去相位量子自旋開放系統之Zeno及Anti-Zeno效應

Abstract

去相位量子自旋開放系統之演化方程可經由Magnus展開而得到精確解。量子Zeno效應是當我們對不穩定粒子施以極高頻率的測量來確認粒子所處之量子態時，此不穩定的粒子在測量的過程中會持續停留在原來的狀態。在實驗上當施以頻率較高的量測會使得粒子停留在原來狀態機率增加，則我們稱此現象為量子Zeno效應。如果測量的頻率不夠高則有可能導致量子anti-Zeno效應的發生，也就是隨著測量頻率的增高粒子停留在原來狀態的機率反而降低。我們研究了量子Zeno效應以及量子anti-Zeno效應在量子去相位自旋開放系統裡的問題。我們假定我們的系統一開始是在量子疊家態而環境則是在熱平衡態，由此出發我們有辦法得到精確的粒子存在原來狀態的機率的精確解。我們經由此精確解作留在原來狀態機率對測量次數的圖，我們發現留在原來狀態的機率和測量頻率耦合強度以及環境correlation時間有著非常顯著的關係。

Pure-dephasing spin-boson model resides the property that it’s propagator can be obtained, with Magnus expansion, and the model so is exactly solvable. The quantum Zeno effect is a situation that if the measurements imposed upon the unstable particle are frequent enough, the state evolution of the particle can be frozen. Subsequently it was predicted that an enhancement of decay due to frequent but not sufficiently frequent measurements could lead to the so-called anti-Zeno effect, i.e. the increase of measuring frequency will decrease the survival probability. We study the quantum Zeno effect and anti-Zeno effect on the pure-dephasing spin-boson model. Here we evaluate the decay rate of the system frequently measured by the initial projective operator. Since the total system and environment propagator is known, we can derive the exact analytic form of the probability of the system to remain in its initial state after N times of measurement on the condition that the initial environment is in thermal equilibrium. Given the condition that the environment is in thermal equilibrium mixed state, we know that partial traced density matrices of the system will gradually dephase to mixed state if the initial state is in superposition state. We use the derived equation to investigate the competition between the dephasing ability triggered by the environment and the freezing capability of the successive measurements on the system. We find that the survival probability is highly related to the frequency of the measurements, the coupling strength and the bath correlation time.