Dynamics, thermalization and propagation of quantum systems in complex environments

量子系统通常是开放的，即耦合到一个导致退相干和耗散的环境。开放量子系统(OQS)的理论通常基于这样的假设，即系统和环境之间存在很大的时间尺度分离，这使得人们可以考虑弱耦合和马尔可夫近似。此外，环境通常被建模为一组简谐振子，这使得能够用Caldeira-Legget或自旋玻色子哈密顿量等模型来描述问题。最后，当环境是固体介质或粒子集合时，大多数情况下，粒子被认为是静止的，而不是运动的。本项目的目的是促进对OQS的理解，超越这三种情况。更详细地说：(A)在第一部分中，我们将在不考虑马尔科夫近似和弱耦合近似的情况下，分析与谐振子环境耦合的开放系统的长时间极限动力学。这与在结构环境中的固态物理和量子控制、量子生物学、物理化学和量子光学等上下文中描述OQS有关。(B)在项目的第二部分，我们将环境建模为一组非谐振子，而不是谐振子。例如，这可以描述振动分子的声子浴，包括声子-声子相互作用、相互作用的量子气体或复杂的量子材料。(C)在第三部分中，在光-物质相互作用的背景下，我们分析了量子光场在运动的量子力学介质中传播的性质，正如它在一些涉及原子激光的实验情况中或在通过腔的原子系综中所遇到的那样。在这种情况下，原子介质将扮演量子光场环境的角色，量子光场现在被认为是OQS。光与这种介质相互作用的分析可能导致在量子光学中的重要应用，如实现光隔离和单向光传输。

Quantum systems are in general open, i.e. coupled to an environment that induces decoherence and dissipation. The theory of open quantum systems (OQS) is often based on the assumption that there is a large separation of time scales between the system and the environment, which allows one to consider a weak coupling and Markov approximation. In addition, the environment is often modeled as a set of harmonic oscillators, which enables the description of the problem with models such as the Caldeira-Legget or spin-boson Hamiltonians. Finally, when the environment is a solid medium or an ensemble of particles, in most cases it is considered that the particles are not moving but stationary.The purpose of this project is to advance the understanding of OQSs beyond these three situations. In more detail:(a) In a first part, we will analyze the long-time limit dynamics of an open system coupled to a harmonic oscillator environment without considering the Markov and weak coupling approximations. This is relevant to describe OQS in contexts such as solid state physics and quantum control, quantum biology, physical chemistry, and quantum optics in structured environments.(b) In a second part of the project, we model the environment as a set of anharmonic oscillators, rather than harmonic oscillators. This may describe for instance a phononic bath of vibrating molecules which includes phonon-phonon interactions, interacting quantum gases or complex quantum materials.(c) In a third part, and within the context of light-matter interaction, we analyze the properties of a quantum light field propagating in a moving quantum mechanical medium, as it can be encountered in some experimental situations involving atom lasers or in atomic ensembles flying through a cavity. In this case, the atomic medium would play the role of an environment for the quantum light field, which is now considered to be the OQS. The analysis of light interacting with such media may lead to important applications in quantum optics, like the achievement of optical isolation and unidirectional light transport.