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Dynamics of an open quantum system interacting with a quantum environment

Athreya Shankar, S. Lakshmibala, V. Balakrishnan

Published Aug 17, 2016• 6 citations
OpenAlex

Abstract

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).

Related papers

Dynamics of an open quantum system interacting with a quantum environment

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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 $Q$ 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).

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Generation of Entanglement Between Two Noninteracting Qubits via Interaction with Nonclassical Radiation Field

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We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes–Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.

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Chaos and entanglement in atomic systems interacting with photons

Alexander V. Gorokhov

The influence of chaotic behavior of coherent state (CS) parameters on entanglement dynamics in system of two level atoms and photons in cavity is investigated. The initial state of the system is chosen as factorized production of photon and atomic coherent states. To find a solution of the Schrödinger equation, we presented the time-dependent wave function in the form of a wave packet in CS representation. The phase portraits and Poincare sections for classical dynamics of CS were computed, and time dependence of the mean number of photons level populations and atomic entropy were calculated in quantum case. The analysis showed that the chaotic behavior in quantum-optical Dicke model increases the degree of entanglement in the atomic subsystem. At the same time greater entanglement is generated when selecting the initial atomic CS parameters near the center of the corresponding Poincare sections. It is considered dynamics of two identical two-level atoms in non-ideal cavity (nonideal Tavis-Cummings model). Accounting for decay showed that the generation of atomic entanglement is accompanied by the return of the initial separable state (”death” of entanglement), but this behavior with the increase of the initial parameter of the field CS is only at sufficiently small times. Influence of detuning and damping constants are considered.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 26, 2013•7 citations
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 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.
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.
In this paper, an analytical model for the interaction between a moving -type three-level atom and a two-mode radiation field is presented with two-photon transition and in the intensity-dependent coupling regime. After specifying the initial conditions for the atom and the field, the explicit form of the state vector of the entire system is obtained via the time evolution operator. In order to study the entanglement between subsystems, atom and field, temporal behavior of the von Neumann entropy, as a measure of entanglement, is examined.
We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes–Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.
The influence of chaotic behavior of coherent state (CS) parameters on entanglement dynamics in system of two level atoms and photons in cavity is investigated. The initial state of the system is chosen as factorized production of photon and atomic coherent states. To find a solution of the Schrödinger equation, we presented the time-dependent wave function in the form of a wave packet in CS representation. The phase portraits and Poincare sections for classical dynamics of CS were computed, and time dependence of the mean number of photons level populations and atomic entropy were calculated in quantum case. The analysis showed that the chaotic behavior in quantum-optical Dicke model increases the degree of entanglement in the atomic subsystem. At the same time greater entanglement is generated when selecting the initial atomic CS parameters near the center of the corresponding Poincare sections. It is considered dynamics of two identical two-level atoms in non-ideal cavity (nonideal Tavis-Cummings model). Accounting for decay showed that the generation of atomic entanglement is accompanied by the return of the initial separable state (”death” of entanglement), but this behavior with the increase of the initial parameter of the field CS is only at sufficiently small times. Influence of detuning and damping constants are considered.