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

在FOR 2692之前的第一个资助期内，我们对“周期热力学”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Floquetstate占用概率的概率分布。特别是，我们已经证明了周期性驱动顺磁性材料的非平衡磁化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-state cooling”的新概念，证明了从量子系统的基态出现的Floquet状态在强驱动力的存在下可以携带比热平衡中的基态更高的人口。这些结果仍然依赖于一种与通常的Born-Markov近似等效的方法，忽略了准能谱密度的潜在复杂性。因此，在第二个资助期，我们将把上述发现扩展到该命题的范围之外，转向真正“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驱动量子系统耦合到N浴振子，可以用广义Husimi变换解析求解N，并探索如何逼近无限大N的极限。另一方面，我们将数值研究由两种粒子占据的周期性驱动玻色子约瑟夫森结模型，一种代表周期性驱动系统，另一种代表一个浴。这样，周期热力学类玻恩-马尔可夫公式所隐含的预测就可以得到严格的检验。此外，在第一个项目期间完成的工作中产生的两方面的发展将继续进行，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，以及大系统的Floquet状态的变分计算，这可能不适用于目前使用的标准数值方法。作为连接这些子主题的长期目标，我们还考虑了弱相互作用原子玻色气体在时间周期调制俘获势中的Floquet凝聚的可行性，它可能表现出一些相当不寻常的特征。

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.