Based On Optical Media Quantum PT Dynamics Simulations

The non-Hermitian Hamiltonians are usually used to describe the dissipative behavior of the systems. But the latest studies have shown that there are a class of non-Hermitian quantum systems with real eigenvalues, which is named as parity-time inversion (PT) symmetric quantum systems. Since the term of PT symmetry was first proposed, such quantum systems have received extensive attention and become one of the research focuses. Since non-Herimtian systems with PT symmetry does not exist in nature, the related investigation stayed in the level of theoretical research for a long time. How to experimentally verify the dynamical properties of such systems predicted by the theoretic study has been an important topic. As we know, the spatial diffraction of laser beams and temporal dispersion of laser pulses obey the equivalent schrodinger equations in quantum mechanics. Optical systems are one of the most prominent candidates for quantum simulators. With the development in the study of optical experimental technology and novel materials, optical experiments have been widely used to inspect the validation of the basic principles of quantum mechanics and coherent phenomena.In this paper, we investigate the dynamics of time-dependent quantum systems with PT symmetry and propose a scheme of optical experiment. The main content of this thesis are as follows:The eigenvalues of some typical PT-symmetric quantum systems is discussed, which shows that PT-symmetric Hamiltonians may be considered as some kind of complex extensions of Hermitian Hamiltonians and have real eigenvalues.A scheme of optical experiment is proposed to simulate the dynamics of time-dependent quantum systems with PT symmetry. The propagation behavior of the laser beam in an optical medium that satisfies the PT symmetry condition is studied. In some conditions, the dynamics of the system can be described precisely through a simplified two-level model with non-Hermitian Hamiltonian.Our results indicate that the optical experiment platform is an effective alternative simulator for time-dependent quantum systems with non-Hermitian Hamiltonian.