Quantum Signatures of Chaos in Anisotropic Quantum Rabi Model

Quantum chaos is an intriguing topic and has attracted a great deal of interests in quantum mechanics and black hole physics. Recently, the exponential growth of out-of-time-ordered correlator (OTOC) has been proposed to diagnose quantum chaos and verify the correspondence principle. Here, good correspondence is found between the linear entanglement entropy and the semiclassical phase space structures in the anisotropic quantum Rabi model. The Loschmidt echo in the chaotic sea decays more faster than that in the stable island. However, the OTOCs grow exponentially at early times for the initial states centered both in the chaotic and stable regions. The exponential growth of the OTOC is attributed to quantum collapse that provides a novel mechanism of yielding exponential growth of the OTOC in quantum systems. Moreover, the quantum collapse effect is more obvious for the initial states centered in the chaotic one. The results show that in the anisotropic quantum Rabi model, the linear entanglement entropy, and Loschmidt echo are more effective than OTOC for diagnosing quantum chaotic signals.