In recent years, the cavity quantum photomechanics has been developed rapidly, and played a very important role in quantum information processing, quantum basic principle verification, and high-precision measurement. The kinds of quantum mechanical behaviors have also been explored and discovered in the study of cavity mechanics. By placing the Kerr medium in the system, quantum nonlinearity is introduced into the optomechanical system. Quantum phase transition is a relatively important part in the research of condensed matter physics. Since Dicke quantum phase transition was successfully observed experimentally, the problem of quantum phase transition in the optical cavity has attracted more attention. The spin-coherent-state variation method and the Holstein-Primakoff transformation are used to theoretically calculate the ground state energy functional, and the rich structure of the macroscopic multi-particle quantum state is given by adjusting the parameters. The quantum phase transition evolution equation describes the relationship between each phase and the time of generating a new phase when reaching the critical phase transition point. At the same time, the mode squeezing of multi-mode hybrid optomechanical system has also became one of the basic problems of quantum mechanical behavior in cavity quantum dynamics.
In this article, we explore the quantum dynamics of optomechanical devices including single-cavity and dual-cavities. We find that the system will undergo a dynamic phase transition, which is similar to the Dicke-Hepp-Lieb superradiant type phase transition, and a new dynamic critical point appears in the coupling between the momentum quadratures of the two optical fields. By manipulating the coupling parameters, we can achieve selective energy exchange between any two modes and the critical coupling point corresponds to selective energy exchange. Mode squeezing, which is easy to measure by applying the quantum uncertainty relationship, is also revealed and consistent with selective energy exchange. The study of coordinate and momentum variances gives us the revelation that the compressed orthogonal variables are the most suitable for measurement because of the small quantum noise. In fact, phononic modes can store energy in a longer duration, while photonic modes can transfer energy in a long distance. This phenomenon makes the hybrid optomechanical cavities useful in the next-generation quantum communications and quantum information processing units.
DownLoad:
