N-Photon Emission from Uniform Acceleration

TL;DR

This work develops a complete $n^ ext{th}$-order framework for a uniformly accelerated Unruh–DeWitt detector interacting with a massless scalar field, deriving exact final $n$-photon states via the Dyson series in Unruh-mode formalism. The analysis reveals two resonance classes in even orders (detector-mediated and field-mediated) and an explicit thermal factor $e^{- ext{$\pi$}\omega/(2a)}$ for odd orders, yielding Boltzmann-like detailed balance $P(e o g)/P(g o e)=e^{2\pi\omega/a}$. It also uncovers multipartite entanglement among emitted photons and demonstrates how acceleration imprints non-trivial vacuum correlations beyond bipartite entanglement. Together, these results provide a unified, nonperturbative tool for exploring entanglement generation and thermal phenomena in non-inertial frames with potential implications for relativistic quantum information processing.

Abstract

We present a generalized framework for $n$-photon processes involving a uniformly accelerated Unruh-DeWitt detector interacting with a massless scalar field. We utilize the $n^\text{th}$ order Dyson series to derive the final quantum state for an arbitrary number of interactions. Our analysis covers both even-order processes, which return the detector to its initial state, and odd-order processes, which result in a change of the detector's state. By employing a unified formalism and performing a complete, time-ordered integration, we obtain exact analytical expressions for the $n$-photon states. The results reveal a rich structure of resonant denominators corresponding to multi-particle processes, including new field-mediated resonances independent of the detector's energy gap for $n>2$. Crucially, the analysis of odd-order transitions reveals an exponential factor, $\exp(-πω/a)$, characteristic of the Unruh thermal bath. By considering processes starting from the detector's excited state, we demonstrate that the ratio of excitation to de-excitation amplitudes precisely recovers the Boltzmann factor, providing a higher-order confirmation of thermal detailed balance for the Unruh effect. This work provides a unified tool for studying multipartite entanglement and thermal phenomena in non-inertial frames.

Figures (3)

• Figure 1: A diagram illustrating the exponential factors governing the transition rates for excitation ($\ket{g} \to \ket{e}$) and de-excitation ($\ket{e} \to \ket{g}$) processes. The excitation is exponentially suppressed, while de-excitation is enhanced, consistent with thermal detailed balance.
• Figure 2: Density plots of the four-photon emission amplitude $|\mathcal{A}^{(4)}|$ for various directional channels. The axes represent the Unruh frequencies of two of the emitted photons. The bright lines indicate resonances. The solid lines are detector-mediated resonances, dependent on $\omega$, while the dashed lines are field-mediated resonances, independent of $\omega$. The different kinematic constraints for each channel are clearly visible.
• Figure 3: The logarithm of the total probability for the n=3 ($g \to e$) emission process versus the ratio of detector gap to acceleration, $\omega/a$. The red dots are the results of numerical integration of the squared amplitude. The dashed black line is the best-fit theoretical curve, which is dominated by the linear slope of $-\pi$ characteristic of the Unruh thermal factor. This provides strong visual confirmation of the Boltzmann-like suppression of excitation.