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arXiv:quant-ph/0603020 · Journal of Physics B Atomic Molecular and Optical Physics

Wave packet dynamics of entangled two-mode states

C Sudheesh, S Lakshmibala, V Balakrishnan

Published Aug 8, 2006• 21 citations
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Abstract

We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The 'overlap fidelity' of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglement in the vicinity of near-revivals. The expectation values and higher moments of suitable quadrature variables are also examined, with reference to possible squeezing and higher order squeezing. The power spectra of the time series generated by the mean photon number are presented for initial states corresponding, respectively, to a coherent state and a photon-added coherent state. When the nonlinearity in the Hamiltonian is weak, these show signatures of quasiperiodicity.

DOI
10.1088/0953-4075/39/16/017

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We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The 'overlap fidelity' of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglement in the vicinity of near-revivals. The expectation values and higher moments of suitable quadrature variables are also examined, with reference to possible squeezing and higher order squeezing. The power spectra of the time series generated by the mean photon number are presented for initial states corresponding, respectively, to a coherent state and a photon-added coherent state. When the nonlinearity in the Hamiltonian is weak, these show signatures of quasiperiodicity.
We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium, and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state, or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The ``overlap fidelity'' of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglement in the vicinity of near-revivals. The expectation values and higher moments of suitable quadrature variables are also examined, with reference to possible squeezing and higher-order squeezing.
Abstract. We examine the dynamics of subsystems of bipartite and tripartite quantum systems with nonlinear Hamiltonians. We consider two models which capture the generic features of open quantum systems: a three-level atom interacting with a single-mode radiation field, and a three-level atom interacting with two field modes which do not directly interact with each other. The entanglement of specific initially unentangled states of the atom-field system is examined through the time-varying subsystem von Neumann entropy (SVNE). The counterparts of near-revivals and fractional revivals of the initial state are clearly identifiable in the SVNE in all cases where revival phenomena occur. The MandelQ parameter corresponding to the photon number of a radiation field is obtained as a function of time in both models. In those cases where revivals are absent, a time series analysis of the mean photon number reveals a variety of ergodicity properties (as manifested in return maps, recurrence-time distributions and Lyapunov exponents), depending on the strength of the nonlinearity and the degree of coherence of the initial state of the radiation field(s).
We examine the dynamics of subsystems of bipartite and tripartite quantum systems with nonlinear Hamiltonians. We consider two models which capture the generic features of open quantum systems: a three-level atom interacting with a single-mode radiation field, and a three-level atom interacting with two field modes which do not directly interact with each other. The entanglement of specific initially unentangled states of the atom-field system is examined through the time-varying subsystem von Neumann entropy (SVNE). The counterparts of near-revivals and fractional revivals of the initial state are clearly identifiable in the SVNE in all cases where revival phenomena occur. The Mandel QQQ parameter corresponding to the photon number of a radiation field is obtained as a function of time in both models. In those cases where revivals are absent, a time series analysis of the mean photon number reveals a variety of ergodicity properties (as manifested in return maps, recurrence-time distributions and Lyapunov exponents), depending on the strength of the nonlinearity and the degree of coherence of the initial state of the radiation field(s).
We show in the framework of a tractable model that revivals and fractional revivals of wave packets afford clear signatures of the extent of departure from coherence and from Poisson statistics of an initial state of the radiation field propagating in a nonlinear medium. We establish this by considering a generic Hamiltonian which models wave packet propagation in a Kerr-like medium, and comparing the non-classical effects displayed by an initial photon-added coherent state with that of an inital ideal coherent state.
Abstract This paper explores the wave packet dynamics of a math-type q-deformed field interacting with atoms in a Kerr-type nonlinear medium. The primary focus is on the generation and dynamics of entanglement using the q-deformed field, with the quantification of entanglement accomplished through the von Neumann entropy. Two distinct initial q-deformed states, the q-deformed Fock state, and the q-deformed coherent state, are investigated. The entanglement dynamics reveal characteristics of periodic, quasi-periodic, and chaotic behaviour. Non-deformed initial states display wave packet near revivals and fractional revivals in entanglement dynamics while introducing q-deformation eliminates these features. The q-deformation significantly influences wave packet revivals and fractional revivals, with even a slight introduction causing their disappearance. For large values of q, the entanglement dynamics exhibit a chaotic nature. In the case of a beam splitter-type interaction applied to the initial deformed Fock state, an optimal deformation parameter q is identified, leading to maximum entanglement exceeding the non-deformed scenario.
Treating the ideal coherent state as a reference state, the effects due to departure from coherence of an initial wave packet propagating through a nonlinear medium, were examined, specifically in the context of non-classical effects such as revivals, fractional revivals, squeezing and higher-order squeezing during its temporal evolution. Further, these studies were extended to examine the role of quantum entanglement in bipartite systems. The dynamics of quantum expectation values were tracked carefully in various cases and the conditions under which a wave packet spreads chaotically, were investigated.