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arXiv:1504.06583 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Measuring the entanglement of analogue Hawking radiation by the density-density correlation function

Jeff Steinhauer

Published Jul 28, 2015• 81 citations

Abstract

We theoretically study the entanglement of Hawking radiation pairs emitted by an analogue black hole. We find that this entanglement can be measured by the experimentally accessible density-density correlation function, vastly simplifying the measurement. We find that while the Hawking radiation exiting the black hole might be Planck-distributed, the correlations between the Hawking radiation and the partner particles has a distribution which is weaker but broader than Planckian. Thus, the high-energy tail of the distribution of Hawking radiation should be entangled, whereas the low-energy part should not be. This confirms previous studies. The full Peres-Horodecki criterion is considered, as well as a simpler criterion in the stationary, homogeneous case. Our method applies to systems which are sufficiently cold that the thermal phonons can be neglected.

DOI: 10.1103/physrevd.92.024043

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Observing quantum particle creation by black holes (Hawking radiation) in the astrophysical context is, in ordinary situations, hopeless. Nevertheless the Hawking effect, which depends only on kinematical properties of wave propagation in the presence of horizons, is present also in nongravitational contexts, for instance in stationary fluids undergoing supersonic flow. We present results on how to observe the analog Hawking radiation in Bose-Einstein condensates by a direct measurement of the density correlations due to the phonon pairs (Hawking quanta-partner) created by the acoustic horizon.

Hawking radiation is a fundamental spontaneous phenomenon in which the event horizon of a black hole transforms the vacuum state into a pair of correlated particles: the Hawking radiation and its partner. This emission can also be stimulated by a state other than the vacuum. A similar phenomenon, known as analogue Hawking radiation, has been observed across various physical systems, but experimental realizations have largely remained in the classical regime. This work presents an experimental verification of analogue Hawking radiation stimulated by a single-particle state, producing a verifiably single-photon Hawking output. Using heralded single photons generated via spontaneous four-wave mixing, we stimulate the analogue Hawking effect in an optical fiber. We characterize the resulting Hawking signal by measuring its spectral dependence, intensity scaling, and heralded second-order correlation. Our results establish a platform for exploring quantum correlations and entanglement in analogue gravity. Researchers experimentally demonstrate analogue Hawking radiation stimulated by a single photon in an optical fiber. This work enables new studies of quantum effects in nonlinear optics and analogue gravity.

We study the quantum entanglement of the quasiparticle pairs emitted by analog black holes. We use a phenomenological description of the spectra in dispersive media to study the domains in parameter space where the final state is nonseparable. In stationary flows, three modes are involved in each sector of fixed frequency, and not two as in homogeneous situations. The third spectator mode acts as an environment for the pairs, and the strength of the coupling significantly reduces the quantum coherence. The nonseparability of the pairs emitted by white holes is also considered and compared with that of black holes.

The quantum information content of Hawking radiation holds the key to understanding black-hole evaporation and the fate of unitarity. Motivated by recent advances in cold-atom experiments, we develop a lattice-regularization approach aimed at simulating the coarse-grained entanglement scaling of a quantum field in a 1+1D analogue black-hole background. We provide the first concrete demonstration that logarithmic negativity -- an entanglement monotone that typically exhibits a UV-divergent log-scaling for the conformal vacuum -- acquires a UV-finite volume term from the nonlocal correlations seeded by Hawking radiation. We show that this volume term encodes the number density as well as the spatial distribution of entangled Hawking pairs along the black-hole interior and exterior. We highlight its prospective detection in currently realizable experiments and its implications beyond the analogue paradigm, in particular for black-hole thermodynamics.

We introduce a method to numerically compute the entanglement entropy of an acoustic black hole. It is shown that the entanglement entropy of sufficiently large subregions scales linearly with size and thus shows a volume law instead of an area law. The origin of this scaling can be traced back to the non-separable long-distance correlations due to the production of phonon pairs at the horizon. The system is shown to be locally thermal, such that the part of the entanglement entropy scaling with volume is well approximated by the thermal entropy of the outgoing Hawking radiation.