Boundary Effects Achieve Coherence Amplification with Three Unruh-Dewitt Detectors

Researchers are increasingly investigating how to harness vacuum fluctuations as a usable resource, and a new study details how reflecting boundaries impact this process. Shu-Min Wu, Xiao-Ying Jiang (Department of Physics, Liaoning Normal University), and Xiang-Yue Yu, Zhihong Liu et al. demonstrate that the presence of a perfectly reflecting boundary can both degrade and surprisingly enhance the extraction of coherence from the vacuum. This is significant because it reveals a crucial distinction between coherence and another related quantity, termed ‘’, showing that coherence is more readily accessible and robust in structured vacuum fields. The team’s findings, based on modelling Unruh-DeWitt detectors, highlight the potential for selectively activating and enhancing energy harvesting through careful control of boundary effects and detector configurations.

Furthermore, the research establishes that orthogonal detector configurations consistently outperform parallel arrangements in coherence harvesting, demonstrating the quantitative influence of detector geometry on the process. This work opens new avenues for exploring the fundamental relationship between quantum coherence and entanglement, with potential implications for advancements in quantum technologies and information processing. The research meticulously quantifies these effects, revealing that while both coherence and entanglement exhibit similar overall behaviour, subtle geometric arrangements can significantly impact harvesting efficiency. The findings demonstrate that boundary-induced modifications of the vacuum fluctuations have distinct impacts on different quantum resources, offering a pathway to selectively control and enhance specific quantum phenomena. This detailed analysis provides a crucial step towards harnessing the quantum vacuum as a practical resource for future quantum technologies, potentially enabling new approaches to quantum metrology, cryptography, and computation.

Unruh detector coherence and energy harvesting near boundaries

The experimental setup involved defining the spacetime trajectories of the detectors A, B, and C when aligned parallel to the boundary. Transition probabilities, denoted as PD, and correlation terms, C and X, were then calculated using established equations, requiring the application of the Wightman function for vacuum massless free scalar fields derived through the method of images: W(xD, x′D) = −1 4π2 1 (t −t′ −iǫ)2 −(x −x′)2 −(y −y′)2 −(z −z′)2 − 1 (t −t′ −iǫ)2 −(x −x′)2 −(y −y′)2 −(z + z′)2. Substituting these trajectories and the Wightman function into the relevant equations yielded direct calculation of the transition probabilities. Scientists further refined the analysis by evaluating correlation terms CAB and XAB between detectors A and B as CAB = λ2 4√πe−(ΩB−ΩA)2σ2 4 fAB(L) −fAB( p L2 + 4∆z2) and XAB = −λ2 4√πe−(ΩB+ΩA)2σ2 4 gAB(L) −gAB( p L2 + 4∆z2), utilising auxiliary functions fAB(L) and gAB(L) to account for the detector separation and energy gaps.

To determine CAC, XAC, fAC(L), and gAC(L), researchers replaced ΩB with ΩC and adjusted the separation distance to 2L. The team established the condition ∆ΩCB := ΩC−ΩB ≥0 and ∆ΩBA := ΩB−ΩA ≥0, noting that correlation terms vanish when the duration parameter is significantly smaller than the energy-gap difference. Numerical calculations of the l1-norm of coherence were performed to assess the impact of detector separation and boundary distance. Results revealed a monotonic decrease in coherence with increasing detector separation L/σ, indicating that closer proximity enhances coherence harvesting. Moreover, the study demonstrated that as detectors move further from the reflecting boundary, harvested coherence increases, saturating at a finite value, signifying boundary-induced suppression at short distances.

Boundary effects modulate coherence in Unruh-DeWitt detectors

Despite exhibiting similar overall behaviour, orthogonal detector configurations outperformed parallel ones in coherence harvesting, highlighting the quantitative influence of detector geometry. The team measured quantum coherence, denoted as Cv l1, as a function of the separation L/σ, demonstrating that for the same detector-boundary distance of ∆z/σ = 1 and identical spectral parameters, the orthogonal alignment systematically yielded larger coherence than the parallel one. Accordingly, the curves in the orthogonal configuration consistently lay above those in the parallel configuration. Results demonstrate that orienting the detector array perpendicular to the reflecting boundary effectively alleviates the boundary-induced suppression of quantum coherence under identical geometric and spectral conditions.

Further measurements of quantum coherence Cv l1 as a function of the normalized distance ∆z/σ between the detectors and the reflecting boundary showed that coherence initially increased monotonically with ∆z/σ, gradually saturating at a steady value, indicating diminishing boundary influence with increasing separation. Notably, Cv l1 did not vanish at ∆z/σ = 0 for the perpendicular alignment, and the overall coherence level was higher across the range, attributed to a larger effective coupling distance between the detector system and the boundary. Data shows that the amount of harvested quantum coherence was maximized when all three detectors shared identical energy gaps, while energy-gap asymmetry significantly suppressed coherence extraction. This behaviour indicates that energy-gap asymmetry acts as an inhibiting factor for coherence harvesting, contrasting with observations for quantum entanglement, where detector non-identicality facilitates generation and enhancement. Analysis revealed a fundamental structural property of tripartite coherence, demonstrating that the total coherence of the three-detector system is exactly equal to the sum of all pairwise coherences, implying no global tripartite coherence can be extracted from the quantum vacuum.

Coherence-entanglement trade-offs near reflecting boundaries are a fascinating

Their analysis considered both parallel and orthogonal detector alignments, alongside a hierarchy of detector energy gaps. Furthermore, the study reveals that differing detector energy gaps inhibit coherence extraction, yet substantially enhance entanglement generation and extend the range over which entanglement can be achieved. Detector geometry also influences coherence harvesting, with orthogonal configurations consistently outperforming parallel arrangements. Importantly, the total coherence among the three detectors is fully accounted for by bipartite contributions, establishing a monogamy relation for tripartite coherence. These findings highlight the complementary roles of coherence and entanglement in relativistic quantum information processing and offer guidance for optimising detector configurations to harvest specific quantum resources.