Non-Markovian environment induced Schrödinger cat state transfer in an optical Newton's cradle

Abstract

In this manuscript, we study the Schrödinger cat state transfer in a quantum optical version of Newton's cradle in non-Markovian environment. Based on a non-Markovian master equation, we show that the cat state can be transferred purely through the memory effect of the non-Markovian common environment, even without any direct couplings between neighbor cavities. The mechanism of the environment induced cat state transfer is analyzed both analytically and numerically to demonstrate that the transfer is a unique phenomenon in non-Markovian regime. From this example, the non-Markovian environment is shown to be qualitatively different from the Markovian environment reflected by the finite versus zero residue coherence. Besides, we also show the influence of environmental parameters are crucial for the transfer. We hope the cat state transfer studied in this work may shed more light on the fundamental difference between non-Markovian and Markovian environments.

Figures (7)

• Figure 1: Schematic diagram of a coupled $N$-cavity array (a quantum optical analog of the classical Newton's cradle Feng2019PRAppl) interacting with a common environment. In this manuscript, we mainly focus on the “ no direct coupling” case $\lambda_{i}=0$.
• Figure 2: Cat state transfer in two cavities ($N=2$) without direct couplings $(\lambda_{i}=0)$. (a) Time evolution of the transferred fidelity $\mathcal{F}_{2}$. The transition from Markovian to non-Markovian regime is reflected by the increasing $\tau$ in the $y$-axis. (b)-(g) are the Wigner functions at the positions pointed by the markers in (a), respectively. The initial size of the cat state is $\alpha=2$. The other parameters are $\Omega_{1}=\Omega_{2}=\Omega=1$, $\Delta=10$, $\Gamma=1$.
• Figure 3: Influence of the central frequency $\Delta$ of the environmental density spectrum. (a) Time evolution of the transferred fidelity $\mathcal{F}_{2}$. (b) to (e) are the Wigner functions at the positions pointed by the markers in (a). The parameters are $\alpha=2$, $\gamma=0.3$, $\Omega_{1}=\Omega_{2}=\Omega=1$, $\lambda_{i}=0$, $\Gamma=1$.
• Figure 4: Non-Markovian impact on the long-term ($t\approx\infty$) behavior of the coefficient $F$. The real and imaginary part of $F$ are plotted in (a) with environmental parameters $\Delta$ and $\tau$. (b) The ratio of $\Im(F)/\Re(F)$.
• Figure 5: Cat state transfer from $1^{{\rm st}}$ cavity to $3^{{\rm rd}}$ cavity without direct couplings $(\lambda_{i}=0)$. Solid curve indicates the maximum fidelity $\mathcal{F}_{3}$ achievable with the asymmetric parameter $\eta$. The inset plot is the Wigner function of the $3^{{\rm rd}}$ cavity when $\log_{10}(\eta)\approx-0.3$ ($\eta=0.5$, $\delta l=0.5$). The parameters are $\Omega_{i}=1$, $\gamma=0.1$, $\Delta=5$,