric

M. S. Ateto

Published Jul 1, 2013• 1 citation
Publisher

Abstract

We introduce new features of the connection between entanglement induced by interaction and geometric phase acquired by a composite quantum system. Geometric phase, that reflects Bell angle between input and output photons in atom-cavity interaction, for a bipartite system under the inuence of a dielectric of Lorentzian permitti vity, is examined. We show that, with adjustment of Bell angle, typical features of atom-cavity entanglement can be obtained by considering a three- level appropriately positioned with respect to macroscopic bodies. We find that, due to the strong non-Mark ovian memory effects, phase Rabi oscillations, a principal signature of strong symmetrically or antisymmetrically photons evolution, ar e stimulated with atom farther from a medium with low oscillation frequency. On death of Rabi oscillations, which means symmetric entangled photons, a strong long-time-scale atom-cavity entanglement can be produced, specially, below the band gap region where the radiative decay dominates. This feature conicts the case of pure vacuum where atom-cavity entanglement decays exponentially. The feature that, our system is acting as a beam splitter (BS), is also, in detail, discussed. The results are of strong applications in constru ction of the universal quantum logic gates.

DOI
10.12785/qir/010202

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We introduce new features of the connection between entanglement induced by interaction and geometric phase acquired by a composite quantum system. Geometric phase, that reflects Bell angle between input and output photons in atom-cavity interaction, for a bipartite system under the inuence of a dielectric of Lorentzian permitti vity, is examined. We show that, with adjustment of Bell angle, typical features of atom-cavity entanglement can be obtained by considering a three- level appropriately positioned with respect to macroscopic bodies. We find that, due to the strong non-Mark ovian memory effects, phase Rabi oscillations, a principal signature of strong symmetrically or antisymmetrically photons evolution, ar e stimulated with atom farther from a medium with low oscillation frequency. On death of Rabi oscillations, which means symmetric entangled photons, a strong long-time-scale atom-cavity entanglement can be produced, specially, below the band gap region where the radiative decay dominates. This feature conicts the case of pure vacuum where atom-cavity entanglement decays exponentially. The feature that, our system is acting as a beam splitter (BS), is also, in detail, discussed. The results are of strong applications in constru ction of the universal quantum logic gates.
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.
Within the framework of exact quantum electrodynamics in dielectric, we study the topological Berry phase of a classically pumped ΛΛΛ-type three-level atom, prepared initially in a superposition of its two pumped levels and located near a planar dielectric half-space with model permittivity of Lorentz type, interacts with a vacuum field. The effects of material losses, expressed in terms of the Green tensor of the dielectric-matter formation including dispersion and absorption, on the topological Berry phase of the photon transition between the pumped levels have been studied. The outcomes are compared with that of an atom in free space. We expect, the additional noise due to presence of the dielectric will modify, in a unified way, the behavior and values measured of the phase shift between the wavefunction evolution and its original state. It is shown that for small separation distance between atom and the dielectric surface, the angle separation between the wavefunction evolution and the original state reduced noticeably that is of strong applications in construction of the universal quantum logic gates. Further, the study opens routes for new challenging applications of atomically systems as various sources of coherent light emitted by pumped atoms in dielectric surroundings.
Quantum entanglement is one of most remarkable features of quantum mechanics,and in recent years it has played a more and more important role in quantum information.However,real quantum system inevitably interacts with the environment,resulting in the entanglement decay or even entanglement sudden death,so it is necessary to study the entanglement dynamical properties of an open system under different environments.In this paper,we investigate the entanglement dynamic behaviors of three interacting two-level atoms in an optical cavity which is coupled to a structured zero-temperature bosonic reservoir.Laplace transform,LBC and other methods are utilized,through numerical method we analyze the entanglement dynamic behavios of tripartite of three atoms and bipartite of cavity and reservoir.We also discuss how the coupling parameters affect the entanglement dynamics.Results show that in a short time,the entanglement of tripartite increases with coupling strength of three atoms increasing,and a periodic oscillation appears, but entanglement of bipartite decreases.The entanglement of tripartite decreases with the coupling strength between atoms and cavity increasing and damping oscillation appears,but the entanglement of bipartite increases.In a long-time limit,the entanglement approaches to a steady value.The non-Markovian dynamics of the qubits is determined by both the coupling strength and the spectral width.The strong system-reservoir coupling regime results in the non-Markovian dynamics of system.As the spectral width increases,the system of three atoms transforms from non-Markovian regime to Markovian regime.The increasing of spectral width results in the Markovian dynamic behavior of system,but the system of the atoms falls into the non-Markovian regime once more.When the coupling between the cavity and reservoir is weak,the entanglement of three atoms increases as the detuning of the cavity and reservoir increases,but it is not obvious.When the coupling between the cavity and reservoir is strong,the entanglement of three atoms increases and a periodic oscillation appears with increasing the detuning between the cavity and reservoir,so we can effectively restrain the effects of dissipation of reservoir on entanglement decay by adjusting the detuning between the cavity and reservoir.
Quantum Rabi oscillation in cavity quantum electrodynamics is at the very heart of the interaction of an atomic system with a single electromagnetic field in a resonator. It has proved a powerful tool to entangle the atom with the field in the case of an empty cavity (vacuum Rabi oscillation). On the other side, as soon as the field is macroscopic, its state seems unaffected and one observes the well-known phenomenon of classical Rabi oscillation which only affects the atomic populations. We propose to experimentally investigate the frontier between those two behaviours, when one has to take into account the fluctations of the photon number. In order to do so, we let interact circular Rydberg atoms with a microwave resonator in which a mesocopic field is injected (a few tens of photons). We observe a strong correlation between specific atomic states and the phase of the injected field, which is measured by a homodyne technique. Those correlations explain in an easy way all the standard features of quantum Rabi oscillations (especially the collapses and revivals). Moreover they allow for the preparation of atom-field entangled state as well as non classical Schroedinger cat like states for the field.
The temporal evolution of two coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons. The general state of the system is a linear superposition of symmetric and antisymmetric states with the symmetric states controlled by two of the four eigenfrequencies and the antisymmetric states by the other two. The system undergoes Rabi oscillations between the two symmetric (antisymmetric) states. There is state transfer between the cavities when both atoms are in the ground state and two photons are exchanged. In addition, there is also Rabi ``flopping'' whereby one atom is in the excited state and the other in the ground state and the roles are reversed in a periodic fashion by the exchange of two photons. The generation of entanglement can be explicitly given as a function of time. Models of coupled cavities are of interest in distributed quantum information and computation.
We present a feasible scheme to investigate the geometric phase for an atom trapped in an optical cavity induced by the effective decay process due to cavity photon loss. The cavity mode, together with the external driving fields, acts as the engineered environment of the atom. When the parameters of the reservoir is adiabatically and cyclically changed, the system initially in the nontrivial dark state of the effective Lindblad operator undergoes a cyclic evolution and acquires a geometric phase. The geometric phase can be observed with the atomic Ramsey interference oscillation in the decoherence-free subspace.