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arXiv:1510.06159 · Communications in Theoretical Physics

Temporal Behavior of Rabi Oscillation in Nanomechanical QED System with a Nonlinear Resonator

Xiao Xiao, Mingyue Zhao, Shu-Min 书敏 Yu 于, Yibo Gao

Published Mar 1, 2016• 2 citations
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Abstract

Abstract In nanomechanical QED system, consisting of a charge qubit and a nanomechanical resonator with intrinsic nonlinearity, we study the temporal behavior of Rabi oscillation in the nonlinear Jaynes–Cummings model. Using microscopic master equation approach, we solve time evolution of the density operator describing this model. Also, the probability of excited state of charge qubit is calculated. These analytic calculations show how nonlinearity parameter and decay rates of two different excited states of the qubit-resonator system affect time-oscillating and decaying of Rabi oscillation.

DOI
10.1088/0253-6102/65/3/273

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Abstract In nanomechanical QED system, consisting of a charge qubit and a nanomechanical resonator with intrinsic nonlinearity, we study the temporal behavior of Rabi oscillation in the nonlinear Jaynes–Cummings model. Using microscopic master equation approach, we solve time evolution of the density operator describing this model. Also, the probability of excited state of charge qubit is calculated. These analytic calculations show how nonlinearity parameter and decay rates of two different excited states of the qubit-resonator system affect time-oscillating and decaying of Rabi oscillation.
Considering the intrinsic nonlinearity in a nanomechanical resonator coupled to a charge qubit, vacuum Rabi splitting effect is studied in a nanomechanical QED (qubit-resonator) system. A driven nonlinear Jaynes-Cummings model describes the dynamics of this qubit-resonator system. Using quantum regression theorem and master equation approach, we have calculated the two-time correlation spectrum analytically. In the weak driving limit, these analytical results clarify the influence of the driving strength and nonlinearity parameter on the correlation spectrum. Also, numerical calculations confirm these analytical results.
在 nanomechanical 证完系统，与内在的非线性由费用 qubit 和一个 nanomechanical 共鸣器组成，我们在非线性的 JaynesCummings 模型学习 Rabi 摆动的时间的行为。用显微镜的主人方程途径，我们解决描述这个模型的密度操作员的时间进化。另外，费用 qubit 的激动的状态的概率是计算的。这些分析计算显示出 qubit 共鸣器系统的二个不同激动的状态的非线性参数和腐烂率怎么影响 Rabi 震荡时间、腐烂摆动。
When the nonlinearity of nanomechanical resonator is not negligible, the quantum decoherence of charge qubit is studied analytically. Using nonlinear Jaynes—Cummings model, one explores the possibility of being quantum data bus for nonlinear nanomechanical resonator, the nonlinearity destroys the dynamical quantum information-storage and maintains the revival of quantum coherence of charge qubit. With the calculation of decoherence factor, we demonstrate the influence of the nonlinearity of nanomechanical resonator on engineered decoherence of charge qubit.
We propose and study an "intrinsic probing" approach, without introducing any external detector, to mimic cavity QED effects in a qubit-nanomechanical resonator system. This metallic nanomechanical resonator can act as an intrinsic detector when a weak driving current passes through it. The nanomechanical resonator acts as both the cavity and the detector. A cavity QED-like effect is demonstrated by the correlation spectrum of the electromotive force between the two ends of the nanomechanical resonator. Using the quantum regression theorem and perturbation theory, we analytically calculate the correlation spectrum. In the weak driving limit, we study the effect on the vacuum Rabi splitting of both the strength of the driving as well as the frequency-detuning between the charge qubit and the nanomechanical resonator. Numerical calculations confirm the validity of our intrinsic probing approach.
Environmental influences on the dynamics of a coupled qubit-oscillator system are studied analytically in a regime where deviations from the exactly solvable Jaynes–Cummings model are important. We investigate the case of a quasi-degenerate qubit within the ultra-strong coupling regime for which the qubit frequency is much smaller than the frequency of the oscillator, and the coupling between the qubit and the oscillator is large, both of which invalidate the usually employed rotating wave approximation. In contrast to the standard quantum optics master equation, we explicitly take the qubit-oscillator coupling into account while microscopically deriving a dressed state master equation. Using the derived master equation, we discuss a spectroscopic technique which can be used to probe the dressed energy-level structure of the qubit-oscillator system.
The dynamics of charge qubits coupled to a nanomechanical resonator under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits is considered. The focus of our analysis is devoted to multi partite entanglement and the effects arising from the coupling to the reservoir. It is shown that despite losses, entanglement formation may still persist for relatively long times and it is especially robust against temperature dependence of the reservoir. Together with control of system parameters, the system may therefore be especially suited for quantum information processing. Furthermore, our results shed light on the evolution of open quantum many-body systems. For instance, due to intrinsic qubit-qubit couplings our model is related to a driven XY spin model.