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arXiv:1403.3637 · Physical Review A

Nonlinearity-induced entanglement stability in a qubit-oscillator system

Víctor Montenegro, Alessandro Ferraro, Sougato Bose

Published Jul 23, 2014• 16 citations
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Abstract

We consider a system composed of a qubit interacting with a quartic (undriven) nonlinear oscillator (NLO) through a conditional displacement Hamiltonian. We show that even a modest nonlinearity can enhance and stabilize the quantum entanglement dynamically generated between the qubit and the NLO. In contrast to the linear case, in which the entanglement is known to oscillate periodically between zero and its maximal value, the nonlinearity suppresses the dynamical decay of the entanglement once it is established. While the entanglement generation is due to the conditional displacements, as noted in several works before, the suppression of its decay is related to the presence of squeezing and other complex processes induced by two- and four-phonon interactions. Finally, we solve the respective Markovian master equation, showing that the previous features are preserved also when the system is open.

DOI
10.1103/physreva.90.013829

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An analytical solution for a master equation describing the dynamics of a qubit interacting with a nonlinear Kerr-like cavity through intensity-dependent coupling is established. A superposition of squeezed coherent states is propped as the initial cavity field. The dynamics of the entangled qubit-cavity states are explored by negativity for different deformed function of the intensity-dependent coupling. We have examined the effects of the Kerr-like nonlinearity and the qubit-cavity detuning as well as the phase cavity damping on the generated entanglement. The intensity-dependent coupling increases the sensitivity of the generated entanglement to the phase-damping. The stability and the strength of the entanglement are controlled by the Kerr-like nonlinearity, the qubit-cavity detuning, and the initial cavity non-classicality. These physical parameters enhance the robustness of the qubit-cavity entanglement against the cavity phase-damping. The high initial cavity non-classicality enhances the robustness of the qubit-cavity entanglement against the phase-damping effect.
We study a particular form of interaction Hamiltonian between qubits and quantum harmonic oscillators, whose closed system dynamics results in qubit controlled displacement operations. We show how this interaction is realizable in many setups, including nanomechanical systems, ion traps, cavity QED and circuit QED, and in each context we provide quantitative estimates for the relevant parameters. The dynamics of the system is investigated through a master equation, including typical decoherence mechanisms resulting from the coupling of the qubit and oscillator to a thermal Markovian environment. We show how to solve the master equation by adopting a phase-space representation for the oscillator, and derive analytical and approximate solutions for many special cases of interest. Finally, our techniques are applied to a relevant example by studying the dynamics of qubit-oscillator entanglement and the preparation of oscillator states with negative Wigner function.
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness--Bloch--Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
In this paper, we present a theoretical scheme for the generation and manipulation of bipartite atom–atom entanglement in a dissipative optomechanical system containing two atoms in the presence of linear and nonlinear (quadratic) couplings. To achieve the goal of paper, we first obtain the interaction Hamiltonian in the interaction picture, and then, by considering some resonance conditions and applying the rotating wave approximation, the effective Hamiltonian, which is independent of time, is derived. In the continuation, the system solution was obtained via solving the Lindblad master equation, which includes atomic, optical and mechanical dissipation effects. Finally, bipartite atom–atom entanglement is quantitatively discussed, by evaluating the negativity, which is a well-known measure of entanglement. Our numerical simulations show that a significant degree of entanglement can be reached via adjusting the system parameters. It is noticeable that the optical and mechanical decay rates play an important role in the quasi-stability and even stability of the obtained atom–atom entanglement.