環境耦合下奈米力學系統之非馬可夫動力及量子糾纏現象

Abstract

量子糾纏態在量子傳輸及量子通訊上扮演極為重要的角色。因此探討開放系統之量子糾纏態隨時間的動力演變是現今一個重要的課題。我們假設四個相關之奈米力學開放系統模型, 並僅使用微擾法導出各別量子系統之non-Markovian master equation。然而在之前的文獻中大都使用Markovian 或rotating-wave 近似法來處理問題, 但non-Markovian 對於真實系統的描述更貼近於實驗觀察。 因此我們採用non-Markovian 來處理我們的問題。從此些方程出發, 我們使用two-mode squeezed vacuum state 為我們的初始態並引用logarithmic negativity來定義量子糾纏的程度。我們發現在完全沒有環境作用的情況下, 量子糾纏隨時間的演變為週 期性振盪或維持定值。但若考慮環境的影響, 量子糾纏將會隨時間而遞減且週期性現象會逐漸消失。當環境與系統間的作用越強時, 量子糾纏存在的時間越短。我們發現當兩個系統與同一環 境作用下之情況量子糾纏態存在的時間遠比兩個系統各自與不同的環境作用來得久。我們也發現原本沒有糾纏性質的量子態可透過系統間的交互作用或與同一環境作用而產生量子糾纏。此 外, 在我們所採用的參數條件下(低溫及低系統振盪頻率下), Markovian 及rotating-wave 近似法不能獲得良好的近似結果, 因此以non-Markovian 來處理此類系統是必需且必要的。

Quantum entangled states play a crucial role in the quantum teleportation and quantum information science, hence the research of the dynamics of entanglement has become an important topic and has attracted much attention recently. We use perturbative method to derive non-Markovian master equations, which were derived in the literature before by other extra approximations such as rotating-wave and Markovian approximations, of four different but related models of the open nanomechanical systems respectively. Markovian approximation is close to physical phenomena only under the long time regime so we use the non-Markovian instead of Markovian approximation to deal with our models. We use two-mode squeezed vacuum state as our initial entangled state and use the definition of logarithmic negativity to quantify the degree of entanglement. We find that the dynamics of quantum entanglement varies periodically or maintains constant under environment free condition. However, under the influence of environment, entanglement will decrease with time and the periodic or revival behaviors dies out gradually. As the interaction between the environment and system increases, the time span during which entanglement exists decrease. We find that the entanglement can be sustained much longer when two subsystems are coupled to a common bath than respectively to independent reservoirs. Furthermore, we find that a separable state can become entangled through the interaction of two subsystems or coupling to a common bath. We also find that under some conditions (e.g. at low temperature or low system vibration frequency) Markovian and rotatingwave approximations are not the good approximations. So non-Markovian case is essential in order to obtain the accurate results of the system's entanglement time evolution.