Non-Hermitian Phase Transition from a Polariton Bose-Einstein Condensate to a Photon Laser
Abstract
We propose here a novel mechanism for a nonequilibrium phase transition in a $U(1)$-broken phase of an electron-hole-photon system, from a Bose-Einstein condensate of polaritons to a photon laser, induced by the non-Hermitian nature of the condensate. We show that a (uniform) steady state of the condensate can always be classified into two types, namely, arising either from lower or upper-branch polaritons. We prove (for a general model) and demonstrate (for a particular model of polaritons) that an exceptional point where the two types coalesce marks the end point of a first-order-like phase boundary between the two types, similar to a critical point in a liquid-gas phase transition. Since the phase transition found in this paper is not in general triggered by population inversion, our result implies that the second threshold observed in experiments is not necessarily a strong-to-weak-coupling transition, contrary to the widely believed understanding. Although our calculation mainly aims to clarify polariton physics, our discussion is applicable to general driven-dissipative condensates composed of two complex fields.
- Authors:
-
- Univ. of Chicago, IL (United States). James Franck Inst. Dept. of Physics; Osaka Univ., Toyonaka (Japan). Dept. of Physics
- Univ. of Chicago, IL (United States). James Franck Inst. Dept. of Physics; Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
- Keio Univ., Yokohama (Japan). Dept. of Physics
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States); Osaka Univ., Toyonaka (Japan); Keio Univ., Yokohama (Japan)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); Japan Society for the Promotion of Science (JSPS); Ministry of Education, Culture, Sports, Science and Technology (MEXT) (Japan)
- OSTI Identifier:
- 1542179
- Alternate Identifier(s):
- OSTI ID: 1511515
- Grant/Contract Number:
- AC02-06CH11357; 17J01238; JP18K11345; JP18H05406; JP16K05503
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 122; Journal Issue: 18; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Hanai, Ryo, Edelman, Alexander, Ohashi, Yoji, and Littlewood, Peter B. Non-Hermitian Phase Transition from a Polariton Bose-Einstein Condensate to a Photon Laser. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.122.185301.
Hanai, Ryo, Edelman, Alexander, Ohashi, Yoji, & Littlewood, Peter B. Non-Hermitian Phase Transition from a Polariton Bose-Einstein Condensate to a Photon Laser. United States. https://doi.org/10.1103/PhysRevLett.122.185301
Hanai, Ryo, Edelman, Alexander, Ohashi, Yoji, and Littlewood, Peter B. Wed .
"Non-Hermitian Phase Transition from a Polariton Bose-Einstein Condensate to a Photon Laser". United States. https://doi.org/10.1103/PhysRevLett.122.185301. https://www.osti.gov/servlets/purl/1542179.
@article{osti_1542179,
title = {Non-Hermitian Phase Transition from a Polariton Bose-Einstein Condensate to a Photon Laser},
author = {Hanai, Ryo and Edelman, Alexander and Ohashi, Yoji and Littlewood, Peter B.},
abstractNote = {We propose here a novel mechanism for a nonequilibrium phase transition in a $U(1)$-broken phase of an electron-hole-photon system, from a Bose-Einstein condensate of polaritons to a photon laser, induced by the non-Hermitian nature of the condensate. We show that a (uniform) steady state of the condensate can always be classified into two types, namely, arising either from lower or upper-branch polaritons. We prove (for a general model) and demonstrate (for a particular model of polaritons) that an exceptional point where the two types coalesce marks the end point of a first-order-like phase boundary between the two types, similar to a critical point in a liquid-gas phase transition. Since the phase transition found in this paper is not in general triggered by population inversion, our result implies that the second threshold observed in experiments is not necessarily a strong-to-weak-coupling transition, contrary to the widely believed understanding. Although our calculation mainly aims to clarify polariton physics, our discussion is applicable to general driven-dissipative condensates composed of two complex fields.},
doi = {10.1103/PhysRevLett.122.185301},
journal = {Physical Review Letters},
number = 18,
volume = 122,
place = {United States},
year = {2019},
month = {5}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 2 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor
journal, July 1995
- Anderson, M. H.; Ensher, J. R.; Matthews, M. R.
- Science, Vol. 269, Issue 5221
Temperature dependence of pulsed polariton lasing in a GaAs microcavity
journal, August 2012
- Tempel, Jean-Sebastian; Veit, Franziska; Aßmann, Marc
- New Journal of Physics, Vol. 14, Issue 8
Dynamical instability of a driven-dissipative electron-hole condensate in the BCS-BEC crossover region
journal, September 2017
- Hanai, Ryo; Littlewood, Peter B.; Ohashi, Yoji
- Physical Review B, Vol. 96, Issue 12
Exciton–Mott Physics in Two-Dimensional Electron–Hole Systems: Phase Diagram and Single-Particle Spectra
journal, August 2014
- Asano, Kenichi; Yoshioka, Takuya
- Journal of the Physical Society of Japan, Vol. 83, Issue 8
Exciton-polariton Bose-Einstein condensation
journal, May 2010
- Deng, Hui; Haug, Hartmut; Yamamoto, Yoshihisa
- Reviews of Modern Physics, Vol. 82, Issue 2
Polariton lasing vs. photon lasing in a semiconductor microcavity
journal, December 2003
- Deng, H.; Weihs, G.; Snoke, D.
- Proceedings of the National Academy of Sciences, Vol. 100, Issue 26
Spatial Coherence and Stability in a Disordered Organic Polariton Condensate
journal, July 2015
- Daskalakis, K. S.; Maier, S. A.; Kéna-Cohen, S.
- Physical Review Letters, Vol. 115, Issue 3
Nonequilibrium condensates and lasers without inversion: Exciton-polariton lasers
journal, June 1996
- Imamog¯lu, A.; Ram, R. J.; Pau, S.
- Physical Review A, Vol. 53, Issue 6
Exceptional points of non-Hermitian operators
journal, January 2004
- Heiss, W. D.
- Journal of Physics A: Mathematical and General, Vol. 37, Issue 6
Characterization of two-threshold behavior of the emission from a GaAs microcavity
journal, February 2012
- Tempel, Jean-Sebastian; Veit, Franziska; Aßmann, Marc
- Physical Review B, Vol. 85, Issue 7
Bose-Einstein Condensation of Magnons under Incoherent Pumping
journal, May 2009
- Chumak, A. V.; Melkov, G. A.; Demidov, V. E.
- Physical Review Letters, Vol. 102, Issue 18
Temperature Dependence of Highly Excited Exciton Polaritons in Semiconductor Microcavities
journal, August 2013
- Horikiri, Tomoyuki; Matsuo, Yasuhiro; Shikano, Yutaka
- Journal of the Physical Society of Japan, Vol. 82, Issue 8
An electrically pumped polariton laser
journal, May 2013
- Schneider, Christian; Rahimi-Iman, Arash; Kim, Na Young
- Nature, Vol. 497, Issue 7449
Lasing threshold doubling at the crossover from strong to weak coupling regime in GaAs microcavity
journal, February 2012
- Tsotsis, P.; Eldridge, P. S.; Gao, T.
- New Journal of Physics, Vol. 14, Issue 2
Phases of wave functions and level repulsion
journal, August 1999
- Heiss, W. D.
- The European Physical Journal D - Atomic, Molecular and Optical Physics, Vol. 7, Issue 1
Bose-Einstein Condensation in a Gas of Sodium Atoms
journal, November 1995
- Davis, K. B.; Mewes, M. -O.; Andrews, M. R.
- Physical Review Letters, Vol. 75, Issue 22
Nonequilibrium Quantum Condensation in an Incoherently Pumped Dissipative System
journal, June 2006
- Szymańska, M. H.; Keeling, J.; Littlewood, P. B.
- Physical Review Letters, Vol. 96, Issue 23
Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl3
journal, May 2003
- Rüegg, Ch.; Cavadini, N.; Furrer, A.
- Nature, Vol. 423, Issue 6935
Excitations in a Nonequilibrium Bose-Einstein Condensate of Exciton Polaritons
journal, October 2007
- Wouters, Michiel; Carusotto, Iacopo
- Physical Review Letters, Vol. 99, Issue 14
Model of a -symmetric Bose-Einstein condensate in a -function double-well potential
journal, July 2012
- Cartarius, Holger; Wunner, Günter
- Physical Review A, Vol. 86, Issue 1
Supersolid formation in a quantum gas breaking a continuous translational symmetry
journal, March 2017
- Léonard, Julian; Morales, Andrea; Zupancic, Philip
- Nature, Vol. 543, Issue 7643
Coherent Polariton Laser
journal, March 2016
- Kim, Seonghoon; Zhang, Bo; Wang, Zhaorong
- Physical Review X, Vol. 6, Issue 1
Real Spectra in Non-Hermitian Hamiltonians Having Symmetry
journal, June 1998
- Bender, Carl M.; Boettcher, Stefan
- Physical Review Letters, Vol. 80, Issue 24
Observation of the Transition from Lasing Driven by a Bosonic to a Fermionic Reservoir in a GaAs Quantum Well Microcavity
journal, September 2016
- Brodbeck, S.; Suchomel, H.; Amthor, M.
- Physical Review Letters, Vol. 117, Issue 12
Blueshifted Flat Dispersion Relation of Exciton–Polariton Condensates in a CuBr Microcavity
journal, May 2016
- Nakayama, Masaaki; Murakami, Katsuya; Kim, DaeGwi
- Journal of the Physical Society of Japan, Vol. 85, Issue 5
Dynamical Instability of a Nonequilibrium Exciton-Polariton Condensate
journal, August 2017
- Bobrovska, Nataliya; Matuszewski, Michał; Daskalakis, Konstantinos S.
- ACS Photonics, Vol. 5, Issue 1
Observation of diffusive and dispersive profiles of the nonequilibrium polariton-condensate dispersion relation in a CuBr microcavity
journal, March 2017
- Nakayama, Masaaki; Ueda, Masafumi
- Physical Review B, Vol. 95, Issue 12
Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping
journal, September 2006
- Demokritov, S. O.; Demidov, V. E.; Dzyapko, O.
- Nature, Vol. 443, Issue 7110
Quantum well excitons in semiconductor microcavities: Unified treatment of weak and strong coupling regimes
journal, March 1995
- Savona, V.; Andreani, L. C.; Schwendimann, P.
- Solid State Communications, Vol. 93, Issue 9
Observation of an Exceptional Point in a Chaotic Optical Microcavity
journal, September 2009
- Lee, Sang-Bum; Yang, Juhee; Moon, Songky
- Physical Review Letters, Vol. 103, Issue 13
Exciton–polariton condensates
journal, October 2014
- Byrnes, Tim; Kim, Na Young; Yamamoto, Yoshihisa
- Nature Physics, Vol. 10, Issue 11
Generating functional approach for spontaneous coherence in semiconductor electron-hole-photon systems
journal, March 2015
- Yamaguchi, Makoto; Nii, Ryota; Kamide, Kenji
- Physical Review B, Vol. 91, Issue 11
From polariton condensates to highly photonic quantum degenerate states of bosonic matter
journal, January 2011
- Aßmann, Marc; Tempel, Jean-Sebastian; Veit, Franziska
- Proceedings of the National Academy of Sciences, Vol. 108, Issue 5
Bose–Einstein condensation of photons in an optical microcavity
journal, November 2010
- Klaers, Jan; Schmitt, Julian; Vewinger, Frank
- Nature, Vol. 468, Issue 7323
Bose–Einstein condensation in a plasmonic lattice
journal, April 2018
- Hakala, Tommi K.; Moilanen, Antti J.; Väkeväinen, Aaro I.
- Nature Physics, Vol. 14, Issue 7
Encircling an exceptional point
journal, May 2004
- Dembowski, C.; Dietz, B.; Gräf, H. -D.
- Physical Review E, Vol. 69, Issue 5
Polariton Laser Using Single Micropillar Semiconductor Cavities
journal, January 2008
- Bajoni, Daniele; Senellart, Pascale; Wertz, Esther
- Physical Review Letters, Vol. 100, Issue 4
Mean-field theory and fluctuation spectrum of a pumped decaying Bose-Fermi system across the quantum condensation transition
journal, May 2007
- Szymańska, M. H.; Keeling, J.; Littlewood, P. B.
- Physical Review B, Vol. 75, Issue 19
BEC–BCS-laser crossover in Coulomb-correlated electron–hole–photon systems
journal, June 2012
- Yamaguchi, M.; Kamide, K.; Ogawa, T.
- New Journal of Physics, Vol. 14, Issue 6
Second Thresholds in BEC-BCS-Laser Crossover of Exciton-Polariton Systems
journal, July 2013
- Yamaguchi, Makoto; Kamide, Kenji; Nii, Ryota
- Physical Review Letters, Vol. 111, Issue 2
Experimental Observation of the Topological Structure of Exceptional Points
journal, January 2001
- Dembowski, C.; Gräf, H. -D.; Harney, H. L.
- Physical Review Letters, Vol. 86, Issue 5
Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
journal, October 2015
- Gao, T.; Estrecho, E.; Bliokh, K. Y.
- Nature, Vol. 526, Issue 7574
Superfluidity and collective modes in a uniform gas of Fermi atoms with a Feshbach resonance
journal, June 2003
- Ohashi, Y.; Griffin, A.
- Physical Review A, Vol. 67, Issue 6
Quantum fluids of light
journal, February 2013
- Carusotto, Iacopo; Ciuti, Cristiano
- Reviews of Modern Physics, Vol. 85, Issue 1
Stationary states of a PT symmetric two-mode Bose–Einstein condensate
journal, October 2012
- Graefe, Eva-Maria
- Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 44
The physics of exceptional points
journal, October 2012
- Heiss, W. D.
- Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 44
Bose–Einstein condensation of exciton polaritons
journal, September 2006
- Kasprzak, J.; Richard, M.; Kundermann, S.
- Nature, Vol. 443, Issue 7110
Role of the stress trap in the polariton quasiequilibrium condensation in GaAs microcavities
journal, February 2009
- Balili, R.; Nelsen, B.; Snoke, D. W.
- Physical Review B, Vol. 79, Issue 7
Lasing and polariton condensation: Two distinct transitions in GaAs microcavities with stress traps
journal, June 2009
- Nelsen, B.; Balili, R.; Snoke, D. W.
- Journal of Applied Physics, Vol. 105, Issue 12
Non-equilibrium Properties of a Pumped-Decaying Bose-Condensed Electron–Hole Gas in the BCS–BEC Crossover Region
journal, March 2016
- Hanai, R.; Littlewood, P. B.; Ohashi, Y.
- Journal of Low Temperature Physics, Vol. 183, Issue 3-4
BCS-BEC crossover in a system of microcavity polaritons
journal, September 2005
- Keeling, Jonathan; Eastham, P. R.; Szymanska, M. H.
- Physical Review B, Vol. 72, Issue 11
Exciton Bose condensation : the ground state of an electron-hole gas - I. Mean field description of a simplified model
journal, January 1982
- Comte, C.; Nozières, P.
- Journal de Physique, Vol. 43, Issue 7
Self-consistent T-matrix theory of semiconductor light-absorption and luminescence
journal, April 2009
- Kwong, N. H.; Rupper, G.; Binder, R.
- Physical Review B, Vol. 79, Issue 15
Photoluminescence and gain/absorption spectra of a driven-dissipative electron-hole-photon condensate
journal, June 2018
- Hanai, Ryo; Littlewood, Peter B.; Ohashi, Yoji
- Physical Review B, Vol. 97, Issue 24
Dynamical screening and self-energy of excitons in the electron–hole plasma
journal, November 1978
- Zimmermann, R.; Kilimann, K.; Kraeft, W. D.
- Physica Status Solidi (b), Vol. 90, Issue 1
Anomalies of a Nonequilibrium Spinor Polariton Condensate in a Magnetic Field
journal, March 2014
- Fischer, J.; Brodbeck, S.; Chernenko, A. V.
- Physical Review Letters, Vol. 112, Issue 9
A Bose-Einstein condensate in a 𝒫𝒯 symmetric double well
journal, June 2012
- Dast, D.; Haag, D.; Cartarius, H.
- Fortschritte der Physik, Vol. 61, Issue 2-3
An exciton-polariton laser based on biologically produced fluorescent protein
journal, August 2016
- Dietrich, Christof P.; Steude, Anja; Tropf, Laura
- Science Advances, Vol. 2, Issue 8
Unstable and stable regimes of polariton condensation
journal, January 2018
- Baboux, F.; De Bernardis, D.; Goblot, V.
- Optica, Vol. 5, Issue 10
Quantum Optics
journal, May 1995
- Walls, D. F.; Milburn, G. J.; Garrison, John C.
- American Journal of Physics, Vol. 63, Issue 5
Experimental Observation of the Topological Structure of Exceptional Points
text, January 2001
- Dembowski, C.; Gräf, H. -D.; Harney, H. L.
- The American Physical Society
Quantum Optics
journal, June 1995
- Walls, Daniel F.; Milburn, Gerard J.; Schleich, Wolfgang P.
- Physics Today, Vol. 48, Issue 6
Bose-Einstein Condensation in a Gas of Sodium Atoms
conference, January 1996
- Davis, K. B.; Mewes, M. -O.; Andrews, M. R.
- EQEC'96. 1996 European Quantum Electronic Conference, EQEC 96 1996 European Quantum Electronic Conference EQEC-96
The role of the stress trap in polariton quasiequilibrium condensation in GaAs microcavities
text, January 2008
- Balili, R.; Nelsen, B.; Snoke, D. W.
- arXiv
Bose-Einstein condensation of magnons under incoherent pumping
text, January 2008
- Chumak, A. V.; Melkov, G. A.; Demidov, V. E.
- arXiv
Observation of an exceptional point in a chaotic optical microcavity
text, January 2009
- Lee, Sang-Bum; Yang, Juhee; Moon, Songky
- arXiv
Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
text, January 2012
- Graefe, Eva-Maria
- arXiv
Exciton-Mott Physics in Two-Dimensional Electron-Hole Systems: Phase Diagram and Single-Particle Spectra
text, January 2014
- Asano, Kenichi; Yoshioka, Takuya
- arXiv
Exciton-polariton condensates
text, January 2014
- Byrnes, Tim; Kim, Na Young; Yamamoto, Yoshihisa
- arXiv
Spatial coherence and stability in a disordered organic polariton condensate
text, January 2015
- Daskalakis, Konstantinos S.; Maier, Stefan A.; Kéna-Cohen, Stéphane
- arXiv
Unstable and stable regimes of polariton condensation
text, January 2017
- Baboux, F.; De Bernardis, D.; Goblot, V.
- arXiv
Photoluminescence and gain/absorption spectra of a driven-dissipative electron-hole-photon condensate
text, January 2018
- Hanai, Ryo; Littlewood, Peter B.; Ohashi, Yoji
- arXiv
Superfluidity and collective modes in a uniform gas of Fermi atoms with a Feshbach resonance
text, January 2003
- Ohashi, Y.; Griffin, A.
- arXiv
BCS-BEC crossover in a system of microcavity polaritons
text, January 2005
- Keeling, Jonathan; Eastham, P. R.; Szymanska, M. H.
- arXiv