Stimulated Hawking effect and quasinormal mode resonance in a polariton simulator of field theory on curved spacetime

TL;DR

The paper investigates stimulated Hawking radiation in a polaritonic quantum fluid of light by injecting a weak coherent probe upstream of a horizon engineered in a driven-dissipative system. It combines mean-field and Bogoliubov analyses with a local-density approximation to map the dispersion and mode structure, reveals a frequency window where negative-norm channels enable pseudo-unitary mixing and amplification, and identifies a near-horizon quasinormal mode that produces a sharp resonant peak in transmission at $\,oldsymbol{ extOmega}_{ ext{qnm}}$. The study shows that, for $oldsymbol{ extomega}$ between $oldsymbol{ extomega}_{ ext{min}}$ and $oldsymbol{ extomega}_{ ext{max}}$, the interface couples positive- and negative-norm modes with amplification into the dn channel, while outside this window the process becomes unitary. The quasinormal mode acts as both a dynamical signature and a mediator of stimulated emission, enabling horizon spectroscopy that can guide future experiments on quantum field dynamics in curved spacetime analogues.

Abstract

The Hawking effect amplifies fluctuations in the vicinity of horizons, both in black holes and in analogue platforms. Here, we consider a polariton simulator and numerically examine the \emph{stimulated} Hawking effect using a coherent probe incident on the horizon from the exterior. We implement an experimentally realistic effective spacetime that supports a quasinormal mode (QNM) in the vicinity of the horizon. We find that the stimulated Hawking effect manifests as transmission into a negative-energy Bogoliubov channel inside the horizon, consistent with pseudo-unitary Bogoliubov scattering. Moreover, transmission across the horizon peaks at the QNM frequency. The computed spectral signatures provide a practical guide for future experimental investigations of the Hawking effect and its interplay with QNMs, an open question in quantum field theory in curved spacetime.

Figures (2)

• Figure 1: Polariton mean-field. Mean-field profile with downstream density support. a) Bistability loop for $k_\mathrm{up}=0.27\per µm$ (green) and $k_\mathrm{down}=0.539\per µm$ (turquoise). b) Bogoliubov sound speed $c_\mathrm{B}$ (blue) and background fluid velocity $v_0$ (red). Dispersion of Bogoliubov excitations. c)–d) The colour map shows the numerical dispersion relation, while the dashed lines show the LDA prediction \ref{['eq:lfdisp']}. c) upstream; d) downstream. e), f), LDA dispersion. Blue: positive-norm modes $\omega^{\mathrm B}_+$; orange: negative-norm modes $\omega^{\mathrm B}_-$. Brown dots: in modes in (upstream), p and d (downstream); green dots: out modes HR (upstream), down and dn (downstream). We stimulate the Hawking effect by injecting a finite-amplitude continuous-wave (CW) probe into the input mode in.
• Figure 2: Numerical simulation of scattering. Amplitude is injected in mode in at $k_\mathrm{pr},\,\omega_\mathrm{pr}$ and allowed to scatter at the horizon. Amplitudes are normalised to the probe amplitude. All $\omega_\mathrm{pr}$ slices are collated to form the spectra in each region. a) amplitude upstream (linear scale); b) amplitude downstream (log scale); c) amplitude downstream (linear scale). Dashed lines: LDA dispersion \ref{['eq:lfdisp']}. Spectral properties of the quasinormal mode. d) Spectrum of Bogoliubov excitations. Red: negative-norm; black: positive-norm; blue: zero-norm. Zero-norm modes at low frequency are spurious artefacts of the numerical boundaries and are localised outside the near-horizon region. The response near $\omega_\mathrm{qnm}$ is a damped QNM response of the Bogoliubov field. e) Amplitude in mode down.