Acoustic horizons and the Hawking effect in polariton fluids of light

These lecture notes develop polariton fluids of light as programmable simulators of quantum fields on tailored curved spacetimes, with emphasis on acoustic horizons and the Hawking effect. After introducing exciton-polariton physics in semiconductor microcavities, we detail the theoretical tools to study the mean field and the quantum hydrodynamics of this driven-dissipative quantum system. We derive the mapping to relativistic field theories and cast horizon physics as a pseudounitary stationary scattering problem. We present the Gaussian optics circuit that describes observables and fixes detection weights for the horizon modes in near- and far-field measurements. We provide a practical experimental toolkit (phase-imprinted flows, coherent pump-probe spectroscopy, balanced and homodyne detection) and a step-by-step workflow to extract amplification, quadrature squeezing, and entanglement among correlations. Finally, we discuss the potential of this platform to investigate open questions in quantum field theory in curved spacetime, such as near horizon effects and quasinormal modes, as well as other phenomena universal to rotating geometries, from rotational superradiance to dynamical instabilities. We further outline the interplay between rotational superradiance and the Hawking effect, proposing to spatially resolve measurements as a roadmap for `dumb hole spectroscopy’ and the study of entanglement dynamics in curved spacetimes.

💡 Research Summary

This set of lecture notes develops exciton‑polariton fluids in semiconductor microcavities into a programmable analogue‑gravity platform capable of simulating quantum fields on curved spacetimes. After a concise introduction to the underlying single‑particle physics—cavity photons with an effective in‑plane mass and quantum‑well excitons with hydrogen‑like spectra—the authors describe the strong‑coupling regime that yields lower‑polariton (LP) quasiparticles. The LP branch inherits a tiny photonic mass while retaining appreciable excitonic non‑linearity, making it an ideal quantum fluid of light.

The driven‑dissipative Gross‑Pitaevskii equation (ddGPE) governs the mean‑field dynamics of the LP fluid under coherent pumping. Linearising the ddGPE around a stationary background gives a Bogoliubov‑de Gennes (BdG) problem with particle‑hole spinors (u, v). In the long‑wavelength limit the phase fluctuation obeys an effective Klein‑Gordon equation on an acoustic metric whose components are set by the local flow velocity v₀ and the sound speed cₛ. Where the normal component of the flow equals cₛ, a Killing (acoustic) horizon forms, providing the kinematic basis for Hawking radiation.

Section 3 presents a concrete “waterfall” horizon geometry obtained by spatially imprinting the pump phase with a spatial‑light modulator. The authors analyse the local dispersion, identify three scattering channels—Hawking radiation (H), its partner (P), and a downstream witness mode (W)—and construct a pseudo‑unitary stationary scattering matrix S(ω) that respects the σ₃ symplectic metric. The quantum field‑theoretic description is complemented by a Gaussian quantum‑optics formalism: the Bogoliubov amplitudes define near‑field density weights D = u + v and far‑field photon‑number weights N = |u|² + |v|², while anomalous pair weights A_{ij} encode two‑mode squeezing.

Observables are mapped onto experimentally accessible quantities. Near‑field density–density correlations ⟨δn δn⟩ reveal the spatial structure of the Hawking pair, whereas far‑field intensity correlations ⟨a†a⟩ measured in momentum space give access to the squeezing parameter r(ω) and entanglement measures. The authors provide a full Gaussian optics circuit that translates these correlations into measurable photocurrents, including the necessary detection weights for each channel.

Section 4 details the experimental toolbox. Phase‑imprinted flows are generated with an SLM; coherent pump‑probe spectroscopy supplies the linear response function and the Bogoliubov dispersion; balanced detection extracts intensity correlations with shot‑noise limited sensitivity; homodyne detection with a local oscillator enables quadrature squeezing measurements. A step‑by‑step workflow is given for calibrating pump detuning, extracting the healing length ξ, determining the Hawking frequency window (ω_min, ω_max), and reconstructing the scattering matrix from measured correlations.

Finally, the authors discuss future directions. They propose spatially resolved “dumb‑hole spectroscopy” to disentangle Hawking radiation from rotational superradiance in rotating flows, enabling the study of quasinormal modes and their damping rates. The platform also offers a route to probe entanglement dynamics in curved spacetimes, potentially shedding light on information‑loss questions. By integrating relativistic field‑theory mapping, detailed quantum‑optical detection schemes, and a practical experimental protocol, this work positions polariton fluids of light as a versatile testbed for quantum field theory in curved spacetime, opening avenues that were previously inaccessible to tabletop experiments.