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

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.

💡 Research Summary

The paper investigates a continuous‑variable quantum system consisting of a single target cavity coupled to an infinite two‑dimensional (2D) coupled‑cavity array (CCA). The authors derive an exact master equation for the reduced state of the target cavity, incorporating non‑Markovian memory kernels that fully encode the reservoir’s spectral properties. By Fourier‑transforming the CCA, they obtain a dispersion ω(k)=ω₀−2ξ₀(cos kₓ+cos k_y) with a bandwidth of 8ξ₀ and a momentum‑dependent coupling V(k)=2ξ e^{ik·r₀}(cos kₓ+cos k_y)=η e^{ik·r₀}