Exact decoherence-free state of two distant quantum systems in a non-Markovian environment

TL;DR

This paper derives an exact, distance-dependent decoherence-free state for two distant quantum systems in a non-Markovian environment, revealing its connection to bound states in the continuum and enabling experimental realization.

Contribution

It provides the first analytical expression for the exact DFS of two spatially separated systems in a non-Markovian environment, linking it to BICs and specifying conditions for its formation.

Findings

DFS exists only in one-dimensional environments.

The DFS corresponds to the system-reduced state of a BIC.

An explicit criterion for DFS formation is derived.

Abstract

Decoherence-free state (DFS) encoding supplies a useful way to avoid the detrimental influence of the environment on quantum information processing. The DFS was previously well established in either the two subsystems locating at the same spatial position or the dynamics under the Born--Markovian approximation. Here, we investigate the exact DFS of two spatially separated quantum systems consisting of two-level systems or harmonic oscillators coupled to a common non-Markovian zero-temperature bosonic environment. The exact distance-dependent DFS and the explicit criterion for forming the DFS are obtained analytically, which reveals that the DFS can arise only in one-dimensional environment. It is remarkable to further find that the DFS is just the system-reduced state of the famous bound state in the continuum (BIC) of the total system predicted by Wigner and von Neumann. On the one hand our result gives insight into the physical nature of the DFS, and on the other hand it supplies an experimentally accessible scheme to realize the mathematically curious BIC in the standard quantum optical systems.