The Study Of Dynamical Casimir Effect

Since 1900 the establishment of quantum mechanics has naturally become one of the two pillars of modern physics. It fundamentally changed people’s understanding of the physical world. Quantum mechanics caused the technological innovations which directly promoted the development of social productivity, the applications of atomic energy, the understanding of superconducting and superfluid, the large-scale development of semiconductor technology, etc., all of them are the product of quantum mechanics.One of the most well-known illustrations of mechanical effects related to the quantum vacuum field is the Casimir effect. The attractive force exerted by the vacuum fluctuations of the electromagnetic field on two neutral, parallel, and perfectly conducting plates was calculated by Hendrik Casimir in 1948. The miracle of quantum mechanics has been measured by M.J.Sparnaay for the first time in 1958. The attractive Casimir-Lifshitz force between metal surfaces has been measured by Steve Lamoreaux with great precision in 1997. In 2009, Steve Lamoreaux and Munday et al. reported the first experimental measurement of a repulsive Casimir-Lifshitz force. Another quantum effect has been realized that photons can be created from vacuum fluctuations when the boundary conditions of the field are time dependent. This effect was first considered by Moore in 1970 which is usually referred as the dynamical Casimir effect.The study is mainly in the following three aspects. Firstly, the system of the Hamiltonian involving a driving part, a single mode part, and a two-mode squeezed one and a two-mode coupled one is discussed using the Lewis–Riesenfeld invariant theory. The time evolution operator is obtained. When the initial state is a coherent state, the quantum fluctuation of the system is calculated, and it is dependent on the squeezed part and the two-mode coupled part, but not dependent on the driving one. Secondly, we discussed dynamical Casimir effect and collective excitations in atom ensemble are investigated in a non-stationary cavity. We respectively obtained the number of the real photons and excitons in vacuum state and an initial thermal equilibrium state. Finally, using quasimodes theory to describe the dissipation of the electromagnetic fields in the non-stationary cavity, we obtained the Hamiltonian and the number of the photons.