Application Of Non-hermitian Hamiltonian Model In Open Quantum Optical Systems

Under the Hermitian quantum mechanics,it assume that the quantum system is in a closed and isolated state.In such an ideal case,the system will not dissipate,and its observable phys ical operator is Hermite operator and has real eigenvalues.In fact,there always exist the channels between system and the environment,which are built through the force driving,dissipation or fluctuation induced-dissipation.Such a system is generally called an open quantum system.Due to the many interference factors of environment to system,Hermite system is not enough suitable to solve these practical phys ical problems.In the field of quantum communication,the optical loss and noise generated by the environment to the squeezed light and entangled light are amplified over a long-distance transmission,which greatly reduces the efficiency of quantum information transmission.This paper focuses on proposing non-Hermitian theory to describe open systems.The interference of environment to the system is introduced into the Hamiltonian of the system as dissipative terms of imaginary parts.The purpose of this paper is to construct a practical non-Hermitian Hamiltonian model,and simulate to solve it.The experimental phenomenon of the second-order phase transition caused by the competition between the coherent interaction’s cavity and environmen and dissipation,which fully reflect the non-Hermitian Hamiltonian model can be popularized in practice.Here’s a summary to the main research work in this paper:1.the historical background and physical s ignificance of Hermitian quantum mechanics to non-Hermitian quantum mechanics are shown.According to the fact that Hermitian operator is not the necessary and sufficient condition of real eigenvalue,the superiority of non-Hermitian theory in describing open systems is highlighted.It shows that it is greatly physical significanct and potential application prospect to introduce non-Hermitian theory into describing dissipation,decay and ionization in open quantum optical system.2.Several possible non-Hermitian Hamiltonian forms involved in the optical parameter process are assumed.The process of non-Hermitian Hamiltonian’s diagonalization and the eigenvalue’s solution are completed by Bogoliubov-like transformation.A Hamiltonian model based on three-resonance optical parametric process is constructed.The dissipation term is included in the Hamiltonian as a non-Hermitian term to reflect the lifetime of the eigenstate.The second-order fluctuation term of the non Hermite Hamiltonian obtained by using the steady-state approximation and the mean field approximation are diagonalized and solved the eigenvalue.Then the quantum noise of quadrature amplitude and quadrature phase components is discussed.3.Combined with the experimental process of producing squeezed light by nondegenerate parametric process,the non-Hermitian Hamiltonian model is constructed to simulate the phase trans ition of the order parameters of pump mode,signal mode and idle mode,the intrins ic spectrum of Hamiltonian,quadrature amplitude and quadrature phase components near the threshold.It explains that the competition between the nonlinear coherent interaction and the transmission loss in the cavity will lead to the dissipative second-order quantum phase transitionThe innovations of this article are is listed below:1.A open quantum system model is simulated.The interaction between the quantum system and the environment is introduced into the non-Hermitian Hamiltonian.And the non-Hermitian part and the Hermitian part of the Hamiltonian and reflects the real energy of the quantum system and the dissipation process and the lifetime of the corresponding eigenstates.2.Using the non-Hermitian quantum model to simulate the quantum fluctuations and quantum phase transitions in the process of optical parametric conversion.At the same time,a new way to solve the eigenvalues of complex Hamiltonian in non-Hermitian system is developed.