CasimirForce In A Cavity With Output Coupling And The Study Of Berry Phase In A Bose-Einstein Condensate

Fluctuation-induced Casimir force between neutral bodies become more andmore important as micromechanical and microfluidic devices enter submicrometre.Casimir efect was frst predicted by Dutch physicist Hendiik Brugt Gerhard Casimirin1948. He calculated the attractive force between two neutral, parallel, infinitelylarge, ideal metal plates due to the zero-point vacuum quantum fuctuations of theelectromagnetic feld. In the last few years the Casimir effect has received widespreadattention in both fundamental and applied physics.This is due to Casimir effect beingone of the few direct macroscopic manifestations of quantum mechanics. In particularthe dramatic progress made in the theoretical understanding and measurement ofCasimir force over the past ten years. In1958, the attractive Casimir force was firstmeasured by M.J.Sparnaay. In1997, the Casimir-Lifshitz force was measured withgreat precision by American physicist Steven Lamoreaux. In2009，Lamoreaux andpartners reported the first experimental measurement of a repulsive Casimir force. In2011,C. M. Wilson firstly observed the dynamical Casimir effect in a superconductingcircuit. Casimir effect play a very important role in promoting many physical subjectssuch as nanotechnology, atom optics, condensed-matter, cavity QED，cosmology, etc.The concept was first introduced by M.V. Berry in1984, who showed that thestate of a quantum system acquires a purely geometric feature in addition to the usualdynamical phase when it is varied slowly and eventually brought back to its initialform. Since the work of Berry, the geometric phase has been extensively studied andgeneralized-for example, to nonadiabatic evolution, mixed states and open systems.Since firstly introduced by Einstein in1925, the Bose-Einstein condensate hasattracted a lot of interest in recent studies due to its advantage of mesoscopicproperties. In the last few years, the study on berry phases of the BEC also attractedlots of interest.The dissertation has three main aspects. Firstly, we simply introduced thedevelopment of Casimir effect about some theoretical concepts and experimentalstudy. Secondly, the Casimir effect between a perfectly conducting wall and adielectric wall in a cavity comprising a transparent dielectric with output coupling isinvestigated based on the contents on the front. We obtain the analysis expression of the force by using full quantum theory. We discussed about the influences of the thecavity size and the feld amplitude refectivity on the Casimir force by numericanalysis. The results showed that the interaction of the two walls in this system isalways repulsive. The Casimir force increased with the feld amplitude refectivity anddecreased with the cavity size. Finally, we simply introduced some knowledge of theBerry phase and BEC, then we investigated the Berry phase of a Bose-Einsteincondensate out of Equilibrium. We obtain the analysis expression of Berry phase anddiscuss about influences of atomic interaction on the berry phase. The results showedthe BEC in such a non-equilibrium system acted like a spin-1/2particle when theatomic interactions were negligible and the Berry phases went to be zero with whenthe atomic interaction is infnite.