Research On Parity-Time Symmetry Based On The Coupling Of Cavity And Atomic Assemble

According to the traditional quantum mechanics,only Hermitian Hamiltonian of a quantum system possesses real eigenvalues.However,recent studies have shown that non-Hermitian Hamiltonians with parity-time(PT)symmetry can also have real eigenvalues,this paves a way to the development of non-Hermitian quantum mechanics.In quantum optics,a hybrid cavity QED system with gain and loss can provide various non-Hermitian Hamiltonian operators.Moreover,through appropriately controlling the parameters of the system,one can achieve a balance between the gain and the loss,thus realize the phase transition between the PT symmetry phase and the PT symmetry broken phase in the non-Hermitian quantum system.So the hybrid cavity QED systems provide ideal platforms for us to study non-Hermitian quantum mechanics and explore its potential applicationsIn this dissertation,we study the PT symmetry in two non-Hermitian quantum systems based on the coupling of cavity field and an atomic assemble.By constructing the non-Hermitian Hamiltonian of the cavity field and the atomic assemble system,we can determine the phase-transition point(also called exceptional point)of the system which corresponds to parameters of the system by solving the eigen equation of the non-Hermitian Hamiltonian.Apparently one can thus control the exceptional point and explore its applications.The content of this dissertation mainly includes the following two aspectsFirstly,we have studied the PT symmetry problem in a cavity optomechanical system with an atomic assemble inside the cavity,and proposed a scheme for precise measurement of the electric charge.The atomic assemble is composed of multiple two-level atoms and can be treated as an atomic mode with Bose characteristics.The interaction between the atomic mode and the cavity field enables us to control the output of the cavity field.In our model,the cavity field is driven by a strong external laser field and it interacts with a weak detecting field as well.The driven cavity field provides a gain to the system,while the atomic mode formed by the two-level atomic assemble acts as the loss of the system.At the same time,The vibrating cavity mirror is coupled to a electric charge to be measured through a Coulomb potential.Our research results show that the system has a parameter-controlled phase transition from the PT symmetry phase to the PT symmetry broken phase.At the exceptional point,by controlling the intensity of the driving field,transmission spectrum with a transmittance greater than 1 can be obtained,providing us a convenient method for high-precision measurement of the electric charge.Our research results indicate that the sensitivity of charge measurement at the exceptional point can be improved by four orders of magnitude.Secondly,we have studied the PT symmetry problem in a cavity QED system with a single-mode cavity containing a two-level atomic assemble.Similarly,the atomic assemble is treated as an atomic mode with Bose characteristics.We assume the atomic assemble is driven by a squeezed vacuum light field,so the atomic mode provides a gain for the system.On the other hand,in this model the cavity field acts as the loss of the system.Our research shows that a phase transition from the PT symmetry phase to the PT symmetry broken phase can occur under a certain condition which depends on the strength of the driving squeezed vacuum light field.But the exceptional point has nothing to do with the phase sensitivity of the squeezed vacuum.