Comptes Rendus
no. S2
Article de recherche
Negative frequencies and negative norms in analogue Hawking radiation systems
[Fréquences négatives et normes négatives dans les systèmes analogiques de rayonnement de Hawking]
Raul Aguero-Santacruz1  ; David Bermudez1
1 Department of Physics, Cinvestav, A.P. 14-740, 07000 Ciudad de México, Mexico
Comptes Rendus. Physique, Online first (2024), pp. 1-17.

Dans ce travail, nous étudions les concepts fondamentaux du rayonnement de Hawking dans les systèmes astrophysiques et analogiques. Nous nous concentrons sur les fréquences négatives et les normes négatives : leur définition, leur relation et leur rôle dans le processus de création de particules de l’effet Hawking. Nous caractérisons la relation de dispersion par les signes de la fréquence et de la norme. Nous concluons que le cadre le plus naturel pour étudier l’effet Hawking est celui dans lequel l’horizon est statique, où le signe de la norme peut être rendu égal au signe de la fréquence décalée par effet Doppler dans ce cadre. Nous utilisons comme exemples les quatre systèmes analogues expérimentaux les plus réussis : les vagues d’eau, les condensats de Bose–Einstein, les fluides à polaritons et les fibres optiques.

In this work, we study the core concepts of Hawking radiation in the astrophysical and analogue systems. We focus on negative frequencies and negative norms: their definition, their relationship, and their role in the particle creation process of the Hawking effect. We characterize the dispersion relation by the signs of the frequency and the norm. We conclude that the most natural frame for studying the Hawking effect is that in which the horizon is static, where the sign of the norm can be made equal to the sign of the Doppler-shifted frequency in that frame. We use as examples the four most successful experimental analogue systems: water waves, Bose–Einstein condensates, polaritons fluids, and optical fibers.

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : 10.5802/crphys.177
Keywords: analogue gravity, negative frequency, negative norm, Hawking radiation, optical pulse, Bose–Einstein condensate, polariton
Mot clés : gravité analogique, fréquence négative, norme négative, rayonnement de Hawking, impulsion optique, condensat de Bose–Einstein, polariton
Raul Aguero-Santacruz 1 ; David Bermudez 1

1 Department of Physics, Cinvestav, A.P. 14-740, 07000 Ciudad de México, Mexico
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRPHYS_2024__25_S2_A2_0,
     author = {Raul Aguero-Santacruz and David Bermudez},
     title = {Negative frequencies and negative norms in analogue {Hawking} radiation systems},
     journal = {Comptes Rendus. Physique},
     publisher = {Acad\'emie des sciences, Paris},
     year = {2024},
     doi = {10.5802/crphys.177},
     language = {en},
     note = {Online first},
}
TY  - JOUR
AU  - Raul Aguero-Santacruz
AU  - David Bermudez
TI  - Negative frequencies and negative norms in analogue Hawking radiation systems
JO  - Comptes Rendus. Physique
PY  - 2024
PB  - Académie des sciences, Paris
N1  - Online first
DO  - 10.5802/crphys.177
LA  - en
ID  - CRPHYS_2024__25_S2_A2_0
ER  - 
%0 Journal Article
%A Raul Aguero-Santacruz
%A David Bermudez
%T Negative frequencies and negative norms in analogue Hawking radiation systems
%J Comptes Rendus. Physique
%D 2024
%I Académie des sciences, Paris
%Z Online first
%R 10.5802/crphys.177
%G en
%F CRPHYS_2024__25_S2_A2_0
Raul Aguero-Santacruz; David Bermudez. Negative frequencies and negative norms in analogue Hawking radiation systems. Comptes Rendus. Physique, Online first (2024), pp. 1-17. doi : 10.5802/crphys.177.

[1] S. W. Hawking Black hole explosions, Nature, Volume 248 (1974) no. 5443, pp. 30-31 | DOI

[2] J. D. Bekenstein Black holes and entropy, Phys. Rev. D, Volume 7 (1973) no. 8, pp. 2333-2346 | DOI

[3] S. W. Hawking Particle creation by black holes, Commun. Math. Phys., Volume 43 (1975) no. 3, pp. 199-220 | DOI

[4] J. Abedi; L. F. Longo Micchi; N. Afshordi GW190521: Search for echoes due to stimulated Hawking radiation from black holes, Phys. Rev. D, Volume 108 (2023) no. 4, 044047 | DOI

[5] N. D. Birrell; P. C. W. Davies Quantum fields in curved space, Cambridge Monographs on Mathematical Physics, 7, Cambridge University Press, 1982 | DOI

[6] A. Almheiri; Th. Hartman; J. Maldacena; E. Shaghoulian; A. Tajdini The entropy of Hawking radiation, Rev. Mod. Phys., Volume 93 (2021) no. 3, 035002 | DOI

[7] U. Leonhardt Lifshitz theory of the cosmological constant, Ann. Phys., Volume 411 (2019), 167973 | DOI

[8] R. Aguero-Santacruz; D. Bermudez Hawking radiation in optics and beyond, Philos. Trans. R. Soc. Lond., Ser. A, Volume 378 (2020) no. 2177, 20190223 | DOI

[9] W. G. Unruh Has Hawking radiation been measured?, Found. Phys., Volume 44 (2014), pp. 532-545 | DOI

[10] W. G. Unruh Experimental black-hole evaporation?, Phys. Rev. Lett., Volume 46 (1981) no. 21, pp. 1351-1353 | DOI

[11] G. Rousseaux; Ch. Mathis; Ph. Maïssa; Th. G. Philbin; U. Leonhardt Observation of negative-frequency waves in a water tank: a classical analogue to the Hawking effect?, New J. Phys., Volume 10 (2008) no. 5, 053015 | DOI

[12] G. Rousseaux; Ph. Maïssa; Ch. Mathis; P. Coullet; Th. G. Philbin; U. Leonhardt Horizon effects with surface waves on moving water, New J. Phys., Volume 12 (2010) no. 9, 095018 | DOI

[13] S. Weinfurtner; E. W. Tedford; M. C. J. Penrice; W. G. Unruh; G. A. Lawrence Measurement of stimulated Hawking emission in an analogue system, Phys. Rev. Lett., Volume 106 (2011) no. 2, p. 021302 | DOI

[14] T. Jacobson; G. E. Volovik Effective spacetime and Hawking radiation from a moving domain wall in a thin film of 3 He-A, JETP Lett., Volume 68 (1998), pp. 874-880 | DOI

[15] M. Novello; M. Visser; G. E. Volovik Artificial black holes, World Scientific, 2002

[16] J. Steinhauer Comment on “Questioning the recent observation of quantum Hawking radiation” [Ann. Phys. (Berlin) 2018, 530, 1700114], Ann. Phys. (Berlin), Volume 530 (2018) no. 5, 1700459 | DOI

[17] J. R. Muñoz de Nova; K. Golubkov; V. I. Kolobov; J. Steinhauer Observation of thermal Hawking radiation and its temperature in an analogue black hole, Nature, Volume 569 (2019) no. 7758, pp. 688-692 | DOI

[18] D. Bermudez; U. Leonhardt Resonant Hawking radiation as an instability, Class. Quant. Grav., Volume 36 (2019) no. 2, 024001 | DOI

[19] Th. G. Philbin; Ch. Kuklewicz; S. Robertson; S. Hill; F. König; U. Leonhardt Fiber-optical analog of the event horizon, Science, Volume 319 (2008) no. 5868, pp. 1367-1370 | DOI

[20] D. Bermudez; U. Leonhardt Hawking spectrum for a fiber-optical analog of the event horizon, Phys. Rev. A, Volume 93 (2016) no. 5, 053820 | DOI

[21] J. Drori; Y. Rosenberg; D. Bermudez; Y. Silberberg; U. Leonhardt Observation of stimulated Hawking radiation in an optical analogue, Phys. Rev. Lett., Volume 122 (2019) no. 1, 010404 | DOI

[22] M. J. Jacquet; M. Joly; F. Claude; L. Giacomelli; Q. Glorieux; A. Bramati; I. Carusotto; E. Giacobino Analogue quantum simulation of the Hawking effect in a polariton superfluid, Eur. Phys. J. D, Atomic Mol. Opt. Plasma Phys., Volume 76 (2022) no. 8, 152 | DOI

[23] M. J. Jacquet; L. Giacomelli; Q. Valnais; M. Joly; F. Claude; E. Giacobino; Q. Glorieux; I. Carusotto; A. Bramati Quantum vacuum excitation of a quasinormal mode in an analog model of black hole spacetime, Phys. Rev. Lett., Volume 130 (2023) no. 11, 111501 | DOI

[24] M. Visser; C. Barceló; S. Liberati Analogue models of and for gravity, Gen. Relativ. Gravit., Volume 34 (2002) no. 10, pp. 1719-1734 | DOI

[25] M. Visser Essential and inessential features of Hawking radiation, Int. J. Mod. Phys. D, Volume 12 (2003) no. 04, pp. 649-661 | DOI

[26] M. F. Linder; R. Schützhold; W. G. Unruh Derivation of Hawking radiation in dispersive dielectric media, Phys. Rev. D, Volume 93 (2016) no. 10, p. 104010 | DOI

[27] M. Isoard; N. Pavloff Departing from thermality of analogue Hawking radiation in a Bose–Einstein condensate, Phys. Rev. Lett., Volume 124 (2020) no. 6, 060401 | DOI

[28] T. Jacobson Black hole evaporation and ultrashort distances, Phys. Rev. D, Volume 44 (1991) no. 6, pp. 1731-1739 | DOI

[29] E. Rubino; J. McLenaghan; S. C. Kehr; F. Belgiorno; D. Townsend; S. Rohr; Ch. Kuklewicz; U. Leonhardt; F. König; D. Faccio Negative-frequency resonant radiation, Phys. Rev. Lett., Volume 108 (2012) no. 25, 253901 | DOI

[30] F. Biancalana Negative frequencies get real, Physics, Volume 5 (2012), 68 | DOI

[31] R. Aguero-Santacruz; D. Bermudez Negative frequencies in pulse propagation equations and the double analytic signal, New J. Phys., Volume 25 (2023) no. 10, 103045 | DOI

[32] R. Brout; S. Massar; R. Parentani; Ph. Spindel Hawking radiation without trans-Planckian frequencies, Phys. Rev. D, Volume 52 (1995) no. 8, pp. 4559-4568 | DOI

[33] V. Mukhanov; S. Winitzki Introduction to quantum effects in gravity, Cambridge University Press, 2007

[34] W. Greiner et al. Relativistic quantum mechanics, 2, Springer, 2000 | DOI

[35] C. R. Almeida; M. J. Jacquet Analogue gravity and the Hawking effect: historical perspective and literature review, Eur. Phys. J. H, Volume 48 (2023) no. 1, 15 | DOI

[36] L. C. Barbado; C. Barceló; L. J. Garay; G. Jannes The Trans-Planckian problem as a guiding principle, J. High Energy Phys., Volume 2011 (2011) no. 11, pp. 1-18 | DOI

[37] S. Robertson The theory of Hawking radiation in laboratory analogues, J. Phys. B. At. Mol. Opt. Phys., Volume 45 (2012) no. 16, 163001 | DOI

[38] S. Amiranashvili Modeling of ultrashort optical pulses in nonlinear fibers (2022) (Technical report)

[39] J. Macher; R. Parentani Black-hole radiation in Bose–Einstein condensates, Phys. Rev. A, Volume 80 (2009) no. 4, pp. 12-26 | DOI

[40] A Recati; N. Pavloff; I. Carusotto Bogoliubov theory of acoustic Hawking radiation in Bose–Einstein condensates, Phys. Rev. A, Volume 80 (2009) no. 4, 043603 | DOI

[41] J. Steinhauer Observation of quantum Hawking radiation and its entanglement in an analogue black hole, Nat. Phys. (2016), pp. 959-965 | DOI

[42] G. Modugno The life of an analogue black hole, Nat. Phys., Volume 17 (2021) no. 3, pp. 300-301 | DOI

[43] H. S. Nguyen; D. Gerace; I. Carusotto; D. Sanvitto; E. Galopin; A. Lemaître; I. Sagnes; J. Bloch; A. Amo Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons, Phys. Rev. Lett., Volume 114 (2015) no. 3, 036402 | DOI

[44] M. J. Jacquet; T. Boulier; F. Claude; A. Maître; E. Cancellieri; C. Adrados; A. Amo; S. Pigeon; Q. Glorieux; A. Bramati; E. Giacobino Polariton fluids for analogue gravity physics, Philos. Trans. R. Soc. Lond., Ser. A, Volume 378 (2020) no. 2177, 20190225 | DOI

[45] D. Vocke; C. Maitland; A. Prain; K. E. Wilson; F. Biancalana; E. M. Wright; F. Marino; D. Faccio Rotating black hole geometries in a two-dimensional photon superfluid, Optica, Volume 5 (2018) no. 9, pp. 1099-1103 | DOI

[46] U. Leonhardt Essential Quantum Optics, Cambridge University Press, 2009

[47] G. P. Agrawal Nonlinear Fiber Optics, Academic Press Inc.; Elsevier science, 2019 (digital format)

[48] Ph. Russell Photonic crystal fibers, Science, Volume 299 (2003) no. 5605, pp. 358-362 | DOI

[49] A. Couairon; E. Brambilla; T. Corti; D. Majus; O. Ramírez-Góngora; M. Kolesik Practitioner’s guide to laser pulse propagation models and simulation, Eur. Phys. J.: Spec. Top., Volume 199 (2011) no. 1, pp. 5-76 | DOI

[50] P. Švančara; P. Smaniotto; L. Solidoro; J. F. MacDonald; S. Patrick; R. Gregory; C. F. Barenghi; S. Weinfurtner Exploring the quantum-to-classical vortex flow: Quantum field theory dynamics on rotating curved spacetimes (2023) (preprint, arXiv:2308.10773) | DOI

[51] J. Steinhauer Confirmation of stimulated Hawking radiation, but not of black hole lasing, Phys. Rev. D, Volume 106 (2022) no. 10, 102007 | DOI

[52] K. Falque; Q. Glorieux; E. Giacobino; A. Bramati; M. J. Jacquet Spectroscopic measurement of the excitation spectrum on effectively curved spacetimes in a polaritonic fluid of light (2023) (preprint, arXiv:2311.01392)

[53] F. Claude; M. J. Jacquet; I. Carusotto; Q. Glorieux; E. Giacobino; A. Bramati Spectrum of collective excitations of a quantum fluid of polaritons, Phys. Rev. B, Volume 107 (2023) no. 17, 174507 | DOI

[54] A. Delhom; K. Guerrero; P. Calizaya; K. Falque; A. J. Brady; I. Agullo; M. J. Jacquet Entanglement from superradiance and rotating quantum fluids of light (2023) (preprint, arXiv:2310.16031) | DOI

[55] R. Felipe-Elizarraras; H. Cruz-Ramirez; K. Garay-Palmett; A. B. U’Ren; D. Bermudez Effective Michelson interference observed in fiber-optical analogue of Hawking radiation, Opt. Express, Volume 30 (2022) no. 5, pp. 8063-8074 | DOI

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Towards analogue black hole merger

Dmitry Solnyshkov; Ismaël Septembre; Guillaume Malpuech

C. R. Phys (2024)

Superradiant phononic emission from the analog spin ergoregion in a two-component Bose–Einstein condensate

Anna Berti; Luca Giacomelli; Iacopo Carusotto

C. R. Phys (2023)

Causal structures in inflation

George F.R. Ellis; Jean-Philippe Uzan

C. R. Phys (2015)