Saving the Unruh Signal: Coherent Cancellation of Spontaneous Emission with Entangled Detectors

TL;DR

The paper tackles the challenge of detecting the Unruh effect, which is hidden by dominant spontaneous emission noise. It introduces a three-Unruh–DeWitt detector setup arranged in a W-state and imposes a resonance condition $rac{ ext{omega}_k}{a_k}= ext{\Lambda}$ to force all detectors to emit into the same on-shell mode, enabling destructive interference that cancels first-order spontaneous emission. The central result is the sine-rule, a geometric constraint on the real-valued W-state amplitudes that achieves simultaneous cancellation of both right- and left-traveling emission channels, isolating the Unruh absorption signal. The work argues for robustness to small preparation and control errors and outlines extensions to $(3+1)$D and analog quantum simulators, proposing a viable route toward the definitive observation of the Unruh signal.

Abstract

The Unruh effect is notoriously difficult to detect, as it is exponentially overwhelmed by Wigner--Weisskopf spontaneous emission. We show that this fundamental obstacle can be overcome by harnessing multi-detector quantum interference. By preparing a system of three entangled Unruh--DeWitt detectors in a specific W-state, the spontaneous emission channels can be forced to destructively interfere and vanish, thereby "saving" the Unruh signal by coherently silencing this dominant noise. Our central result is the derivation of the condition for complete and simultaneous cancellation of all right- and left-traveling emission modes. We find this requires preparing the detectors in a unique entangled state whose real-valued coefficients are fixed by an elegant geometric constraint, given by a ratio of sines of the logarithms of the detector accelerations. This work establishes multi-detector entanglement as a precision tool for noise cancellation in relativistic quantum settings, offering a new pathway toward the definitive observation of the Unruh signal.

Figures (2)

• Figure 1: Spacetime diagram of the proposed scenario. Three UDW detectors (1, 2, 3) follow hyperbolic trajectories with distinct proper accelerations $a_1, a_2, a_3$. Each detector is a two-level system with a unique energy gap $\omega_k$. By preparing the detectors in an entangled state and tuning the parameters to satisfy the resonance condition $\frac{\omega_k}{a_k} = \Lambda$, specific field-mediated transitions can be coherently cancelled.
• Figure 2: The required probabilities $|\alpha_i|^2$ for the entangled W-state that achieves complete spontaneous emission cancellation, plotted as a function of the acceleration ratio $a_1/a_3$. Each subplot shows the solution for a different set of fixed physical parameters $(\Lambda, a_2/a_3)$, demonstrating how the required quantum state depends on both the resonance condition and the geometric configuration of the detectors. The plots show that increasing $\Lambda$ leads to more rapid oscillations, indicating a higher sensitivity to the system's geometry.