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Momentum correlations of the Hawking effect in a quantum fluid

Marcos Gil de Olivera, Malo Joly, Antonio Z. Khoury, Alberto Bramati, Maxime J. Jacquet

TL;DR

The paper addresses the spectral and entanglement structure of the Hawking effect in analog quantum fluids by performing a momentum-space analysis. It introduces a numerical framework based on the truncated Wigner approximation to compute the momentum-space two-point correlation function for a polaritonic fluid of light, applicable to both conservative and driven-dissipative regimes. Using a one-dimensional polariton wire with an engineered horizon, the authors demonstrate mode-resolved Hawking radiation correlations, including HR–dn* and HR–down channels, that are accessible to current experiments. This work establishes a robust framework for diagnosing spontaneous horizon emission, with implications for studying quasi-normal modes and horizon structure on the Hawking spectrum, and for entanglement diagnostics in quantum fluids of light or matter.

Abstract

The Hawking effect -- the spontaneous emission of correlated quanta from horizons -- can be observed in laboratory systems where an acoustic horizon forms when a fluid transitions from subcritical to supercritical flow. Although most theoretical and experimental studies have relied on real-space observables, the frequency-dependent nature of the Hawking process motivates a momentum-space analysis to access its spectral structure and entanglement features. Here, we numerically compute the momentum-space two-point correlation function in a quantum fluid using the truncated Wigner approximation, a general method applicable to both conservative and driven-dissipative systems. We consider a polaritonic fluid of light in a realistic configuration known to yield strong real-space correlations between Hawking, partner, and witness modes. We find signatures that are directly accessible in state-of-the-art experiments and offer a robust diagnostic of spontaneous emission. Our results form the basis for a new theoretical framework to assess a variety of effects, such as quasi-normal mode emission or modifications of the horizon structure on the Hawking spectrum.

Momentum correlations of the Hawking effect in a quantum fluid

TL;DR

The paper addresses the spectral and entanglement structure of the Hawking effect in analog quantum fluids by performing a momentum-space analysis. It introduces a numerical framework based on the truncated Wigner approximation to compute the momentum-space two-point correlation function for a polaritonic fluid of light, applicable to both conservative and driven-dissipative regimes. Using a one-dimensional polariton wire with an engineered horizon, the authors demonstrate mode-resolved Hawking radiation correlations, including HR–dn* and HR–down channels, that are accessible to current experiments. This work establishes a robust framework for diagnosing spontaneous horizon emission, with implications for studying quasi-normal modes and horizon structure on the Hawking spectrum, and for entanglement diagnostics in quantum fluids of light or matter.

Abstract

The Hawking effect -- the spontaneous emission of correlated quanta from horizons -- can be observed in laboratory systems where an acoustic horizon forms when a fluid transitions from subcritical to supercritical flow. Although most theoretical and experimental studies have relied on real-space observables, the frequency-dependent nature of the Hawking process motivates a momentum-space analysis to access its spectral structure and entanglement features. Here, we numerically compute the momentum-space two-point correlation function in a quantum fluid using the truncated Wigner approximation, a general method applicable to both conservative and driven-dissipative systems. We consider a polaritonic fluid of light in a realistic configuration known to yield strong real-space correlations between Hawking, partner, and witness modes. We find signatures that are directly accessible in state-of-the-art experiments and offer a robust diagnostic of spontaneous emission. Our results form the basis for a new theoretical framework to assess a variety of effects, such as quasi-normal mode emission or modifications of the horizon structure on the Hawking spectrum.

Paper Structure

This paper contains 1 section, 6 equations, 2 figures.

Table of Contents

  1. Acknowledgements

Figures (2)

  • Figure 1: (a) Bistability curves Eq. \ref{['eq:bista']}. The dot denotes the working point. (b) Speed of fluid $v$ (orange) and sound cones $c_\mathrm{B}$ (blue) as a function of position with origin at $x_{\mathrm d}$. (c) Dispersion relation. (d) Trajectories according to a particle interpretation (WKB) of the scattering process at $\omega=0.4\per ps$. Blue, a regular mode that travels inwards; green, a lingering mode that eventually escapes as Hawking radiation (HR); red, the 'turning mode' of negative norm that becomes the partner (dn) in dashed. Together, HR and the dn represent the usual outgoing-ingoing relativistic particles (the would-be Hawking pairs) that peel infinitely at the horizon porrotunneling2024. (e) Spatial density correlations $g_2(x,x')-1$.
  • Figure 2: (a) Equal size windows centred at the horizon. (b) Equal size windows on opposite sides of the horizon. (c) Momentum density correlations \ref{['eq:delta_g2']} for the window functions in (a). (d) Momentum density correlations \ref{['eq:delta_g2']} for the window functions in (b). (e) Enlarged view of (d) in the region containing the correlations between modes on opposite sides of the horizon. Dot-dashed lines, $k_\mathrm{up},\,k_\mathrm{down}$.