Reflecting boundary induced modulation of tripartite coherence harvesting

TL;DR

This work studies how a perfect reflecting boundary modulates tripartite coherence harvested by three static Unruh-DeWitt detectors coupled to a massless scalar vacuum. By deriving the detector dynamics with $H(t)$ and tracing over the field, the authors obtain a $C_{l_1}$ measure of coherence, showing that boundary-induced vacuum fluctuations suppress coherence but can preserve or enhance entanglement; coherence is found to be more spatially robust than entanglement and is further reduced by detector-energy-gap asymmetry. The analysis distinguishes parallel and orthogonal geometries, finding that orthogonal alignment yields greater coherence, and reveals a monogamy-like relation where the total tripartite coherence equals the sum of all bipartite coherences: $C^{p/v}_{l_{1}}( ho_{AB})+C^{p/v}_{l_{1}}( ho_{BC})+C^{p/v}_{l_{1}}( ho_{AC})=C^{p/v}_{l_{1}}( ho_{ABC})$. These results illuminate the complementary roles of coherence and entanglement in structured vacuum fields and provide design principles for optimizing quantum resources via geometry and spectral inhomogeneity.

Abstract

We study the extraction of quantum coherence by three static Unruh-DeWitt (UDW) detectors that interact locally with a massless scalar vacuum field in the vicinity of an infinite perfectly reflecting boundary. Depending on the setup, the detectors are positioned either parallel or orthogonal to the boundary, with their energy gaps chosen to satisfy the hierarchy $Ω_C\geq Ω_B\geq Ω_A$. Our analysis reveals that decreasing the detector-boundary separation leads to a monotonic degradation of quantum coherence, whereas the same boundary effect can simultaneously preserve and even amplify the harvested quantum entanglement. Moreover, when the detectors possess distinct energy gaps, coherence extraction is further inhibited; strikingly, such non-identical configurations substantially enhance the efficiency of entanglement harvesting and markedly extend the range of detector separations over which non-negligible entanglement can be generated. Nevertheless, the harvesting of nonlocal quantum coherence is achievable over a significantly broader range of detector separations than that of quantum entanglement. Despite exhibiting similar overall behavior, orthogonal detector configurations outperform parallel ones in coherence harvesting, highlighting the quantitative influence of detector geometry. Overall, our study reveals a hierarchical distinction between quantum coherence and entanglement as operational resources in structured vacuum fields: quantum coherence is not only more readily accessible across space but also more robust than entanglement, whereas entanglement exhibits richer features and can be selectively activated and enhanced through boundary effects and detector non-uniformity.

Figures (7)

• Figure 1: Schematic illustration of three static UDW detectors, designated as $A, B$ and $C$, aligned parallel to a reflecting boundary. Adjacent detectors are separated by a distance $L$ in the vertical direction and are positioned at a fixed distance $\Delta z$ from the boundary.
• Figure 2: Quantum coherence $C^{p}_\mathrm{l_1}$ as a function of detector separation $L/\sigma$, for $\Omega_A\sigma = 0.1$ and $\Delta z = 1$, with different values of $\Omega_B\sigma$ and $\Omega_C\sigma$.
• Figure 3: Quantum coherence $C^{p}_\mathrm{l_1}$ as a function of the distance from the detectors to the boundary $\Delta z/\sigma$, for fixed $\Omega_A\sigma= 0.1$ and $L/\sigma = 1$, with varying values of $\Omega_B\sigma$ and $\Omega_C\sigma$.
• Figure 4: Configuration of three static detectors aligned perpendicular to a reflecting boundary. Adjacent detectors are separated by a distance $L$, and the distance $\Delta z$ represents the separation between the boundary and the detector that is positioned closer to it.
• Figure 5: Quantum coherence $C^{v}_\mathrm{l_1}$ as a function of the distance between the detectors $L/\sigma$ for $\Omega_A\sigma = 0.1$, $\Delta z/\sigma = 1$, and different choices of $\Omega_B\sigma$ and $\Omega_C\sigma$.