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標題: | 在自旋玻色系統中之去相位量子系統和弛豫量子系統的量子Zeno效應和反Zeno效應 Quantum Zeno and Anti-Zeno effects in Spin Boson Models: Pure Dephasing Model versus Relaxation Model |
作者: | 郝鴻 Hong Hao |
指導教授: | 管希聖 Hsi-Sheng Goan |
關鍵字: | 量子茲諾效應,反茲諾效應,去相位量子自旋開放系統,弛豫自旋玻色系統,白噪音, quantum Zeno effect,anti-Zeno effect,pure dephasing model,relaxation model,white noise, |
出版年 : | 2019 |
學位: | 碩士 |
摘要: | 量子茲諾效應(QZE)是個能防止系統狀態發生演化的效應,換句話說,也就是當系統具備足夠高的頻率觀察時,系統的演化就會被"凍住"。反之,反茲諾效應(AZE)說的是當提高觀察的頻率時,系統的狀態變得容易變成其他狀態。而傳統去計算QZE和AZE在開放式量子系統的存活機率的方法由Kofman和Kurizki假設在做完投影測量時,系統與環境的狀態會回到原本的初始狀態,而這樣的計算方法(KKA)它的優點是好算,但這個假設並不總是有效。相反的,在廣義的方法(GA)中,當系統與環境演化到糾纏態的那時刻時 tau = t/N (t是總時間,N是重複的觀察次數),對那個系統做投影測量到初始狀態,環境的狀態會塌縮到對應狀態,正常來說,不會是初始的環境狀態。這是這兩個方法主要的差異。接著透過KKA和GA在這兩種不同的方法下,我們探討QZE和AZE在去相位量子自旋開放系統下的衰變率。 在完全可精確解的去相位量子自旋開放系統下,系統與環境整體的傳播子可以由許多方式得到,例如: Magnus展開。然而,當重複的觀察次數提高時,這樣計算存活機率的方法會變的很複雜而且耗時。最近在Phys.Rev.A96,032101(2017)這篇論文上提出一個方法來研究QZE和 AZE在更廣義的羅倫茲能譜密度於弛豫自旋玻色系統(relaxation spin boson model)並且不需要Born-Markovian 近似。在羅倫茲能譜密度的條件下,可以將環境轉化成由單一的玻色子模態與虛擬的白噪音互相耦合的環境,接著將白噪音的自由度平均掉(trace),將可得Lindblad form的master方程。我們發現由此master方程所計算出來的存活機率與透過精確解的傳播子所得到的結果在某些極限下是相同的。
因此,我們可以用此有效率的master方程加快模擬的速度來研究QZE和AZE於去相位量子系統在更大的重複觀察次數下,並說明在KKA和GA下不同的結果。 Quantum Zeno effect (QZE) is the effect that can prevent system state from changing, i.e., freezing state’s transition, when the system is under sufficiently frequent measurements. On the contrary, anti-Zeno effect(AZE) states that when the measurement frequency increases but is not high enough, the system state will be easier to transit to other state. The traditional approach to calculate the survival probability for QZE and AZE in an open quantum system used by Kofman and Kurizki assumes that after the projective measurement on the system, the system and bath total state will return back to their same initial total state. The advantage of the Kofman-Kurizki approach (KKA) is that the calculation becomes easier. However, the assumption made in the KKA is not generally valid. In contrast, in the general approach (GA), after the system and bath total state evolves to an entangled state at time tau=t/N (t is the total time, and N is the repeated number of measurements), a projective measurement immediately made on the system projects the system back to the initial system state, and the bath state collapses to a corresponding conditional state, normally different from the initial bath state. This is the key difference between the two approaches. We investigate QZE and AZE and show how decay rate behaves in the two different approaches of KKA and GA for a pure dephasing spin-boson model. The total propagator for the system and bath can be obtained for the exactly solvable pure dephasing model by many means, e.g., by the Magnus expansion method. However, when the number of repeated measurements becomes large, the survival probability computed in this way becomes tedious and time consuming. Recently, an approach developed to study QZE and AZE for a more general relaxation spin-boson model with a Lorentzian bath spectral density has been put forward in Phys. Rev. A 96, 032101 (2017) without making the Born-Markovian approximation. The Lorentzian bath spectral density enables the bath to be replaced with a single bosonic mode coupling to a fictitious white reservoir. Tracing over the degrees of freedom of the white noise leads to a master equation in Lindblad form. We find that the results of the survival probability obtained by the master equation of the two-level system and the single bosonic mode is the same as the result obtained by the exact full system-bath propagator method in the relevant limit. We thus use the efficient master equation approach that allows fast simulations to investigate the QZE and AZE with large measurement number for the pure dephasing model and a relaxation model, and illustrate the difference in the results obtained by the KKA and the GA. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/73864 |
DOI: | 10.6342/NTU201903497 |
全文授權: | 未授權 |
顯示於系所單位: | 物理學系 |
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