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arXiv:1404.5754 · Physical Review A

Quantum entanglement due to a modulated dynamical Casimir effect

Xavier Busch, Renaud Parentani, Scott Robertson

Published Jun 6, 2014• 33 citations
arXivHTMLPDF

Abstract

We study the creation and entanglement of quasiparticle pairs due to a periodic variation of the mode frequencies of a homogeneous quantum system. Depending on the values of the parameters describing the periodic modulation, the number of created pairs either oscillates or, in a narrow resonant frequency interval, grows exponentially in time. For a system initially in a thermal state, we determine in which cases the final state is quantum mechanically entangled, i.e., where the bipartite state is nonseparable. We include some weak dissipation, expected to be found in any experimental setup, and study the corresponding reduction of the quantum entanglement. Our findings are used to interpret the results of two recent experiments.

DOI
10.1103/physreva.89.063606

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We study the creation and entanglement of quasiparticle pairs due to a periodic variation of the mode frequencies of a homogeneous quantum system. Depending on the values of the parameters describing the periodic modulation, the number of created pairs either oscillates or, in a narrow resonant frequency interval, grows exponentially in time. For a system initially in a thermal state, we determine in which cases the final state is quantum mechanically entangled, i.e., where the bipartite state is nonseparable. We include some weak dissipation, expected to be found in any experimental setup, and study the corresponding reduction of the quantum entanglement. Our findings are used to interpret the results of two recent experiments.
We study the parametric resonance in a system of two coupled quantum harmonic oscillators when the frequency of one of them (describing the field mode) is modulated at exactly twice the unperturbed eigenfrequency (the case of 'unshifted resonance'). The coordinate–momentum coupling between the two oscillators is chosen in order to simulate the dynamical Casimir effect in a cavity containing a harmonic oscillator detector (LC-contour). Analytical solutions are obtained with the aid of the multiple scales method. For the field mode and detector initially prepared in thermal squeezed states, we calculate the mean numbers of quanta in both modes, as well as the invariant squeezing coefficients, purity and photon distribution functions, analyzing the influence of coupling strength and frequency modulation depth on the dynamics of these quantities. We show that the system goes to strongly squeezed states even for high temperature initial states of the detector. Depending on the relative strength of coupling coefficient and the parametric modulation amplitude, initially separable states go to permanently entangled states or they show periodic appearance and disappearance of entanglement.
We theoretically study the dynamics of the ground-state cooling and the quantum entanglement in a modulated optomechanical system, where the frequency of the mechanical oscillator and the optical field or the strength of the driving laser is time dependent. In this paper, we focus mainly on the fact that the system works in the regime of blue detuning. It is found that in the long-time limit the steady-state phonon number can be decreased significantly so that the mechanical oscillator is cooled to the ground state by appropriately selecting the frequency and the amplitude of the modulation. Further, with the help of the dynamical modulation in the system, the time evolution of the entanglement preevaluation value displays the death and rebirth of quantum entanglement between the mechanical oscillator and the optical field, which correspond, respectively, to the increase and decrease of the effective phonon number of the mechanical oscillator. In particular, when the steady-state dynamics of the system is quasiperiodic, the dynamics of the entanglement preevaluation value exhibits a quasiperiodic behavior, which means that the quantum phenomena can be represented in nonlinear classical dynamics.
We study the entanglement dynamics of two coupled mechanical oscillators, within a modulated optomechanical system. We find that, depending on the strength of the mechanical coupling, one could observe either a stationary or a dynamical behavior of the mechanical entanglement, which is extremely robust against the oscillator temperature. Moreover, we have shown that this entanglement dynamics is strongly related to the stability of the normal modes. Taking mechanical damping effects into account, an analytical expression corresponding to the critical mechanical coupling strength, where the transition from stationary to dynamical entanglement occurs, is also reported. The proposed scheme is analyzed with experimentally realistic parameters, making it a promising means to realize macroscopic quantum entanglement within current state-of-the-art experimental setups.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the generation and evolution of entanglement in terms of the covariance matrix for an arbitrary Gaussian input state. For some values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation or entanglement collapse (entanglement sudden death) take place or even a periodic collapse and revival of entanglement. We show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuousvariable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment.Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the generation and evolution of entanglement in terms of the covariance matrix for an arbitrary Gaussian input state.For some values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled.In other cases, entanglement generation or entanglement collapse (entanglement sudden death) take place or even a periodic collapse and revival of entanglement.We show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable.We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.
We propose a theoretical approach for entangling two Dicke states in a periodic modulated quantum system. By considering two qubit ensembles that are nonuniformly coupled to a common resonator, we can derive an effective Hamiltonian whose energy levels depend nonlinearly on the excitation number of each qubit ensemble. A more simplified effective Hamiltonian can be obtained by selecting the appropriate driving parameters and initial state. Based on the dynamic evolution of the effective Hamiltonian, we can selectively achieve Dicke state transitions and generate entangled Dicke states controllably. For a special case, we can obtain ensemble-ensemble entangled states by performing a projective even-odd cat-state measurement. By implementing Gaussian soft temporal modulation, we can effectively suppress off-resonant contributions in the interaction and enhance the fidelity of target states. Furthermore, by utilizing the Holstein-Primakoff transformation, we study the resonator-ensemble coupling system in the thermodynamic limit and investigate the generation of entangled magnon states. Additionally, we propose a scheme of creating magnon NOON states through frequency modulation and study the influence of decoherence on the fidelity of target states.