Emergence of nonequilibrium steady states in periodically driven closed composite quantum systems

在FOR 2692的前一个资助期内，我们对“周期性量子化学”领域做出了贡献，并确定了控制理论和实验兴趣的周期性驱动开放量子系统的Floquet态占据概率的概率分布。特别是，我们已经证明了周期性驱动的顺磁材料的非平衡磁化强度受到有关自旋与其环境耦合的细节的强烈影响，并建立了“Floquet状态冷却”的新概念，这表明，从量子系统的基态出现的Floquet态在强驱动力的存在下可以携带甚至显着更高的人口，在热平衡下的基态。这些结果仍然停留在一个方法，这是相当于通常的Born-Markov近似，忽略潜在的并发症，由于密集的quasienergy频谱。因此，在第二个供资期，我们将把上述研究结果扩展到该提议的范围之外，走向实际“感受”到时间周期驱动力的环境。为此，我们将研究特定的周期性驱动的量子系统耦合到N浴振荡器，可以解析地解决了一个N通过广义Husimi变换，并探讨如何无限大N的极限接近。另一方面，我们将数值研究模型的周期性驱动的玻色约瑟夫森结占据两个粒子物种，一个代表一个周期性驱动的系统，另一个浴。这样，周期热力学的玻恩-马尔可夫式公式所隐含的预测就可以进行严格的检验。此外，在第一个项目期间完成的工作所产生的两股发展将继续进行，即通过适当设计的系统浴耦合和状态的浴密度有选择地填充某些"共振“Floquet状态的任务，以及可能不适合目前使用的标准数值方法的大型系统的Floquet状态的变分计算。作为一个长期的目标，连接这些子课题中的几个，我们还考虑了Floquet凝聚的弱相互作用的原子玻色气体的时间周期性调制的捕获势，这可能会表现出一些相当不寻常的功能的可行性。

Within the previous first funding period of FOR 2692 we have contributed to the area of ``periodic thermodynamics'', and have determined the probability distributions which govern the Floquetstate occupation probabilities for periodically driven open quantum systems of theoretical and experimental interest. In particular, we have demonstrated that the nonequilibrium magnetization of a periodically driven paramagnetic material is strongly affected by details concerning the spins' coupling to their environment, and have established the novel concept of ``Floquet-state cooling'', demonstrating that a Floquet state emerging from the ground state of a quantum system can carry even significantly higher population in the presence of a strong driving force than that ground state in thermal equilibrium. These results still rest on an approach which is equivalent to the usual Born-Markov approximation, disregarding potential complications due to the denseness of the quasienergy spectrum. In the second funding period we will therefore extend the above findings beyond the scope of that proposition, moving towards environments which actually ``feel'' the time-periodic driving force. To this end, we will study particular periodically driven quantum systems coupled to N bath oscillators which can be solved analytically for an N by means of a generalized Husimi transformation, and explore how the limit of infinitely large N is approached. On the other hand, we will numerically investigate models of periodically driven bosonic Josephson junctions occupied by two particle species, one representing a periodically driven system, the other a bath. In this way, predictions implied by the Born-Markov-like formulation of periodic thermodynamics can be put to a hard test. In addition, two strands of development arising out of the work accomplished in the first project period will be continued, namely, the task of selectively populating certain ``resonant'' Floquet states by means of suitably designed system-bath couplings and bath densities of states, and the variational computation of Floquet states of large systems which may not be amenable to the presently used standard numerical methods. As a long-term goal linking several of these subtopics we also consider the feasibility of Floquet condensates of weakly interacting atomic Bose gases in time-periodically modulated trapping potentials, which may exhibit some fairly unusual features.