Squeezing characteristics of cavity field in dynamic Casimir effect

The dynamic Casimir effect refers to the phenomenon of photons generated in a cavity with periodically vibrating wall. The Hamiltonian of the dynamic Casimir effect includes the square term of the photon creation (annihilation) operator, which connects to the squeezing light. Here we discuss in detail the squeezing characteristics of the cavity field in the dynamic Casimir effect. When the cavity wall is driven classically, semi classical theory is adopted; When cavity wall vibration needs to be described by phonons, full quantum theory is used. The squeezing properties of the light field are different according to these two theory. In semi classical theory, the squeezing properties depend on the system parameter |B/A|. When |B/A| > 1, the squeezing value changes periodically, and the squeezing weakens as |B/A| increases. When |B/A| < 1, it is necessary to use optimized squeezing value to measure squeezing, which shows steady value of -0.25. In full quantum theory, we find that the squeezing of the cavity field weakens as the initial average phonon number decreases. This is because the smaller the average phonon number, the more pronounced the quantum properties of cavity wall vibration. During evolution, phonons and photons become entangled, disrupting the squeezing of the cavity field. The quantum properties of phonons have a negative impact on the squeezing of the light field. We also found that in full quantum theory, the optimized squeezing value should be used to better describe the squeezing, and the maximum squeezing can be achieved by controlling the initial average phonon number of the cavity wall without photon divergence. Most studies focus on resonance frequency, so the innovation points of this paper are of the large detuning frequency.. This work has significance for a deeper understanding of the quantum properties of the cavity field in the dynamic Casimir effect, and helps to generate squeezing microwaves using the parameter dynamic Casimir effect.