Space-time geometry of quantum dielectrics

Leónhardt, Ulf

doi:10.1103/physreva.62.012111

Cited by 55 publications

(73 citation statements)

References 45 publications

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“…Remarkably, light turns out to experience the moving medium as an emergent spacetime geometry [62,111,113,137,151,152]. To understand why, consider the simplest case, our one-dimensional medium with large ε.…”

Section: Space-time Geometrymentioning

confidence: 99%

“…The effective metric of light in moving media [62,113] does not cover all possible space-time manifolds, but the generated geometries are rich enough to include horizons. The horizon is the place where the flow speed u exceeds the speed of light in the medium, c ′ .…”

Section: Horizonmentioning

confidence: 99%

“…The medium perceives the electromagnetic field as a space-time geometry as well. Light and dielectric matter see each other as geometries [113].…”

Section: Space-time Geometrymentioning

confidence: 99%

“…Consider for simplicity a one-dimensional medium moving with the spatially varying flow speed u(x). The Lagrangian of the electromagnetic field is the Lorentz scalar [97,113] …”

Section: Light In Moving Mediamentioning

confidence: 99%

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Quantum physics of simple optical instruments

2003

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Simple optical instruments are linear optical networks where the incident light modes are turned into equal numbers of outgoing modes by linear transformations. For example, such instruments are beam splitters, multiports, interferometers, fibre couplers, polarizers, gravitational lenses, parametric amplifiers, phase-conjugating mirrors and also black holes. The article develops the quantum theory of simple optical instruments and applies the theory to a few characteristic situations, to the splitting and interference of photons and to the manifestation of Einstein-Podolsky-Rosen correlations in parametric downconversion. How to model irreversible devices such as absorbers and amplifiers is also shown. Finally, the article develops the theory of Hawking radiation for a simple optical black hole. The paper is intended as a primer, as a nearly self-consistent tutorial. The reader should be familiar with basic quantum mechanics and statistics, and perhaps with optics and some elementary field theory. The quantum theory of light in dielectrics serves as the starting point and, in the concluding section, as a guide to understand quantum black holes.

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Section: Space-time Geometrymentioning

confidence: 99%

Section: Horizonmentioning

confidence: 99%

“…The medium perceives the electromagnetic field as a space-time geometry as well. Light and dielectric matter see each other as geometries [113].…”

Section: Space-time Geometrymentioning

confidence: 99%

“…Consider for simplicity a one-dimensional medium moving with the spatially varying flow speed u(x). The Lagrangian of the electromagnetic field is the Lorentz scalar [97,113] …”

Section: Light In Moving Mediamentioning

confidence: 99%

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Quantum physics of simple optical instruments

2003

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“…With the advent of effective curved spacetime theories, it became apparent that the Painlevé-Gullstrand representation of the metric appears in a host of such theories. They comprise, besides the conventional Euler fluid [4,6], superfluid 3 He-A [7,8], atomic Bosecondensed vapors [9,10], and general dielectric (quantum) matter [11,12,13]. An interesting and important feature of the Painlevé-Gullstrand metric is that it continues to give an appropriate physical description for quasiparticle propagation even when the effective space-time possesses a horizon [14].…”

Section: Introductionmentioning

confidence: 99%

On the space-time curvature experienced by quasiparticle excitations in the Painlevé–Gullstrand effective geometry

Fischer

Visser

2003

Annals of Physics

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We consider quasiparticle propagation in constant-speed-of-sound (iso-tachic) and almost incompressible (iso-pycnal) hydrodynamic flows, using the technical machinery of general relativity to investigate the "effective space-time geometry" that is probed by the quasiparticles. This effective geometry, described for the quasiparticles of condensed matter systems by the Painlevé-Gullstrand metric, generally exhibits curvature (in the sense of Riemann), and many features of quasiparticle propagation can be re-phrased in terms of null geodesics, Killing vectors, and Jacobi fields. As particular examples of hydrodynamic flow we consider shear flow, a constant-circulation vortex, flow past an impenetrable cylinder, and rigid rotation.

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Linear pre-metric electrodynamics and deduction of the light cone

Rubilar

2002

Ann. Phys.

106

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We formulate a general framework for describing the electromagnetic properties of spacetime. These properties are encoded in the 'constitutive tensor of the vacuum', a quantity analogous to that used in the description of material media. We give a generally covariant derivation of the Fresnel equation describing the local properties of the propagation of electromagnetic waves for the case of the most general possible linear constitutive tensor. We also study the particular case in which a light cone structure is induced and the circumstances under which such a structure emerges. In particular, we will study the relationship between the dual operators defined by the constitutive tensor under certain conditions and the existence of a conformal metric. Closure and symmetry of the constitutive tensor will be found as conditions which ensure the existence of a conformal metric. We will also see how the metric components can be explicitly deduced from the constitutive tensor if these two conditions are met. Finally, we will apply the same method to explore the consequences of relaxing the condition of symmetry and how this affects the emergence of the light cone. * Email: grubilar at udec dot cl.

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Space-time geometry of quantum dielectrics

Cited by 55 publications

References 45 publications

Quantum physics of simple optical instruments

Quantum physics of simple optical instruments

On the space-time curvature experienced by quasiparticle excitations in the Painlevé–Gullstrand effective geometry

Linear pre-metric electrodynamics and deduction of the light cone

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