Zeno and anti-Zeno effects in dark-state dynamics under thermal dephasing

Abstract

The quantum Zeno and anti-Zeno effects describe how frequent measurements can either suppress or accelerate quantum dynamics. While extensively studied in various platforms, their manifestation in dark-state dynamics remains largely unexplored. Here we investigate the stability of dark states in a cavity QED system consisting of two atoms coupled to a single-mode cavity, subject to thermal dephasing that models continuous quantum non-demolition monitoring. Using the Tavis--Cummings model within a Lindblad master equation framework, we numerically analyze how measurement-induced dephasing affects dark-state retention and stabilization time. We identify distinct parameter regimes corresponding to Zeno and anti-Zeno behavior: at low dephasing intensities, increasing the measurement strength accelerates the loss of dark-state coherence (anti-Zeno regime), while at higher intensities, it slows down the dynamics and partially recovers dark-state weight (Zeno regime). The transition between these regimes is controlled by the dephasing rates, the cavity photon exchange, and the asymmetry in atom-field couplings. We show that even under strong dephasing, a finite dark-state component persists, demonstrating remarkable robustness. Our results provide insights into the interplay between measurement back-action and decoherence in open quantum systems, with implications for quantum control and information storage.

Figures (10)

• Figure 1: (online color) Influence of cavity photon exchange on dark-state retention under thermal dephasing. The operators $\hat{\mathcal{L}}_1$, $\hat{\mathcal{L}}_2$, $\hat{\mathcal{L}}_3$ and $\hat{\mathcal{L}}_4$ correspond to $\hat{\mathcal{L}}_{in}$, $\hat{\mathcal{L}}_{out}$, $\hat{\mathcal{L}}_{deph,1}$ and $\hat{\mathcal{L}}_{deph,2}$, respectively. Parameters: $\omega = 1\,\mathrm{GHz}$, $g_1 = 30\,\mathrm{MHz}$, $g_2 = 50\,\mathrm{MHz}$, $\gamma_{out}=20\,\mathrm{MHz}$, $\gamma_{in}=10\,\mathrm{MHz}$, and $\gamma_{deph,1} = \gamma_{deph,2} = 20\,\mathrm{MHz}$.
• Figure 2: (online color) Heatmaps of dark-state retention and stabilization time versus dephasing rates $\gamma_{deph,1}$ and $\gamma_{deph,2}$. Panels (a) and (b) show $P_{ret}$, while panels (c) and (d) show $T_{stab}$. The coupling strengths $\gamma_{deph,1}$ and $\gamma_{deph,2}$ are both given in $\mathrm{MHz}$. Parameters: $\omega = 1\,\mathrm{GHz}$, $g_1 = 30\,\mathrm{MHz}$, $g_2 = 30\,\mathrm{MHz}$, $\gamma_{out}=10\,\mathrm{MHz}$, $\gamma_{in}=3\,\mathrm{MHz}$.
• Figure 3: (online color) Trends of $T_{stab}$ and $P_{ret}$ along the line $\gamma_{deph,1}=\gamma_{deph,2}$. In panel (a), the black dashed curve marks the anti-Zeno to Zeno boundary. Its intersection with the white diagonal gives the point where $\gamma_{deph,1}=\gamma_{deph,2}=\gamma_{\min}$. The dephasing rates $\gamma_{deph,1}$ and $\gamma_{deph,2}$ are given in $\mathrm{MHz}$. Parameters: $\mu_{ph}=0.3$, $\gamma_{out}=10\,\mathrm{MHz}$, $\gamma_{in}=3\,\mathrm{MHz}$.$g_1 = 2\,\mathrm{MHz}$, $g_2 = 2\,\mathrm{MHz}$.
• Figure 4: (online color) Cross-sections along the line $\gamma_{deph,1}=\gamma_{deph,2}$. Panel (a) shows $T_{stab}$ and the location of $\gamma_{\min}$, while panel (b) shows $P_{ret}$. The data illustrate the strong robustness of dark states: after a shallow initial decrease, $P_{ret}$ rises slowly with increasing dephasing, consistent with the anti-Zeno to Zeno crossover. Parameters: $\mu_{ph}=0.3$, $\gamma_{out}=10\,\mathrm{MHz}$, $\gamma_{in}=3\,\mathrm{MHz}$.$g_1 = 2\,\mathrm{MHz}$, $g_2 = 2\,\mathrm{MHz}$.
• Figure 5: (online color) Field-factor dependence of optimal quantities under symmetric dephasing $\gamma_{deph,1}=\gamma_{deph,2}$. Panel (a) shows the minimum stabilization time $T_{stab}^{min}$, panel (b) shows the corresponding optimal dephasing rate $\gamma_{\min}$, and panel (c) shows the minimum dark-state retention $P_{ret}^{min}$.