Abstract
Recently a new type of system exhibiting spontaneous coherence has emergedâthe excitonâpolariton condensate. Excitonâpolaritons (or polaritons for short) are bosonic quasiparticles that exist inside semiconductor microcavities, consisting of a superposition of an exciton and a cavity photon. Above a threshold density the polaritons macroscopically occupy the same quantum state, forming a condensate. The polaritons have a lifetime that is typically comparable to or shorter than thermalization times, giving them an inherently non-equilibrium nature. Nevertheless, they exhibit many of the features that would be expected of equilibrium BoseâEinstein condensates (BECs). The non-equilibrium nature of the system raises fundamental questions as to what it means for a system to be a BEC, and introduces new physics beyond that seen in other macroscopically coherent systems. In this review we focus on several physical phenomena exhibited by excitonâpolariton condensates. In particular, we examine topics such as the difference between a polariton BEC, a polariton laser and a photon laser, as well as physical phenomena such as superfluidity, vortex formation, and BerezinskiiâKosterlitzâThouless and BardeenâCooperâSchrieffer physics. We also discuss the physics and applications of engineered polariton structures.
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Change history
13 November 2014
In the version of this Review Article originally published, the sources of two images in Fig. 5a were incorrect. The first and second images from the left in Fig. 5a were taken from ref. 114 and ref. 99, respectively. This error has now been corrected in the online versions of the Review Article.
References
Sargent, M., Scully, M. O. & Lamb, W. E. Laser Physics (Addison-Wesley, 1978).
Pitaevskii, L. & Stringari, S. BoseâEinstein Condensation (Oxford Science Publications, 2003).
Tilley, D. R. & Tilley, J. Superfluidity and Superconductivity (IOP Publishing, 1990).
Leggett, A. Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford Univ. Press, 2006).
Kasprzak, J. et al. BoseâEinstein condensation of exciton polaritons. Nature 443, 409â414 (2006).
Balili, R., Hartwell, V., Snoke, D., Pfeiffer, L. & West, K. BoseâEinstein condensation of microcavity polaritons in a trap. Science 316, 1007â1010 (2007).
Deng, H., Weihs, G., Santori, C., Bloch, J. & Yamamoto, Y. Condensation of semiconductor microcavity exciton polaritons. Science 298, 199â202 (2002).
Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of BoseâEinstein condensation in a dilute atomic vapor. Science 269, 198â201 (1995).
Davis, K. et al. BoseâEinstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969â3973 (1995).
Nikuni, T., Oshikawa, M., Oosawa, A. & Tanaka, H. BoseâEinstein condensation of dilute magnons in TlCuCl3 . Phys. Rev. Lett. 84, 5868â5871 (2000).
Demokritov, S. O. et al. BoseâEinstein condensation of quasi-equilibrium magnons at room temperature under pumping. Nature 443, 430â433 (2006).
Klaers, J., Schmitt, J., Vewinger, F. & Weitz, M. BoseâEinstein condensation of photons in an optical microcavity. Nature 468, 545â548 (2010).
Christopoulos, S. et al. Room-temperature polariton lasing in semiconductor microcavities. Phys. Rev. Lett. 98, 126405 (2007).
Baumberg, J. J. et al. Spontaneous polarization buildup in a room-temperature polariton laser. Phys. Rev. Lett. 101, 136409 (2008).
Kéna-Cohen, S. & Forrest, S. R. Room-temperature polariton lasing in an organic single-crystal microcavity. Nature Photon. 4, 371â375 (2010).
Guillet, T. et al. Polariton lasing in a hybrid bulk ZnO microcavity. Appl. Phys. Lett. 99, 161104 (2011).
Plumhof, J. D., Stöferle, T., Mai, L., Scherf, U. & Mahrt, R. F. Room-temperature BoseâEinstein condensation of cavity excitonâpolaritons in a polymer. Nature Mater. 13, 247â252 (2014).
Deng, H., Haug, H. & Yamamoto, Y. Excitonâpolariton BoseâEinstein condensation. Rev. Mod. Phys. 82, 1489â1537 (2010).
Kavokin, A. Excitonâpolaritons in microcavities: Recent discoveries and perspectives. Phys. Status Solidi B 247, 1898â1906 (2010).
Richard, M. et al. Excitonâpolariton BoseâEinstein condensation: Advances and issues. Int. J. Nanotech. 7, 668â683 (2010).
Snoke, D. & Littlewood, P. Polariton condensates. Phys. Today 63, 42â47 (2010).
Keeling, J. & Berloff, N. G. Excitonâpolariton condensation. Contemp. Phys. 52, 131â151 (2011).
Timofeev, V. & Sanvitto, D. (eds) Exciton Polaritons in Microcavities Vol. 172 (Springer, 2012).
Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299â366 (2013).
Yamamoto, Y. & Imamoglu, A. Mesoscopic Quantum Optics (John Wiley and Sons, 1999).
Weisbuch, C., Nishioka, M., Ishikawa, A. & Arakawa, Y. Observation of the coupled excitonâphoton mode splitting in a semiconductor quantum microcavity. Phys. Rev. Lett. 69, 3314â3317 (1992).
Nelsen, B. et al. Dissipationless flow and sharp threshold of a polariton condensate with long lifetime. Phys. Rev. X 3, 041015 (2013).
Tanese, D. et al. Polariton condensation in solitonic gap states in a one-dimensional periodic potential. Nature Commun. 4, 1749 (2013).
Schmitt-Rink, S., Chemla, D. S. & Miller, D. A. B. Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures. Phys. Rev. B 32, 6601â6609 (1985).
Ciuti, C., Savona, V., Piermarocchi, C., Quattropani, A. & Schwendimann, P. Role of the exchange of carriers in elastic excitonâexciton scattering in quantum wells. Phys. Rev. B 58, 7926â7933 (1998).
Del Valle, E. et al. Dynamics of the formation and decay of coherence in a polariton condensate. Phys. Rev. Lett. 103, 096404 (2009).
Tassone, F. & Yamamoto, Y. Excitonâexciton scattering dynamics in a semiconductor microcavity and stimulated scattering into polaritons. Phys. Rev. B 59, 10830â10842 (1999).
Pau, S., Björk, G., Jacobson, J., Cao, H. & Yamamoto, Y. Stimulated emission of a microcavity dressed exciton and suppression of phonon scattering. Phys. Rev. B 51, 7090â7100 (1995).
Tassone, F., Piermarocchi, C., Savona, V., Quattropani, A. & Schwendimann, P. Bottleneck effects in the relaxation and photoluminescence of microcavity polaritons. Phys. Rev. B 56, 7554â7563 (1997).
Spano, R. et al. Coherence properties of exciton polariton OPO condensates in one and two dimensions. New J. Phys. 14, 075018 (2012).
Deng, H., Weihs, G., Snoke, D., Bloch, J. & Yamamoto, Y. Polariton lasing vs. photon lasing in a semiconductor microcavity. Proc. Natl Acad. Sci. USA 100, 15318â15323 (2003).
Kira, M. et al. Quantum theory of nonlinear semiconductor microcavity luminescence explaining âBoserâ experiments. Phys. Rev. Lett. 79, 5170â5173 (1997).
Butov, L. V. A polariton laser. Nature 447, 540â541 (2007).
Butov, L. V. & Kavokin, A. V. The behaviour of excitonâpolaritons. Nature Photon. 6, 2 (2012).
Deveaud-Plédran, B. The behaviour of excitonâpolaritons. Nature Photon. 6, 205 (2012).
Imamoglu, A., Ram, R. J., Pau, S. & Yamamoto, Y. Nonequilibrium condensates and lasers without inversion: Excitonâpolariton lasers. Phys. Rev. A 53, 4250â4253 (1996).
Snoke, D. Polariton condensation and lasing. in ExcitonâPolaritons in Microcavities Vol. 172 (eds Tomofeev, V. & Sanvitto, D.) 307â327 (Springer, 2012).
Kasprzak, J., Solnyshkov, D. D., André, R., Dang, L. S. & Malpuech, G. Formation of an exciton polariton condensate: Thermodynamic versus kinetic regimes. Phys. Rev. Lett. 101, 146404 (2008).
Dang, L. S., Heger, D., André, R., BÅuf, F. & Romestain, R. Stimulation of polariton photoluminescence in semiconductor microcavity. Phys. Rev. Lett. 81, 3920â3923 (1998).
Laussy, F. P., Malpuech, G., Kavokin, A. & Bigenwald, P. Spontaneous coherence buildup in a polariton laser. Phys. Rev. Lett. 93, 016402 (1997).
Deng, H. et al. Quantum degenerate excitonâpolaritons in thermal equilibrium. Phys. Rev. Lett. 97, 146402 (2006).
Deng, H., Solomon, G. S., Hey, R., Ploog, K. H. & Yamamoto, Y. Spatial coherence of a polariton condensate. Phys. Rev. Lett. 99, 126403 (2007).
Schneider, C. et al. An electrically pumped polariton laser. Nature 497, 348â352 (2013).
Assmann, M. et al. From polariton condensates to highly photonic quantum degenerate states of bosonic matter. Proc. Natl Acad. Sci. USA 108, 1804â1809 (2011).
Tempel, J-S. et al. Characterization of two-threshold behavior of the emission from a GaAs microcavity. Phys. Rev. B 85, 075318 (2012).
Yamaguchi, M., Kamide, K., Nii, R., Ogawa, T. & Yamamoto, Y. Second thresholds in BECâBCS-laser crossover of excitonâpolariton systems. Phys. Rev. Lett. 111, 026404 (2013).
Carusotto, I., Hu, S. X., Collins, L. A. & Smerzi, A. BogoliubovâCerenkov radiation in a BoseâEinstein condensate flowing against an obstacle. Phys. Rev. Lett. 97, 260403 (2006).
Utsunomiya, S. et al. Observation of Bogoliubov excitations in excitonâpolariton condensates. Nature Phys. 4, 700â705 (2008).
Kohnle, V. et al. From single particle to superfluid excitations in a dissipative polariton gas. Phys. Rev. Lett. 106, 255302 (2011).
Wouters, M. & Carusotto, I. Excitations in a nonequilibrium BoseâEinstein condensate of exciton polaritons. Phys. Rev. Lett. 99, 140402 (2007).
Byrnes, T., Horikiri, T., Ishida, N., Fraser, M. & Yamamoto, Y. The negative Bogoliubov dispersion in excitonâpolariton condensates. Phys. Rev. B. 85, 075130 (2012).
Carusotto, I. & Ciuti, C. Probing microcavity polariton superfluidity through resonant Rayleigh scattering. Phys. Rev. Lett. 93, 166401 (2004).
Wouters, M. & Carusotto, I. Superfluidity and critical velocities in nonequilibrium BoseâEinstein condensates. Phys. Rev. Lett. 105, 020602 (2010).
Keeling, J. Superfluid density of an open dissipative condensate. Phys. Rev. Lett. 107, 080402 (2011).
Janot, A., Hyart, T., Eastham, P. R. & Rosenow, B. Superfluid stiffness of a driven dissipative condensate with disorder. Phys. Rev. Lett. 111, 230403 (2013).
Amo, A. et al. Superfluidity of polaritons in semiconductor microcavities. Nature Phys. 5, 805â810 (2009).
Amo, A. et al. Collective fluid dynamics of a polariton condensate in a semiconductor microcavity. Nature 457, 291â295 (2009).
Sanvitto, D. et al. Persistent currents and quantized vortices in a polariton superfluid. Nature Phys. 6, 527â533 (2010).
Wouters, M. & Carusotto, I. Probing the excitation spectrum of polariton condensates. Phys. Rev. B 79, 125311 (2009).
Hohenberg, P. C. Existence of long-range order in one and two dimensions. Phys. Rev. 158, 383â386 (1967).
Mermin, N. D. & Wagner, H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett. 17, 1133â1136 (1967).
Berezkinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems processing a continuous symmetry group. II. quantum systems. Sov. Phys. JETP 34, 610â616 (1972).
Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181â1203 (1973).
Hadzibabic, Z. & Dalibard, J. Two-dimensional Bose fluids: An atomic physics perspective. Riv. Nuovo Cimento 34, 389â434 (2011).
Lagoudakis, K. G. et al. Quantized vortices in an excitonâpolariton condensate. Nature Phys. 4, 706â710 (2008).
Lagoudakis, K. G. et al. Observation of half-quantum vortices in an excitonâpolariton condensate. Science 326, 974â976 (2009).
Roumpos, G. et al. Single vortexâantivortex pair in an excitonâpolariton condensate. Nature Phys. 7, 129â133 (2011).
Manni, F. et al. Dissociation dynamics of singly charged vortices into half-quantum vortex pairs. Nature Commun. 3, 1309 (2012).
Tosi, G. et al. Onset and dynamics of vortexâantivortex pairs in polariton optical parametric oscillator superfluids. Phys. Rev. Lett. 107, 036401 (2011).
Wertz, E. et al. Spontaneous formation and optical manipulation of extended polariton condensates. Nature Phys. 6, 860â864 (2010).
Manni, F. et al. Polariton condensation in a one-dimensional disordered potential. Phys. Rev. Lett. 106, 176401 (2011).
Roumpos, G. et al. Power-law decay of the spatial correlation function in excitonâpolariton condensates. Proc. Natl Acad. Sci. USA 109, 6467â6472 (2012).
Nitsche, W. H. et al. Algebraic order and the BerezinskiiâKosterlitzâThouless transition in an excitonâpolariton gas. Preprint at http://arxiv.org/abs/1401.0756 (2014).
Pigeon, S., Carusotto, I. & Ciuti, C. Hydrodynamic nucleation of vortices and solitons in a resonantly excited polariton superfluid. Phys. Rev. B 83, 144513 (2011).
Amo, A. et al. Polariton superfluids reveal quantum hydrodynamic solitons. Science 332, 1167â1170 (2011).
Grosso, G., Nardin, G., Morier-Genoud, F., Léger, Y. & Deveaud-Plédran, B. Dynamics of dark-soliton formation in a polariton quantum fluid. Phys. Rev. B 86, 020509(R) (2012).
Sich, M. et al. Observation of bright polariton solitons in a semiconductor microcavity. Nature Photon. 6, 50â55 (2012).
Cilibrizzi, P. et al. Linear wave dynamics explains observations attributed to dark-solitons in a polariton quantum fluid. Phys. Rev. Lett. 113, 103901 (2014).
Keldysh, L. V. & Kozlov, A. N. Collective properties of excitons in semiconductors. Sov. Phys. JETP 27, 521â528 (1968).
Comte, C. & Nozières, P. Exciton Bose condensation: The ground state of an electron-hole gas. I. mean field description of a simplified model. J. Phys. 43, 1069â1081 (1982).
Keeling, J., Eastham, P. R., Szymanska, M. H. & Littlewood, P. B. Polariton condensation with localized excitons and propagating photons. Phys. Rev. Lett. 93, 226403 (2004).
Keeling, J., Eastham, P. R., Szymanska, M. H. & Littlewood, P. B. BCSâBEC crossover in a system of microcavity polaritons. Phys. Rev. B 72, 115320 (2005).
Byrnes, T., Horikiri, T., Ishida, N. & Yamamoto, Y. BCS wave-function approach to the BECâBCS crossover of excitonâpolariton condensates. Phys. Rev. Lett. 105, 186402 (2010).
Kamide, K. & Ogawa, T. What determines the wave function of electronâhole pairs in polariton condensates? Phys. Rev. Lett. 105, 056401 (2010).
Horikiri, T. et al. Temperature dependence of highly excited exciton polaritons in semiconductor microcavities. J. Phys. Soc. Jpn 82, 084709 (2013).
Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39â44 (2002).
Buluta, I. & Nori, F. Quantum simulators. Science 326, 108â111 (2009).
Jacqmin, T. et al. Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons. Phys. Rev. Lett. 112, 116402 (2014).
Tosi, G. et al. Geometrically locked vortex lattices in semiconductor quantum fluids. Nature Commun. 3, 1243 (2012).
Cerda-Mendez, E. A. et al. Polariton condensation in dynamic acoustic lattices. Phys. Rev. Lett. 105, 116402 (2010).
Lai, C. W. et al. Coherent zero-state and pi-state in an excitonâpolariton condensate array. Nature 450, 529â532 (2007).
Kim, N. Y. et al. Dynamical d-wave condensation of excitonâpolaritons in a two-dimensional square-lattice potential. Nature Phys. 7, 681â686 (2011).
Kaitouni, R. I. et al. Engineering the spatial confinement of exciton polaritons in semiconductors. Phys. Rev. B 74, 155311 (2006).
Nardin, G., Leger, Y., Pietka, B., Morier-Genoud, F. & Deveaud-Pledran, B. Phase-resolved imaging of confined excitonâpolariton wave functions in elliptical traps. Phys. Rev. B 82, 045304 (2010).
Galbiati, M. et al. Polariton condensation in photonic molecules. Phys. Rev. Lett. 108, 126403 (2011).
Masumoto, N. et al. Excitonâpolariton condensates with flat bands in a two-dimensional kagome lattice. New J. Phys. 14, 065002 (2012).
Kim, N. Y. et al. Excitonâpolariton condensates near the Dirac point in a triangular lattice. New J. Phys. 15, 035032 (2013).
Kusudo, K. et al. Stochastic formation of polariton condensates in two degenerate orbital states. Phys. Rev. B 87, 214503 (2013).
Backhaus, S. et al. Discovery of a metastable Ï-state in a superfluid 3He weak link. Nature 392, 687â690 (1998).
Deveaud-Plédran, B. Polaritronics in view. Nature 453, 297â298 (2008).
Liew, T. C. H., Kavokin, A. & Shelykh, I. A. Optical circuits based on polariton neurons in semiconductor microcavities. Phys. Rev. Lett. 101, 016402 (2008).
Amo, A. et al. Excitonâpolariton spin switches. Nature Photon. 4, 361â366 (2010).
Nguyen, H. S. et al. Realization of a double-barrier resonant tunneling diode for cavity polaritons. Phys. Rev. Lett. 110, 236601 (2013).
Ballarini, D. et al. All-optical polariton transistor. Nature Commun. 4, 1778 (2013).
Byrnes, T., Yamamoto, Y. & van Loock, P. Unconditional generation of bright coherent non-Gaussian light from excitonâpolariton condensates. Phys. Rev. B 87, 201301(R) (2013).
Bhattacharya, P., Xiao, B., Das, A., Bhowmick, S. & Heo, J. Solid state electrically injected excitonâpolariton laser. Phys. Rev. Lett. 110, 206403 (2013).
Snoke, D. A feature rather than a bug. Nature Phys. 4, 673 (2008).
Love, A. P. D. et al. Intrinsic decoherence mechanisms in the microcavity polariton condensate. Phys. Rev. Lett. 101, 067404 (2008).
Bajoni, D. et al. Polariton laser using single micropillar GaAsâGaAlAs semiconductor cavities. Phys. Rev. Lett. 100, 047401 (2008).
De Lima, M. M. Jr et al. Phonon-induced polariton superlattices. Phys. Rev. Lett. 97, 045501 (2006).
Acknowledgements
We thank B. Devaud-Plédran for providing valuable comments on the manuscript. This work is supported by the FIRST program through JSPS, the Okawa Foundation, the Transdisciplinary Research Integration Center, and DARPA QuEST program through Navy/SPAWAR Grant N66001-09-1-2024, the Inamori Foundation, NTT Basic Laboratories and JSPS Kakenhi Grant Number 26790061.
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Byrnes, T., Kim, N. & Yamamoto, Y. Excitonâpolariton condensates. Nature Phys 10, 803â813 (2014). https://doi.org/10.1038/nphys3143
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DOI: https://doi.org/10.1038/nphys3143
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