Analog Hawking radiation emitted by a perfectly reflecting mirror

TL;DR

This work tackles the challenge of modeling analog Hawking radiation from a perfectly reflecting mirror in (1+3)D flat spacetime, where solving the wave equation with a dynamical boundary is intractable. By analyzing the reflected frequency and momentum using Einsteinian Doppler shifts and Fourier decompositions, the authors derive a conservative lower bound on particle production that relies on normal-incidence modes, and they connect (1+1)D results to (1+3)D behavior. In the infinite-area limit, the spectrum reduces to a Planck-like distribution with $T_H=\kappa/(2\pi)$; for finite-size mirrors, diffraction introduces sinc/jinc form factors, yielding area- and geometry-dependent spectra and yields. Applying parameters relevant to the AnaBHEL experiment, they estimate $T_H\approx 0.03\ \mathrm{eV}$ and a per-shot yield $N\gtrsim 16$, suggesting feasible detection and motivating further exploration of classical-analog mimics and entanglement properties. The approach provides a practical framework for predicting observable signatures of analog Hawking radiation in laboratory settings. $T_H$ and $N$ appear as central quantities guiding experimental design.$

Abstract

Analog Hawking radiation emitted by a perfectly reflecting mirror in (1+3)-dimensional flat spacetime is investigated. This is accomplished by studying the reflected frequency and momentum based on Einstein's mirror, instead of the canonical way of solving, if possible, wave equations subjected to a dynamical Dirichlet boundary condition. In the case of a finite-size mirror, diffraction pattern appears in the radiation spectrum. Based on the relevant parameters in the proposed Analog Black Hole Evaporation via Lasers experiment, in which the Hawking temperature $T_{H}\simeq 0.03$ eV and the mirror area $A\simeq (50\;μ\mathrm{m})^{2}$, the Hawking photon yield is estimated to be $N\simeq 16$/laser shot.

Figures (5)

• Figure 1: Contours of integration that integrate each wave modes reflected by the mirror starting from $x_{-}^{*}$ to $x_{-}$ once. Blue: mirror's worldline.
• Figure 2: Reflection of plane waves by a relativistically receding perfect mirror in (1+1)-dimensions. Blue: mirror's trajectory. Dashed line: observer $\mathcal{O}_{1}$'s worldline $x_{+}=x_{+}(\mathcal{O}_{1})$. Dotted line: observer $\mathcal{O}_{2}$'s worldline $x=x(\mathcal{O}_{2})$.
• Figure 3: Reflection of plane waves by a relativistically receding perfect mirror in higher dimensions. Blue: mirror's trajectory. Dashed line: observer $\mathcal{O}_{1}$'s worldline $x=x(\mathcal{O}_{1})$.
• Figure 4: Frequency spectrum per unit time of analog Hawking radiation. The mild bump around $0.04$ eV is not a numerical artifact but a real diffraction effect due to the finite size of the mirror.
• Figure 5: Angular spectrum per unit time of analog Hawking radiation.