The Quantum Mechanics of Coupled Oscillators.

M. Sebawe Abdalla

Xin-Chang Liu, Xiao-Dong Shi, Xiao-Lei Zhang +2 more

Quantum squeezing in macroscopic oscillator systems plays a critical role in bridging quantum mechanics with classical-scale phenomena, enabling high-precision measurements and fundamental tests of quantum physics. In this work, we investigate the effect of squeezing on the phonon state in a hybrid macroscopic mechanical system consisting of an ensemble of Rydberg atoms coupled to two macroscopic mechanical oscillators. We notice that the dipole–dipole coupling between atoms and mechanical oscillators can be transferred to the indirectly coupled mechanical interaction, and the nonlinear effective Hamiltonian can be solved to generate a squeezed effect on the mechanical mode. We also discuss the noise effects induced by amplitude and phase fluctuations on the squeezed quadratures of the system.

Yujie Li, Li Deng, Tai-Shuang Yin +1 more

In this study, we investigated the properties of entanglement of an optomechanical system including two mechanical oscillators, where two mechanical oscillators are coupled with the cavity field in different coupling modes: the interaction between one mechanical oscillator and cavity field is first-order coupling, and the interaction between the other and the cavity field is quadratic coupling. On the one hand, the entanglement between two mechanical oscillators is studied. The influence of the frequency of the cavity field, the mass of mechanical oscillators, and the temperature of mechanical oscillators on the entanglement between two mechanical oscillators are investigated. On the other hand, for the given parameters of the system, we also obtained the entanglement between the cavity field and the mechanical oscillator that has a quadratic coupling. Compared with the entanglement between microscopic particles, the stable macroscopic quantum entanglement between two mechanical oscillators has the characteristics of long existence life and can be reused, and it also plays an important role in quantum information processing and quantum network construction.

Biswabibek Bandyopadhyay, Tanmoy Banerjee

Restoration of oscillations from an oscillation suppressed state in coupled oscillators is an important topic of research and has been studied widely in recent years. However, the same in the quantum regime has not been explored yet. Recent works established that under certain coupling conditions, coupled quantum oscillators are susceptible to suppression of oscillations, such as amplitude death and oscillation death. In this paper, for the first time, we demonstrate that quantum oscillation suppression states can be revoked and rhythmogenesis can be established in coupled quantum oscillators by controlling a feedback parameter in the coupling path. However, in sharp contrast to the classical system, we show that in the deep quantum regime, the feedback parameter fails to revive oscillations, and rather results in a transition from a quantum amplitude death state to the recently discovered quantum oscillation death state. We use the formalism of an open quantum system and a phase space representation of quantum mechanics to establish our results. Therefore, our study establishes that the revival scheme proposed for classical systems does not always result in restoration of oscillations in quantum systems, but in the deep quantum regime, it may give counterintuitive behaviors that are of a pure quantum mechanical origin.

Thomas A. Garrity