對於驅動開放量子系統的系統與環境初始相關在態製備的影響和變分極化子方法

Effects of initial system-environment correlations on state preparation and variational polaron method for driven open quantum systems

陳建彰(Chien-Chang Chen)

指導教授 ： 管希聖

國立臺灣大學/理學院/物理學研究所/博士(2017年)

https://doi.org/10.6342/NTU201700124

摘要

我們研究藉由外場對一個二能階（量子位元）系統從一個系統與環境的共同平衡或相關態製備一個目標初始態。這個系統與環境的共同平衡或相關態起因於系統和其環境之間不可避免的交互作用。 我們引進在延伸輔助的劉維爾空間(extended auxiliary Liouville space)中的一個有效率的方法，來描述在強外場和系統與環境初始相關的存在下，一個非馬可夫(non-Markovian)開放量子系統的動力學。 我們藉由使用分佈差(population difference)的時間演化、布洛赫球(Bloch sphere)表示下的態軌線(state trajectory)，以及開放量子系統的兩個約化系統態之間的軌跡距離(trace distance)，來研究系統與環境的初始相關對系統態製備的影響。 在我們的微擾理論處理中，我們對軌跡距離引進了上限和下限以描述在系統態的製備後，各式各樣相關態之間軌跡距離的動力學的多樣行為。這些我們所提出比在文獻中類似之界限還要更好計算的上下界限，對軌跡距離的增加給了一個充分條件與一個必要條件，並且關連到見證非馬可夫性質 (non-Markovianity)以及系統與環境浴場初始相關性質。
此外，我們發展了一個結合了傳統的變分極化子主方程式方法和混合反旋的旋波(counter-rotating-hybridized rotating-wave)方法的實用的方法，來描述一個在系統與環境弱或強耦合的狀況下，被驅動開放量子系統的動力學。我們的方法，稱做CHRW變分極化子方法，在旋波近似(RWA)不適用的廣大參數範圍中仍然有效，換言之，也能夠處理強驅動和遠非共振（大失諧）的狀況。我們藉由一個驅動自旋與玻色子耦合模型來說明我們的方法、並討論我們的CHRW變分極化子主方程式的適用準則，且給出其有效物理狀況的參數邊界。我們指出我們得到的結果可還原到由系統與環境弱耦合法和完全極化子(full-polaron)法於他們合適的參數極限下所得到的結果。因此我們多方面適用的CHRW變分極化子方法能夠内補插(interpolate)於這兩個方法，並且結合系統與環境弱耦合法，能夠對於驅動開放量子系統在一個非常廣的參數空間下獲取到正確的行為。

關鍵字

開放量子系統 ； 初始相關 ； 旋波近似 ； 軌跡距離 ； 變分極化子轉換 ； 自由能最小化

並列摘要

We investigate the preparation of a target initial state for a two-level (qubit) system from a system-environment equilibrium or correlated state by an external field. The system-environment equilibrium or correlated state results from the inevitable interaction of the system with its environment. An efficient method in an extended auxiliary Liouville space is introduced to describe the dynamics of the non-Markovian open quantum system in the presence of a strong field and an initial system-environment correlation. By using the time evolutions of the population difference, the state trajectory in the Bloch sphere representation, and the trace distance between two reduced system states of the open quantum system, the effect of initial system-environment correlations on the preparation of a system state is studied. We introduce an upper bound and a lower bound for the trace distance within our perturbation formalism to describe the diverse behaviors of the dynamics of the trace distance between various correlated states after the system state preparation. These bounds, that are much more computable than similar bounds in the literature, give a sufficient condition and a necessary condition for the increase of the trace distance and are related to the witnesses of non-Markovianity and initial system-bath correlation.

In addition, we develop a practical method that combines the traditional variational polaron master equation approach with the counter-rotating-hybridized rotating-wave (CHRW) method to describe the dynamics of a driven open quantum system in a weak or strong system-environment coupling regime. Our method, called the CHRW variational polaron method, is valid over a broad range of parameters beyond the rotating wave approximation (RWA), i.e., also capable of dealing with the cases of strong driving and far off-resonance (large detuning). We illustrate our method through a driven spin-boson model and discuss the criteria for and give the boundaries of regimes of validity of our CHRW variational polaron master equation. We show that the results we obtain reduce to those by the weak-system-bath-coupling method and the full-polaron method in their appropriate parameter limits. Thus our versatile CHRW variational polaron method is able to interpolate between these two methods and, combining with the weak-system-bath-coupling method, can capture the correct behaviors over a very wide parameter space for driven open quantum systems.

並列關鍵字

open quantum system ； initial correlations ； rotating wave approximation ； trace distance ； variational polaron transformation ； free energy minimization

參考文獻

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