Non-Markovian environment induced chaos in optomechanical system

Abstract

In traditional research, chaos is frequently accompanied by non-linearity, which typically stems from non-linear interactions or external driving forces. However, in this paper, we present the chaotic behavior that is completely attributed to the non-linear back-reaction of non-Markovian environment. To be specific, we derive the dynamical equations of an optomechanical system and demonstrate that the non-linearity (cause of chaos) in the equations arises entirely from the time-domain convolutions (TDCs) induced by non-Markovian corrections. Under Markovian conditions, these TDCs are reduced into constants, thereby losing the nonlinearity and ultimately leading to the disappearance of chaos. Furthermore, we also observe chaos generation in the absence of optomechanical couplings, which further confirms that the non-Markovian effect is the sole inducement of chaos and the environmental parameters play important roles in the generation of chaos. We hope these results may open a new direction to investigate chaotic dynamics purely caused by non-Markovian environments.

Figures (6)

• Figure 1: Schematic diagram of double-mirror optomechanical system. An F-P cavity is coupled to two movable mirrors through the radiation pressure. Both mirrors are coupled to a non-Markovian common environment.
• Figure 2: The evolution of maximum LE for physical observable $\langle\hat{q}_{1}\rangle$ with different correlation time $\tau$. The initial conditions are $\langle\hat{q}_{1}\rangle|_{t=0}=\langle\hat{q}_{2}\rangle|_{t=0}=1.1$ and $\langle\hat{p}_{1}\rangle|_{t=0}=\langle\hat{p}_{2}\rangle|_{t=0}=0$ and $\langle\hat{a}^{\dagger}\hat{a}\rangle|_{t=0}=2$. The parameters are $\omega_{1}=\omega_{2}=\omega=1$, $\Omega=0$, $G_{1}=G_{2}=1$, and $\kappa_{1}=\kappa_{2}=1$.
• Figure 3: Time evolution of maximum LE of the TDCs $F_{i}$ with different correlation time $\tau$. The parameters are the same as Fig. \ref{['fig22']}.
• Figure 4: Time evolution of LE of $\langle\hat{p}_{1}\rangle$ with different central frequency $\Omega$ of the environment. The memory time $\tau$ is chosen as $\tau=1$ ($\gamma=1$), and the other parameters are the same as Fig. \ref{['fig22']}.
• Figure 5: The average of LE of $\langle\hat{p}_{1}\rangle$ over $\omega t\in[5,20]$. The parameters are $\gamma=0.5$, $\Omega=0$, $G_{1}=G_{2}=1$, and $\omega_{1}=\omega_{2}=1$. The initial conditions are $\langle\hat{q}_{1}\rangle|_{t=0}=\langle\hat{q}_{2}\rangle|_{t=0}=1$, $\langle\hat{p}_{1}\rangle|_{t=0}=\langle\hat{p}_{2}\rangle|_{t=0}=2$ and $\langle\hat{a}^{\dagger}\hat{a}\rangle|_{t=0}=1$.