Exact dynamics and bound states of a cavity coupled to a two-dimensional reservoir

TL;DR

This work analyzes the exact dynamics of a continuous-variable target cavity coupled to a two-dimensional coupled-cavity array (2D CCA). It reveals that resonant coupling generates a bound state in the continuum ($\mathrm{BIC}$) inside the reservoir band, plus two bound states outside the band ($\mathrm{BOC}$s), leading to rich non-Markovian dynamics. In the weak-coupling, band-center regime, the $\mathrm{BIC}$ yields near-perfect, dissipationless information storage, while off-center detunings produce oscillatory storage due to the interplay with the $\mathrm{BOC}$s; finite temperature preserves the central role of the $\mathrm{BIC}$ in suppressing fluctuations, yet non-Markovian effects emerge from the competition among bound states. The results establish a scalable all-optical quantum-memory platform in photonic lattices and motivate exploration of topological and non-Hermitian reservoir extensions for enhanced memory lifetimes.

Abstract

We demonstrate a robust scheme for quantum information storage based on bound states in a two-dimensional coupled-cavity array. When a target cavity is tuned to resonance with the array, a bound state in the continuum (BIC) emerges, coexisting with two conventional bound states outside the band. The resulting dynamics reflects a delicate interplay between these bound states, which can be fully captured through exact analytical solutions. In the weak-coupling regime, the BIC dominates, enabling perfect and persistent information storage. At stronger coupling, all bound states contribute, leading to oscillatory behavior and reduced storage fidelity. These results, valid at both zero and finite reservoir temperatures and further supported by a single-particle framework, reveal distinctive non-Markovian features in continuous-variable systems and highlight the potential of photonic lattices for scalable all-optical decoherence-free quantum memory platforms.

Figures (9)

• Figure 1: Schematic diagram of the model. (a) The 2D CCA (denoted by green circles) with tight-binding interactions (denoted by the green dotted lines). (b) The target cavity (denoted by a brown circle) located directly above the center $(0,0)$-th cavity of the 2D CCA and its interactions with the 2D CCA (denoted by four brown lines).
• Figure 2: (a) Density of state $\varrho(\omega)$ and (b) spectral density $J(\omega)$ for a target cavity coupled to 2D CCAs. Here we set $\eta=1$.
• Figure 3: Exact dynamics of $|u(t)|$ and its maximum steady value $u^m_s$ for different detunings and coupling strengths. For Figs. (a) and (b), the detuning $\Delta\omega_c=5$. For Figs. (c) and (d), $\Delta\omega_c=0.5$. For Figs. (e) and (f), $\Delta\omega_c=0$. The inset in Fig. (b) shows the maximum steady value $u^m_s$ versus the detuning outside the band when the coupling strength $\eta=1$. In this work, the physical parameters for numerical calculation are the same as the 1D case Wu10: the frequency of the cavities in the reservoir is $\omega_0=12.15\text{GHz}=50.25\mu \text{eV}$, and the coupling between the nearest-neighboring cavities in the reservoir is $\xi_0=1.24\mu \text{eV}$.
• Figure 4: (a) Distribution of the eigenenergies $\{\Delta\Omega_j \}$$(j=\pm,0)$ of the bound states and (b) the corresponding amplitudes $\{Z_j \}$ versus the coupling strength $\eta$. For Figs. (a) and (b), the detuning $\Delta\omega_c=5$. For Figs. (c) and (d), $\Delta\omega_c=0.5$. For Figs. (e) and (f), $\Delta\omega_c=0$.
• Figure 5: Exact dynamics of $v(t)$ and $n(t)$ for different detunings and coupling strengths. Panels (a) and (b) correspond to detuning $\Delta\omega_c=5$, (c) and (d) to $\Delta\omega_c=0.5$, and (e) and (f) to $\Delta\omega_c=0$. Here, $T=2\omega_c$ and the initial photon number is set to $n(0)=10$.