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理论物理通讯：英文版

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

肖骁, 赵明月, 于书敏, 高一波

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

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。

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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。
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.
The standard mathematical formalism of cavity QED leads us to consider photons as excitations of a quantum harmonic oscillator. Although it is one of the most familiar problems of quantum mechanics, some aspects of the quantum harmonic oscillator remain difficult to visualize, particularly in the rather abstract context of an electromagnetic field. Recently, modern microfabrication and refrigeration techniques have begun to allow the creation of nanoscale mechanical oscillators which can be cooled close to the quantum regime. Despite the extreme physical differences between an electromagnetic cavity and a nanomechanical resonator, both systems may be approximated by the same quantum harmonic oscillator model. However, the conceptual consequences of quantum behavior, and the challenges to physical intuition, are quite different in the two cases. Taking a mechanical point of view therefore allows fresh insight into the quantum harmonic oscillator problem. To illustrate the connection and how it may aid our understanding of light, the mathematical parallelism between an electromagnetic cavity and a mechanical resonator is demonstrated. Current nanomechanics experiments are discussed, and some possible quantum measurements are introduced. Finally, the discrepancies between the predictions of quantum mechanics and our experience of classical vibrating beams are considered, with an emphasis on how nanomechanics may be able to offer a new perspective on the nature of photons.
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.