Lingzhen Guo, Zhigang Zheng, Xin-Qi Li, YiJing Yan
We investigate the dynamic quantum tunneling between two attractors of a mesoscopic driven Duffing oscillator. We find that, in addition to inducing remarkable quantum shift of the bifurcation point, the mesoscopic nature also results in a perfect linear scaling behavior for the tunneling rate with the driving distance to the shifted bifurcation point.
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We investigate the nonlinear dynamics of a mesoscopic driven Duffing oscillator in a quantum regime. In terms of Wigner function, we identify the nature of state near the bifurcation point, and analyze the transient process which reveals two distinct stages of quenching and escape. The rate process in the escape stage allows us to extract the transition rate, which displays perfect scaling behavior with the driving distance to the bifurcation point. We numerically determine the scaling exponent, compare it with existing result, and propose open questions to be resolved.
For suitable parameters, the classical Duffing oscillator has a known bistability in its stationary states, with low- and high-amplitude branches. As expected from the analogy with a particle in a double-well potential, transitions between these states become possible either at finite temperature, or in the quantum regime due to tunneling. In this analogy, besides local stability, one can also discuss global stability by comparing the two potential minima. For the Duffing oscillator, the stationary states emerge dynamically so that a priori, a potential-minimum criterion for them does not exis…
Dynamics of the quantum Duffing oscillator in the driving induced bistable regime
研究了非简谐单稳量子力学谐振腔在强周期驱动下的非线性响应。驱动，从而诱导一个有效的双稳态，其中可以识别共振隧穿。在Floquet分析的框架内，可以建立具有时间无关系数的有效Floquet-Born-Markovian主方程，该主方程可以直接求解。将描述包括共振隧穿和多光子跃迁的各种效应。我们的模型在纳米机电设备，如振动悬浮纳米线，以及在非破坏性的读出程序超导量子位涉及读出SQUID的非线性响应中找到应用。
Motivated by recent experimental progress to read out quantum bits implemented in superconducting circuits via the phenomenon of dynamical bifurcation, transitions between steady orbits in a driven anharmonic oscillator, the Duffing oscillator, are analyzed. In the regime of weak dissipation a consistent master equation in the semiclassical limit is derived to capture the intimate relation between finite tunneling and reflection and bath induced quantum fluctuations. From the corresponding steady state distributions analytical expressions for the switching probabilities are obtained. It is sho…
We study the effects of spin accumulation (inside reservoirs) on electronic transport with tunneling and reflections at the gates of a quantum dot. Within the stub model, the calculation focus on the current-current correlation function for the flux of electrons injected into the quantum dot. The linear response theory used allows to obtain the noise power in the regime of thermal crossover as a function of parameters that reveal the spin polarization at the reservoirs. The calculation is performed employing diagrammatic integration within the universal groups (ensembles of Dyson) for a non-id…
Quantum computing and quantum measurement with mesoscopic Josephson junctions
最近对约瑟夫森结的电荷态和通量态的量子相干性的实验证明表明，量子约瑟夫森动力学可以用于开发可扩展的量子逻辑电路。在这篇文章中，我回顾了约瑟夫森隧穿和约瑟夫森结量子比特的基本概念，并讨论了这种隧穿的两个问题的量子计算应用的动机。一个是SQUID系统中的光子辅助共振磁通隧道理论，用来证明磁通的量子相干性。二是SET静电计电荷的量子测量问题。结果表明，在库仑阻塞阈值处的SET静电计是共振隧穿区能量灵敏度达到$\hbar/\sqrt{3}$的量子限探测器。
Dynamics of a mesoscopic qubit under continuous quantum measurement
我们提出的条件量子动力学的电子隧穿两个量子点之间的测量使用低透明度点接触或隧道结。双点系统形成单个量子位，并且测量对应于量子点的占用的连续时间读出。我们说明了量子位的条件和无条件动力学之间的差异。条件动力学的讨论在两个制度取决于隧道通过点接触的速率：量子跳跃，其中个别电子隧道电流事件可以区分，和扩散动力学，其中个别事件被忽略，和时间平均电流被认为是一个连续的扩散变量。我们包括无效的测量和双点/点接触系统的两个隧穿振幅之间的相对相位的影响的效果。
Understanding the interaction between cavity photons and electronic nanocircuits is crucial for the development of Mesoscopic Quantum Electrodynamics (QED). One has to combine ingredients from atomic Cavity QED, like orbital degrees of freedom, with tunneling physics and strong cavity field inhomogeneities, specific to superconducting circuit QED. It is therefore necessary to introduce a formalism which bridges between these two domains. We develop a general method based on a photonic pseudo-potential to describe the electric coupling between electrons in a nanocircuit and cavity photons. In t…
We propose an electromechanical transducer based on a resonant-tunneling configuration that, with respect to the standard tunneling transducers, allows larger tunneling currents while using the same bias voltage. The increased current leads to an increase of the shot noise and an increase of the momentum noise which determine the quantum limit in the system under monitoring. Experiments with micromachined masses at 4.2 K could show dominance of the momentum noise over the Brownian noise, allowing observation of the quantum-mechanical noise at the mesoscopic scale.
Magnetic relaxation of superconducting quantum dot: two-dimensional false vacuum decay
涡旋的量子隧穿是描述高温超导体低温蠕变的一个重要新现象。我们推测，量子隧穿也可能表现在介观超导体由于被Bean-Livingston势垒捕获的涡旋。采用伦敦近似和镜像法对高温超导量子点中的势阱形状进行了估计。为了计算逃逸率，我们使用了瞬子技术。我们用一个量子粒子从二维基态在横向磁场作用下的隧穿来模拟涡旋。所得到的衰变率由瞬子的方法和传统的WKB进行比较，揭示彼此完全一致。
We propose and analyze a simple mesoscopic quantum heat engine that exhibits both high-power and high-efficiency. The system consists of a biased Josephson junction coupled to two microwave cavities, with each cavity coupled to a thermal bath. Resonant Cooper pair tunneling occurs with the exchange of photons between cavities, and a temperature difference between the baths can naturally lead to a current against the voltage, and hence work. As a consequence of the unique properties of Cooper-pair tunneling, the heat current is completely separated from the charge current. This combined with th…
Electron interference in mesoscopic devices in the presence of nonclassical electromagnetic fields
研究了介观干涉器件与非经典电磁场的相互作用。外部量子场在电荷上感应出相位因子。这个相位因子是标准Aharonov-Bohm相位因子的推广，在非经典电磁场的情况下是量子力学算符。它的期望值取决于描述非经典光子的密度矩阵，并决定了干涉。讨论了几个例子，表明非经典光子的量子噪声对电子干涉条纹的破坏很小。一个有趣的应用出现在远程电子干涉装置的背景下，用纠缠光子照射。在这种情况下，两个设备中的干扰电子变得纠缠。同样的想法也适用于非经典电磁场辐照的SQUID环。结果表明，通过约瑟夫森结的库珀对隧穿的统计特性依赖于光子的统计特性。
We propose to use a time-dependent imaginary potential to describe quantum mechanical tunneling through time-varying potential barriers. We use Gamow solutions for stationary tunneling problems to justify our choice of potential, and we apply our method to describe tunneling of a mesoscopic quantum variable: the phase change across a Josephson junction. The Josephson junction phase variable behaves as the position coordinate of a particle moving in a tilted washboard potential, and our general solution to the motion in such a potential with a time-dependent tilt reproduces a number of features…
The toric code based on Majorana fermions on mesoscopic superconducting islands is a promising candidate for quantum information processing. In the limit of vanishing Cooper-pair tunneling, it has been argued that the phase transition separating the topologically ordered phase of the toric code from the trivial one is in the universality class of (2+1)D-XY. On the other hand, in the limit of infinitely large Cooper-pair tunneling, the phase transition is in the universality class of (2+1)D-Ising. In this work, we treat the case of finite Cooper-pair tunneling and address the question of how th…
We demonstrate the control of quantum tunneling in an ultracold lattice gas by the measurement backaction imposed by an imaging process. A {\em in situ} imaging technique is used to acquire repeated images of an ultracold gas confined in a shallow optical lattice. The backaction induced by these position measurements modifies the coherent quantum tunneling of atoms within the lattice. By smoothly varying the rate at which spatial information is extracted from the atomic ensemble, we observe the continuous crossover from the 'weak measurement regime' where position measurements have little infl…
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