Analytical description of quantum emission in optical analogues to gravity
Maxime J Jacquet, Friedrich Koenig
备注：
18 pages, 9 figures, 1 table, comments are welcome! Accepted for publication at Physical Review A. arXiv admin note: substantial text overlap with arXiv:1709.03100
We consider a moving refractive index perturbation in an optical medium as an optical analogue to waves under the influence of gravity. We describe the dielectric medium by the Lagrangian of the Hopfield model. We supplement the field theory in curved spacetime for this model to solve the scattering problem for all modes and frequencies analytically. Because of dispersion, the kinematic scenario of the field modes may contain optical event horizons for some frequencies. We calculate the spectra of spontaneous emission in the frame co-moving with the perturbation and in the laboratory frame. We also calculate the spectrally-resolved photon number correlations in either frame. The emitted multimode field comes in different types depending on the presence of horizons. We show that these types are robust against changes in the system parameters and thus are genuine features of optical and non-optical analogues. These methods and findings pave the way to new observations of analogue gravity in dispersive systems.
This article is an introduction for a theme issue following a Scientific Discussion Meeting on \emph{The next generation of analogue gravity experiments} held at the Royal Society in December 2019. This theme issue comprises a collection of recent advances of the research programme, as well as their philosophical implications, that were presented at the meeting.
Quantum fluctuations on curved spacetimes cause the emission of pairs of particles from the quantum vacuum, as in the Hawking effect from black holes. We use an optical analogue to gravity to investigate the influence of the curvature on quantum emission. Due to dispersion, the spacetime curvature varies with frequency here. We analytically calculate for all frequencies the particle flux, correlations and entanglement. We find that horizons increase the flux with a characteristic spectral shape. The photon number correlations transition from multi- to two-mode, with close to maximal entangleme…
We set up a tunneling approach to the analogue Hawking effect in the case of models of analogue gravity which are affected by dispersive effects. An effective Schroedinger-like equation for the basic scattering phenomenon IN->P+N*, where IN is the incident mode, P is the positive norm reflected mode, and N* is the negative norm one, signalling particle creation, is derived, aimed to an approximate description of the phenomenon. Horizons and barrier penetration play manifestly a key-role in giving rise to pair-creation. The non-dispersive limit is also correctly recovered. Drawbacks of the mode…
We investigate the possibility to generate quantum-correlated quasi-particles utilizing analogue gravity systems. The quantumness of these correlations is a key aspect of analogue gravity effects and their presence allows for a clear separation between classical and quantum analogue gravity effects. However, experiments in analogue systems, such as Bose-Einstein condensates, and shallow water waves, are always conducted at non-ideal conditions, in particular, one is dealing with dispersive media at nonzero temperatures. We analyze the influence of the initial temperature on the entanglement ge…
Taking the principles of quantum mechanics as they stand and applying them to gravity, leads to the conclusion that one might be able to generate superpositions of spacetimes, at least formally. We analyze such a possibility from an analogue gravity perspective. We present an analogue toy model consisting of a Bose-Einstein condensate in a double-well potential and identify the states that could potentially be interpreted as superposition of effective spacetimes. These states are unstable and the source of instability from a microscopic point of view can be related to the absence of a well-def…
We describe how analogues of a Hawking evaporating black hole as well as the Unruh effect for an oscillatory, accelerating photodetector in vacuum may be realized using superconducting, microwave circuits that are fashioned out of Josephson tunnel junction and film bulk acoustic resonator elements.
The quasiparticle content of a quantum field depends on the observer, in particular on its motional state, on the way the observer's detector couples to the quantum field, and on the frequency standard in which the detector carried by the observer measures the quanta to be detected. I review a procedure of making this fundamental property of quantum field theory experimentally manifest using quantum-optical means in Bose-Einstein condensates.
A general geometrical structure of the entanglement entropy for spatial partition of a relativistic QFT system is established by using methods of the effective gravity action and the spectral geometry. A special attention is payed to the subleading terms in the entropy in different dimensions and to behaviour in different states. It is conjectured, on the base of relation between the entropy and the action, that in a fundamental theory the ground state entanglement entropy per unit area equals $1/(4G_N)$, where $G_N$ is the Newton constant in the low-energy gravity sector of the theory. The co…
Analogue gravity enables the study of fields on curved spacetimes in the laboratory. There are numerous experimental platforms in which amplification at the event horizon or the ergoregion has been observed. Here, we demonstrate how optically generating a defect in a polariton microcavity enables the creation of one- and two-dimensional, transsonic fluid flows. We show that this highly tuneable method permits the creation of sonic horizons. Furthermore, we present a rotating geometry akin to the water-wave bathtub vortex. These experiments usher-in the possibility of observing stimulated as we…
We investigate a simple toy model of particle scattering in the flat spacetime limit of an analogue-gravity model. The analogue-gravity medium is treated as a scalar field of phonons that obeys the Klein-Gordon equation and thus admits a Lorentz symmetry with respect to $c_\mathrm{s}$, the speed of sound in the medium. The particle from which the phonons are scattered is external to the system and does not obey the sonic Lorentz symmetry that the phonon field obeys. In-universe observers who use the exchange of sound to operationally measure distance and duration find that the external particl…
We propose the use of a waveguide-like transmission line based on direct-current superconducting quantum interference devices (dc-SQUID) and study the sine-Gordon (SG) equation which characterises the dynamical behavior of the superconducting phase in this transmission line. Guided by the duality between black holes in Jackiw-Teitelboim (JT) dilaton gravity and solitons in sine-Gordon field theory, we show how to, in our setup, realize 1 + 1 dimensional black holes as solitons of the sine-Gordon equation. We also study the analogue Hawking radiation in terms of the quantum soliton evaporation,…
Acoustic Firewalls: Analogue Gravity Perspective on the AMPS Paradox
Nantong University（南通大学）；Kuban State University（库班国立大学）；Joint-Stock Company “Center for Research and Development”（联合股份公司“研究与发展中心”）；Shenzhen MSU-BIT University（深圳北理莫斯科大学）
