【作者】 陈冲；

【导师】 安钧鸿；

【作者基本信息】 兰州大学 ， 物理学·理论物理， 2016， 博士

【摘要】 作为一种普遍采用的量子调控手段,周期性驱动促使量子系统从静态系统变成能量不守恒的非平衡系统。相反地,环境的噪声作用却促使量子系统从非平衡态弛豫到平衡态,二者的结合构成了周期性驱动开放量子系统,两种效应的竞争导致了量子系统表现出丰富多彩的非平衡物理现象。对周期性驱动开放量子系统的研究不仅有助于我们更好的认知和理解复杂的非平衡态行为,而且有助于我们更好的实现对微观系统的单量子态调控。在本文中,我们从三个不同的角度对周期性驱动开放系统进行研究。它们分别是:从系统角度我们研究开放量子系统的退相干控制、从环境角度我们研究周期性驱动二能级系统的共振荧光辐射谱和从驱动角度我们研究周期性驱动系统的Floquet本征热化。首先,我们基于Floquet定理研究自旋1/2粒子在自旋链环境中退相干的周期性驱动控制问题。如何控制开放量子系统的退相干是当今量子工程研究的核心问题。我们发现当系统与环境组成的复合系统的Floquet准能谱中形成束缚态时,系统的退相干就会得到抑制。进一步研究揭示传统相干隧穿破坏方法和动力学退耦方法可以统一纳入到我们提出的退相干抑制的Floquet束缚态机制的物理框架中。相比与传统动力学退耦方法仅适用于退相位噪声控制和敏感地依赖于控制脉冲的参数值,我们的控制方案可有效地抑制耗散噪声且对控制参数的涨落具有鲁棒性。我们所揭示的Floquet束缚态的退相干控制机制为利用周期性驱动实施退相干抑制指明了方向。其次,我们研究超强周期性激光驱动二能级系统的共振荧光辐射谱,该超强驱动使得传统普遍采用的旋波近似不再适用。近年来周期性驱动系统的Floquet物态日益成为备受关注的研究热点问题,但是如何从实验上探测这种含时系统的新奇物态仍是一个亟待解决的问题。我们基于Floquet定理建立了超越旋波近似的共振荧光理论描述。研究结果表明在超强驱动下,不同于旋波近似下的Mollow三峰结构,共振荧光谱将展示出高阶谐波的多峰结构。通过与周期性驱动二能级系统的Floquet准能谱对比,我们发现超强驱动下的荧光谱的多峰结构恰好对应于不同Floquet准能态之间的跃迁能量。该结果铺平了利用共振荧光的手段来探测周期性驱动系统Floquet物态的道路。最后,我们研究周期性驱动量子系统的稳态统计问题。探索与环境弱耦合的周期性驱动系统的稳态是否是Floquet准能态的Gibbs态直接决定了作为当前研究热点问题的Floquet物态的能级填充规则。基于拓展空间的Floquet主方程,我们给出了周期性驱动开放量子系统的Floquet热化规则。按照此规则,我们发现系统的非Floquet热化来源于驱动场和环境之间存在着的稳定能流,从而建立了系统实现Floquet准能态Gibbs态热化行为的能流判据。更进一步,我们发现周期性驱动开放量子系统中存在着具有普适稳态的广义可热化量,并且我们通过引入量子功的概念对其进行了物理解释。这些结果为理解周期性驱动开放量子系统的稳态行为具有积极意义。我们本文对周期性驱动开放量子系统的研究不仅对理解此类系统的非平衡行为具有建设性的意义,而且对利用周期性驱动模拟新奇量子物态具有指导性作用。更多还原

【Abstract】 Periodic driving, as one of the commonly used methods in quantum control, causes quantum systems to be non-equilibrium with nonconserved energy.Environment, on the contrary, induces the relaxation of quantum systems from non-equilibrium to equilibrium states. The combination of these two factors forms the periodically driven open quantum systems, where the competition of the two effects introduces rich non-equilibrium phenomena in the relevant systems. The study on periodically driven open quantum systems is not only helpful for our understanding to the colorful non-equilibrium phenomena but also bene?cial for better control to quantum systems. In this thesis, we investigate the periodically driven open quantum systems from three different perspectives. From the open system perspective, we study the decohernce control of the quantum system by periodic driving. From the environment perspective, we study the resonance ?uorescence spectrum of the periodically driven system. From the driving perspective,we study the Floquet thermalization of the periodically driven system.First, based on Floquet theory, we explore the constructive role of temporal periodic driving in suppressing decoherence of a spin-1/2 particle coupled to a spin chain bath. How to control decoherence is central issue in quantum engineer.We here reveal that, accompanying the formation of a Floquet bound state in the quasienergy spectrum of the whole system including the system and its environment, the dissipation of the spin system can be inhibited. It can be seen as a close analogy to the bound-state induced decoherence suppression by engineering the spectral density in the static system. Comparing with the coherent destruction of the tunneling and the dynamical decoupling methods, we ?nd that both of them can be uni?ed into our Floquet bound state mechanism. Different from the dynamical decoupling method, which works only for dephasing noise and is sensitive to the control pulses, our scheme can work well for the dissipation noise and is robust to the driving parameters. It suggests a promising perspective of periodic driving in decoherence control.Second, we develop a self-consistent Floquet theory for calculating the resonance ?uorescence of a two-level system under ultra-strong driving of a laser,where the traditional rotating-wave approximation breaks down. Recently, the Floquet states of matter of quantum systems under periodic driving attract much attention, which opens a new door to arti?cially realize quantum states of matter by periodic driving. However, it is still an open question that how to detect the novel Floquet states of matter in such time-dependent systems. Based on Floquet theorem and going beyond the rotating-wave approximation, we establish the microscopic description to the resonance ?uorescence of a two-level system under ultra-strong laser driving. It is revealed that different from the standard Mollow’s triplet structure under the rotating-wave approximation, the ?uorescence spectrum shows a multi-peaks structure with high order harmonics. It is remarkable to ?nd that such multiple peaks in the ?uorescence spectrum directly re?ects the transition energies between different Floquet states of the periodically driven system. It paves the way to detect the Floquet states of matter by the resonance?uorescence technique.At last, we investigate the statistical behaviors in the steady state of the periodically driven system. Whether a periodically driven system weakly coupled to a heat bath equilibrates to the steady state obeying the Boltzmann distribution of the Floquet quasi-stationary states or not determines directly the occupation rule of the Floquet states of matter. Based on the Floquet master equation description in the extended Sambe space, we establish a microscopic picture to Floquet thermalization. It reveals that the breakdown of the Floquet thermalization stems from the steady energy ?ow from the driving source to dissipative bath drain. Inspired by this, we give a basic criteria on judging the Floquet thermalization of the periodically driven open quantum system. It only occurs when the corresponding energy ?ow goes to zero. Moreover, we construct a general thermalizable quantity which shows the Floquet-Boltzmann distribution in steady state. A physical interpretation to such thermalizable quantity is given by introducing the concept of quantum work. Our results give constructive understanding to the Boltzmann thermalization in periodically driven open quantum systems.Our series studies on periodically driven systems, on the one hand, provides constructive suggestions on understanding the non-equilibrium behaviors of the driven systems, on the other hand, plays directive roles in simulating novel states of matter by periodic driving.更多还原