Steady-State Coherences under Partial Collective non-Markovian Decoherence

Abstract

Steady-state coherence in open quantum systems is crucial for quantum technologies, yet its behavior is not fully understood due to the interplay between collective and individual decoherence. While collective decoherence is thought to induce steady-state coherence, experiments often fail to observe this because of individual decoherence. We study a system of two harmonic oscillators coupled to both individual and collective environments, introducing a tunable parameter to adjust the decoherence proportions. By analytically solving the exact dynamical equations, we find that steady-state coherence depends on the initial state under collective decoherence, but not under partial decoherence. Interestingly, non-Markovianity induces rich and complex steady-state coherence behaviors. Our results offer new insights into the role of non-Markovian decoherence in quantum systems and serve as a benchmark for evaluating approximate methods in modelling quantum processes.

Figures (5)

• Figure 1: The mean values of the steady state coherence $\langle J_{x}\rangle$ as a function of $\theta$ (in unit of $\pi/2$) for (a) $\gamma=0.1\Gamma$ and (b) $\gamma=10\Gamma$. The other parameters are chosen as $\Gamma=\omega_1$, $\omega_2=\omega_0=\omega_1$, $T=\omega_0$. We set $\omega_1=1$ as a unit for the other parameters.
• Figure 2: The Steady-state thermal coherence as a function of the spectral width $\gamma$ for different proportions of collective decoherence with (a) $\gamma/\Gamma \in [10^{-8}, 10^{-2}]$ and (b) $\gamma/\Gamma \in [10^{-2}, 10^2]$. The parameters are $\kappa = -\pi/4$, $\omega_1 = \omega_2 = \Gamma$, $\omega_0 = \Gamma$, and $T = \omega_0$, with $\Gamma = 1$ as the unit.
• Figure 3: The steady state quantum coherences as a function of the coupling strength $\Gamma$ for (a) $\gamma=0.1\Gamma$ and (b) $\gamma=10\Gamma$ with different proportions of collective decoherence $\theta$. The other parameters are chosen as $\kappa=-\pi/4$, $\omega_0=\omega_2=\omega_1$, and $T=\omega_0$. We set $\omega_1=1$ as a unit for the other parameters.
• Figure 4: The steady state quantum coherences as a function of (a) reservoir's center frequency $\omega_0$ for $T=\omega_1$ and (b) environmental temperature $T$ for $\omega_0=\gamma$ with different proportions of collective decoherence $\theta$. The other parameters are chosen as $\kappa=-\pi/4$, $\gamma=\omega_2=\omega_1$, and We set $\omega_1=1$ as a unit for the other parameters.
• Figure 5: The steady state coherences $|J_x|$ and the steady state population differences $|J_z|$ as a function of frequency difference $\Delta$ from (a) thermal, (b) dissipative, and (c) total difference. The other parameters are chosen as $\kappa=-\pi/4$, $\gamma=0.1\Gamma$, $\omega_1=100\Gamma$, $\omega_0=100\Gamma$, and $T=\omega_0$. We set $\Gamma=1$ as a unit for the other parameters.