量子多态非厄米系统中的非绝热跃迁

在传统的厄米量子力学中，系统直接通过能级排斥相交点時，两个能级之间的跃迁是一个基本物理过程，称为朗道–齐纳跃迁。当一个系统连续经过两个能级排斥相交点时，跃迁概率不仅取决于单个朗道–齐纳跃迁的概率，还取决于整个过程中累积的相位。这种动力学过程在能量动量空间中实现了一种干涉，即朗道–齐纳-斯蒂克尔堡干涉。最近，很多学者进行了许多尝试，努力将朗道–齐纳范式扩展到更复杂的场景，包括具有两个以上能级的多态系统中的朗道–齐纳跃迁，以及量子非厄米系统中的朗道–齐纳跃迁。在这个项目中，出于研究朗道–齐纳跃迁和量子非厄米系统的动机，我们将系统研究多态非厄米系统中的朗道–齐纳跃迁和朗道–齐纳-斯蒂克尔堡干涉，同时将应用多态朗道–齐纳动力学的理论结果于非厄米光学和光子学上，为光信号处理和光束动力学提供新的机会。

For nearly a whole century, the development of quantum mechanics has achieved a great success in revolutionizing the physical world from atomic-scale to mesoscale. Yet quantum mechanics is established on a single axiom that any physical systems are assumed to have real spectra and unitary time evolution, due to the restriction on real-valued energy measurement and conservative probability. Hence, it is widely believed that the Hamiltonian describing any quantum systems should be invariant under Hermitian conjugation (combined operations of matrix transposition and complex conjugation). For many years, the rule of hermiticity was considered unbreakable, as the derivation of it are believed to bring about complex-valued energy. However, there is a paradigm shift since the groundbreaking seminal work of Bender and Boettcher, in which a class of non-Hermitian Hamiltonians with complex potentials were shown to possess real spectra. It soon becomes clear that the real-valued energy spectrum is ensured by the parity–time (PT) symmetry in non-Hermitian systems. The main difference between Hermitian and PT symmetric non-Hermitian systems is that the former one can only be used to describes closed systems isolated from the outer environment, but the later one can be used to describe an open system with two coupled subsystems, each of which is in contact with the outer environment, meanwhile, the probability in one subsystem with gain can flow into another subsystem with loss, so that the whole system is in a dynamical equilibrium. The new rule of pseudo-hermiticity under PT symmetry has opened up countless new opportunities, and has revealed many outstanding applications in quantum systems with inherent open boundaries...The experimental realization of quantum non-Hermitian Hamiltonians is inherent challenging, but the verification of non-Hermitian Hamiltonians in optics and photonics is relatively easier, due to the mathematical equivalence between the single-particle Schrödinger equation and the electromagnetic wave propagation equation under the paraxial approximation, as well as the mature experimental techniques to implementation of non-Hermitian PT symmetry by optical amplification and absorption. The emergence of PT symmetric non-Hermitian optics and photonics has stimulated numerous new designs of light propagation and confinement by utilizing novel optical materials with complex permittivity. Under the strong guidance of non-Hermitian symmetries, the seeming harmful factor of optical loss, when properly exploited, could bring new applications and functionalities in numerous important areas including optical communication, signal processing and biochemical sensing...In conventional Hermitian quantum mechanics, the transitions between two energy levels of a system directly driven through an avoided level crossing is a fundamental physical process, called the Landau-Zener (LZ) transition. When a system is driven through two avoided level crossings successively, the transition probability will depend not only on that of a single LZ transition, but also on the phase accumulated during the entire process. Such a dynamical process realizes a type of interferometry in the energy-momentum space, namely the Landau-Zener-Stückelberg (LZS) interferometry. Recently, there have been many attempts and efforts devoted to extending the LZ paradigm to more complex scenarios, including LZ transition in multistate systems with more than two energy levels, and LZ transition in quantum non-Hermitian systems. In this project, motivated by the interests in both the LZ problem and the PT symmetric non-Hermitian systems, we will systematically investigate the LZ transition and the LZS interferometry in multistate non-Hermitian systems. Based on our theoretical results, we would also examine the multistate LZ dynamics in both non-Hermitian optics and photonics, which may provide new opportunities for signal processing and beam dynamics engineering.