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arXiv:gr-qc/0303028 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

On slow light as a black hole analogue

William George Unruh, Ralf Schützhold

Published Jul 3, 2003• 121 citations
arXivHTMLPDF

Abstract

Although slow light (electromagnetically induced transparency) would seem an ideal medium in which to institute a ``dumb hole'' (black hole analogue), it suffers from a number of problems. We show that the high phase velocity in the slow light regime ensures that the system cannot be used as an analogue displaying Hawking radiation. Even though an appropriately designed slow-light setup may simulate classical features of black holes---such as horizon, mode mixing, ``Bogoliubov'' coefficients, etc.---it does not reproduce the related quantum effects.

DOI
10.1103/physrevd.68.024008

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Although slow light (electromagnetically induced transparency) would seem an ideal medium in which to institute a dumb hole'' (black hole analogue), it suffers from a number of problems. We show that the high phase velocity in the slow light regime ensures that the system cannot be used as an analogue displaying Hawking radiation. Even though an appropriately designed slow-light setup may simulate classical features of black holes---such as horizon, mode mixing, Bogoliubov'' coefficients, etc.---it does not reproduce the related quantum effects.
The Hawking effect can be understood as a broad kinematic phenomenon associated with mode behavior near a horizon. While astrophysical black holes produce one specific realization of this radiation, this perspective inspires extensive theoretical and experimental efforts to create event horizons in diverse physical systems to observe the resulting analogue Hawking emission. One of the most successful realizations is the fiber-optical analogue, based on nonlinear quantum optics. In these notes, we introduce and motivate this system while outlining the theoretical concepts underlying the gravitational analogy. Finally, we review key experiments and discuss their impact on the field.
A black hole laser in analogues of gravity amplifies Hawking radiation, which is unlikely to be measured in real black holes, and makes it observable. There have been proposals to realize such black hole lasers in various systems. However, no progress has been made in electric circuits for a long time, despite their many advantages such as high-precision electromagnetic wave detection. Here we propose a black hole laser in Josephson transmission lines incorporating metamaterial elements capable of producing Hawking-pair propagation modes and a Kerr nonlinearity due to the Josephson nonlinear inductance. A single dark soliton obeying the nonlinear Schrödinger equation produces a black hole-white hole horizon pair that acts as a laser cavity through a change in the refractive index due to the Kerr effect. We show that the resulting laser is a squeezed-state laser characterized by squeezing parameters. We also evaluate the degree of quantum correlation between Hawking and its partner radiations using entanglement entropy which does not require simultaneous measurements between them. As a result, the obtained entanglement entropy depending on the soliton velocity provides strong evidence that the resulting laser is derived from Hawking radiation with quantum correlation generated by pair production from the vacuum.
This paper proposes that black holes can be described as globally coherent quantum systems, despite the emission of Hawking radiation. While the Hawking process induces a weak coupling between the interior and exterior regions, this interaction is demonstrated to be too small to produce significant decoherence for macroscopic and supermassive black holes. By treating the event horizon as a quasi-isolated, semi-transparent quantum interface, this framework reconciles semiclassical gravity with quantum unitarity. The black hole and its emitted radiation are modeled as a single, entangled pure quantum state that evolves unitarily. Key contributions of this work include: Formalization of the black hole-radiation system as a coherent quantum cavity. Mathematical derivation showing that the decoherence rate scales as Γ_dec ∝ M⁻⁸. Demonstration that for astrophysical black holes, the decoherence time τ_D is astronomically larger than the evaporation time t_evap, implying that global quantum coherence is effectively preserved. A potential resolution to the black hole information paradox within a unitary evolution framework. This research contributes to the ongoing theoretical discussion on the nature of event horizons, quantum information, and the holographic principle. Acknowledgements: I would like to express my deepest gratitude to my beloved dog, Milo, and my father, for their constant support, encouragement, and companionship throughout the development of this research.
This thesis explores the links between different ways of modelling the physical world. Finite difference numerical simulations may be used to encode the be-haviour of physical systems, allowing us to gain insight into their workings and even to predict their behaviour. Similarly, one can investigate the properties of gravitational black holes through the use of analogue black holes, physical systems which share at least some part of the physics of the astronomical objects. Con-centrating on black hole analogues using Bose-Einstein condensates, I show how simulations of these systems may be greatly assisted through the use of a proper absorbing boundary condition, the Perfectly Matched Layer. Such a boundary condition allows the efficient truncation of the computational domain, both sav-ing computational time and increasing accuracy. I then apply this technique to the simulation of the supersonic flow of a Bose-Einstein condensate through a Laval nozzle, a black hole analogue, showing that such a flow should be stable and observable in the laboratory. Moving to a related system, I investigate the optical