Dogra Shruti, Madhok Vaibhav, Lakshminarayan Arul
Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
Phys Rev E. 2019 Jun;99(6-1):062217. doi: 10.1103/PhysRevE.99.062217.
Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important-more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to nonintegrability are under active investigation. In this work, we study quantum systems of few qubits collectively modeled as a kicked top, a textbook example of quantum chaos. In particular, we show that the three- and four-qubit cases are exactly solvable and yet, interestingly, can display signatures of ergodicity and thermalization. Deriving analytical expressions for entanglement entropy and concurrence, we see agreement in certain parameter regimes between long-time average values and ensemble averages of random states with permutation symmetry. Comparing with results using the data of a recent transmons-based experiment realizing the three-qubit case, we find agreement for short times, including a peculiar steplike behavior in correlations of some states. In the case of four qubits we point to a precursor of dynamical tunneling between what in the classical limit would be two stable islands. Numerical results for larger number of qubits show the emergence of the classical limit including signatures of a bifurcation.
展现出经典混沌量子特征的精确可解模型既罕见又重要——鉴于孤立量子系统中的遍历行为和热化机制及其与不可积性的联系正在积极研究中，其重要性更是凸显。在这项工作中，我们研究了集体建模为受驱转子的少数量子比特量子系统，这是量子混沌的一个典型例子。特别地，我们表明三比特和四比特的情况是精确可解的，然而，有趣的是，它们可以展现出遍历性和热化的特征。通过推导纠缠熵和并发度的解析表达式，我们发现在某些参数区域，长时间平均值与具有置换对称性的随机态的系综平均值之间存在一致性。与使用最近基于跨导量子比特实现三比特情况的实验数据得到的结果进行比较，我们发现短时间内存在一致性，包括某些态的关联中出现的奇特阶梯状行为。在四比特的情况下，我们指出了在经典极限下将是两个稳定岛之间的动态隧穿的一个先兆。更多量子比特的数值结果显示了经典极限的出现，包括分岔的特征。
