Berry Phase In An Anti-PT Symmetric Quantum Mechanics

The Berry phase is the geometric nature of quantum states and plays a vital role in modern physics.In recent years,the relationship between Berry phase and quantum phase transition has been one of the research hotspots in quantum information processing.Both optical microcavities and nanocrystalline molecules containing metal nanoparticles can enhance the interaction between light and matter,which is a good medium for studying quantum information processing.This paper mainly studies the Berry phase based on non-Hermitic quantum mechanics and quantum information processing based on optical microcavities with rotation,and has obtained the following results:1.In non-Hermitic quantum mechanics,we study a system in which metal quantum particles are coupled by semiconductor quantum dots and meet the anti-PT symmetry requirements under the action of a light field.Compared with the closed Hermitian physical system previously studied,this is a Open systems closer to reality.We have studied the system's analytical solution of eigenfrequency,eigenstate,and the Berry phase,and found that in the symmetric region,the intensity change of the light field changes the dissipation rate of the system without affecting its eigenfrequency;at the symmetry breaking stage,changes in the intensity of the light field change the system's intrinsic frequency without affecting its dissipation.At the same time,we also obtained that the Berry phase only changes in the symmetric broken region.Therefore,in the symmetric region,the Berry phase is very robust against environmental noise.This has important applications in quantum simulation and quantum information processing.It also provides new research ideas for future quantum topology and quantum computing.2.In optical microcavity and quantum information processing,we use a microcavity system with rotation to achieve controllable,non-reciprocal photon blockage that depends on the driving direction under weak nonlinear conditions.Through the coupling between the original optical mode and the backscattering optical mode in the spin microcavity,the non-reciprocal destructive quantum interference caused by one-sided driving prevents the transition path of the quantum state.Controllable non-reciprocal photon blocking that depends on the driving direction is achieved.This conclusion can be used as a new way to realize non-reciprocal optical devices,single photon sources,and non-reciprocal quantum communication.