Worldline-Induced Transparency

TL;DR

The paper investigates how the Unruh response of a single Unruh--DeWitt detector can be controlled when the detector's center of mass is in a coherent superposition of two uniformly accelerated worldlines. By using a path-erasing readout, the excitation amplitudes from the two branches interfere coherently, enabling destructive (dark-port) or constructive (bright-port) interference under a matching condition $\omega_1/a_1=\omega_2/a_2=\Lambda$ and a tunable relative phase $\alpha_2/\alpha_1=-(a_1/a_2)^{\pm i\Lambda}$. The analysis is performed in both Unruh-mode and Minkowski plane-wave formalisms, and finite interaction times are treated to yield a explicit tolerance window, with Gaussian switching giving a closed-form amplitude and bandwidth $\Delta\Omega\sim 1/(aT)$ and a corresponding phase tolerance $|\Delta(\omega/a)|\lesssim c/(T)$. This relativistic analogue of electromagnetically induced transparency (worldline-induced transparency) demonstrates how vacuum-induced excitations can be coherently suppressed or enhanced via interferometric control, with potential implications for quantum-field-theoretic interferometry and analogue experiments.

Abstract

We show that the Unruh response can be interferometrically suppressed or restored in a single Unruh--DeWitt detector whose center-of-mass is prepared in a coherent superposition of two uniformly accelerated worldlines. The two paths remain physically disjoint; the detector is read out in a path-erasing basis so that no which-path information is revealed. If the detector's energy gap is path dependent during the interaction, the branch amplitudes for first-order excitation become operationally indistinguishable and therefore add coherently. With appropriate tuning -- matching the gap-to-acceleration ratios of the two branches and choosing a single relative phase -- the conditional first-order excitation amplitude cancels, while reversing the phase restores the response. We derive these conditions in two complementary formalisms and interpret the mechanism as a relativistic analogue of electromagnetically induced transparency, which we term worldline-induced transparency. We also treat finite switching times explicitly and quantify how imperfect matching produces a residual signal, yielding a tolerance window rather than an idealized infinitely sharp condition.

Figures (3)

• Figure 1: Conceptual schematic of WIT. A single detector is coherently split between two uniformly accelerated, disjoint worldlines ($a_1,a_2$). The excited state is common ($\ket{e}$), while the ground states are branch dependent ($\ket{g_1},\ket{g_2}$) via distinct gaps ($\omega_1,\omega_2$). The lighter purple arm indicates a smaller branch weight in the superposition ($|\alpha_1|$ vs. $|\alpha_2|$).
• Figure 2: Analogy to a three-level $\Lambda$ system. The branch-conditioned detector configurations $\ket{g_1}$ and $\ket{g_2}$ play the role of two long-lived "ground" states coupled to a common excited state $\ket{e}$. The two excitation pathways (one from each branch) interfere in the conditional (path-erasing) readout, i.e., after projecting the branch ancilla onto $\ket{+}=(\ket{a_1}+\ket{a_2})/\sqrt{2}$. In this language the effective coupling strengths are proportional to the first-order branch excitation amplitudes (RTW: $\mathcal{I}_k$, LTW: $\mathcal{I}_k^{*}$ in the adiabatic limit). For the relative phase settings that satisfy the cancellation rules in Eqs. \ref{['match']}--\ref{['eq:WIT_condition']}, the transition amplitude into the postselected $(e,+)$ channel vanishes at first order ("dark" output), while excitation can still appear in the orthogonal $(e,-)$ outcome.
• Figure 3: Conditional interference and spectral cross-check. (Left) Color map ("heatmap") of the normalized conditional excitation probability in the postselected output $(e,+)$ as a function of the relative branch phase $\theta$ and the log-acceleration ratio $r_a\equiv\ln(a_1/a_2)$. Dark regions indicate suppression (destructive interference), while bright regions indicate enhancement (constructive interference). The dashed curves mark the analytic cancellation loci predicted by Eqs. \ref{['eq:RTW_theta']}--\ref{['eq:WIT_condition']}. (Right) Corresponding emitted-radiation spectrum (plotted versus Minkowski frequency $\nu$) for two representative parameter choices. The "on-fringe" choice is taken on a suppression curve in the left panel and yields strong reduction of the spectrum over the plotted range. The "off-fringe" choice includes a small ratio mismatch $\Delta\Lambda\neq 0$ (equivalently $\omega_1/a_1\neq \omega_2/a_2$), so the two branch contributions populate different frequency/Unruh-label bands and do not cancel perfectly, leaving a residual structured spectrum.