The Dynamics Of Periodically Driven Open Quantum Systems

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.