Dynamics And Spectral Features Of Open Quantum System Under The Strong Driving

The thesis presents two major subjects of strongly driven open quan-tum systems. One is about the theoretical descriptions beyond the rotating-wave approximation (RWA) for resonance fluorescence and probe-pump spectroscopy arising from the strongly driven two-level system (TLS). The other is how the intense driving influences the decoherence dynamics in the driven open quantum systems. At present, due to the technique of artificial atoms, the physics of strongly driven quantum system has been realized in the lab. On the other hand, it is well-known that in the intense-driving regimes, the driving RWA breaks down and the counter-rotating (CR) couplings have considerable contributions. It is therefore necessary to develop a non-RWA theory that may illustrate the phenomena associ-ated with the intense driving. This thesis is comprised of six chapters.In Chapter One, we show the background concerning driven open quantum systems, including semiclassical description for driven closed quantum systems, the phenomenological description of driven open quan-tum systems as well as the traditional analytical approaches such as RWA, Floquet theorem, Markov master equation, etcIn Chapter Two, we propose a method based on a unitary transfor-mation to avoid the RWA of driving and calculate the Bloch-Siegert (BS) shift over the entire driving-strength range. In comparison with the nu-merically exact results, we verify that our method succeeds in taking into account the effects of the CR terms. We find that our method predict-s the accurate BS shift from weak to extremely intense driving-strength regimes. In particular, our method is more accurate than previous meth-ods in the extremely strong-driving regimes. In addition, we apply the unitary transformation to solve the optical Bloch equation beyond the RWA and demonstrate the detectable signature related to the BS shift.In Chapter Three, we systematically study the resonance fluorescence and probe-pump spectroscopy from the TLS driven by the monochromatic field by the combination of the unitary transformation and Born-Markov master equation approach. The unitary transformation allows us to take into account of the effects of driving CR terms by an effective RWA-like Hamiltonian, which leads to modified optical Bloch equations. We solve the modified Bloch equations and derive the analytical expressions for the resonance spectrum and probe-pump spectrum, which shows clearly the spectral features associated with the CR terms. Our results demonstrate precisely that the CR terms of the driving induce three spectral features: (ⅰ) the asymmetric spectral profiles; (ⅱ) the generation of the higher-order spectral profiles centered at odd multiples of driving frequency; (ⅲ) the shift of sidebands.In Chapter Four, we study the dissipative dynamics of the TLS driv-en by a harmonic driving and coupled to an Ohmic dissipative bath. By constructing a novel generator for unitary transformation, we propose an analytical method to resolve the time evolution of the driven spin-boson model. The key idea of our treatment is that the unitary transformation is applied to construct an effective Hamiltonian with the main contribu-tions from the driving field as well as the dissipation coupling. Besides, by properly determining the two types of parameters in the unitary transfor-mation, we reformulate the effective Hamiltonian with the RWA-like form. On the other hand, we can derive two special methods from our general treatment. One just takes into account of the effects of the driving CR terms and the other only the effects of dissipative CR terms. In addition to the RWA approach, we systematically study the intrinsic difference among the four methods and reveal the effects of both driving CR terms and dis-sipative CR terms by calculating the population difference and coherence. Our main results are as follows:(ⅰ) in the case of resonant strong driving, both types of CR terms prolong the relaxation and dephasing processes; (ⅱ) in the case of largely detuned strong driving, we study the influence of dissipation on the coherent destruction of tunneling. We show that an almost complete suppression of the tunneling can be achieved for a rela-tively long time; (ⅲ) we identify the relation between our method and the Floquet-Born-Markov (FBM) approach. It turns out our method is more simple and efficient than the FBM approach.In Chapter Five, we study quantum dynamics of the driven TLS in-teracting with a pure dephasing bath. We use two unitary transformations to construct an effective Hamiltonian, by which we take into account the effects of the driving CR terms as well as partial higher-order contribution-s from the TLS-bath coupling. Furthermore, we derive the non-Markov master equation as well as its solutions. In the Super-Ohmic bath and strong-driving regimes, we find that the non-Markov time evolution dif-fers from the Markov one only in slightly quantitative difference. This result is attributed to the effects of driving CR terms, which weakens the coupling between the system and bath. In addition, our method naturally takes account of the Lamb shift. Thus, our method predicts the renormal-ization of the Rabi frequency and BS shift. With a fixed driving strength, both of the Rabi frequency and BS shift decrease as the TLS-bath coupling increases.In Chapter Six, we give the conclusions and discuss the future works.