本論文中，我們研究空腔同時藉由光子吸收/放射與雙光子過程耦合到一個熱庫的非馬可夫動力學。藉由結合海森堡運動方程法與主方程法，我們可以得到空腔的主方程。此主方程可幫助我們分析一些重要的物理量例如空腔的電場、光子數。此空腔系統與熱庫間的雙光子過程將會引起一個感應的雙光子耦合並且只有在弱耦合下此效應才可被忽略。此效應會壓縮系統的量子態並且同時產生量子噪聲與增強熱噪聲。最後，藉由本理論，我們研究了當空腔一開始處在任意高斯態下的演化過程，並且討論了一個簡單的例子即空腔一開始處在相干態。

In this thesis, the exact non-Markovian dynamics of a cavity coupled to a general reservoir with both photon emission/absorption and two-photon processes is solved by combining the Heisenberg's equation of motion approach with the master equation approach. We find that the system-reservoir two-photon coupling induce two-photon processes in the cavity which is negligible only in the weak coupling regime. This reservoir-induced two-photon processes will
squeeze the cavity state and produce both quantum and thermal noises. We also study the time evolution of an arbitrary Gaussian state initially prepared in cavity.

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