1023:
temperature 354 mK was seen by
Yoshioka et al. in 2011. Recent experiments by Stolz et al. using a potential trap have given more evidence at ultralow temperature 37 mK. In a parabolic trap with exciton temperature 200 mK and lifetime broadened to 650ns, the dependence of luminescence on laser intensity has a kink which indicates condensation. The theory of a Bose gas is extended to a mean field interacting gas by a Bogoliubov approach to predict the exciton spectrum; The kink is considered a sign of transition to BEC. Signs were seen for a dense gas BEC in a GaAs quantum well.
1093:, an elementary excitation in superfluid He introduced by Landau, were discussed by Feynman and others. Rotons condense at low temperature. Experiments have been proposed and the expected spectrum has been studied, but roton condensates have not been detected. Phonons were first observed in a condensate in 2004 by ultrashort pulses in a bismuth crystal at 7K.
1034:, electron spin waves, can be controlled by a magnetic field. Densities from the limit of a dilute gas to a strongly interacting Bose liquid are possible. Magnetic ordering is the analog of superfluidity. The condensate appears as the emission of monochromatic microwaves, which are tunable with the applied magnetic field.
486:-point (2.17K); a condensate was proposed by Böer et al. in 1961. Experimental phenomenon were predicted leading to various pulsed laser searches that failed to produce evidence. Signs were first seen by Fuzukawa et al. in 1990, but definite detection was published later in the 2000s. Condensed excitons are a
1022:
started a large number of experimental searches into the 1990s that failed to detect signs. Pulse methods led to overheating, preventing condensate states. Helium cooling allows mili-kelvin setups and continuous wave optics improves on pulsed searches. Relaxation explosion of a condensate at lattice
498:
Excitons results from photons exciting electrons creating holes, which are then attracted and can form bound states. The 1s paraexciton and orthoexciton are possible. The 1s triplet spin state, 12.1meV below the degenerate orthoexciton states(lifetime ~ns), is decoupled and has a long lifetime to an
1077:
in an optical microcavity was first published in Nature in 2006. Semiconductor cavity polariton gases transition to ground state occupation at 19K. Bogoliubov excitations were seen polariton BECs in 2008. The signatures of BEC were observed at room temperature for the first time in 2013, in a large
447:
This can be achieved by cooling and magnetic or optical control of the system. Spectroscopy can detect shifts in peaks indicating thermodynamic phases with condensation. Quasiparticle BEC can be superfluids. Signs of such states include spatial and temporal coherence and polarization changes.
39:
BECs form when low temperatures cause nearly all particles to occupy the lowest quantum state. Condensation of quasiparticles occurs in ultracold gases and materials. The lower masses of material quasiparticles relative to atoms lead to higher BEC temperatures. An ideal Bose gas has a phase
448:
Observation for excitons in solids was seen in 2005 and for magnons in materials and polaritons in microcavities in 2006. Graphene is another important solid state system for studies of condensed matter including quasi particles; It's a 2D electron gas, similar to other thin films.
699:
30:
in materials. Some have integer spins and can be expected to obey Bose–Einstein statistics like traditional particles. Conditions for condensation of various quasiparticles have been predicted and observed. The topic continues to be an active field of study.
499:
optical decay. Dilute gas densities (n~10cm) are possible, but paraexciton generation scales poorly, so significant heating occurs in creating high densities(10cm) preventing BECs. Assuming a thermodynamic phase occurs when separation reaches the
2217:
Kasprzak, J; Richard, M; Kundermann, S; Baas, A; Jeambrun, P; Keeling, JM; Marchetti, FM; Szymańska, MH; André, R; Staehli, JL; Savona, V; Littlewood, PB; Deveaud, B; Dang (28 September 2006). "Bose–Einstein condensation of exciton polaritons".
1936:
Alloing, Mathieu; Beian, Mussie; Lewenstein, Maciej; Fuster, David; González, Yolanda; González, Luisa; Combescot, Roland; Combescot, Monique; Dubin, François (July 2014). "Evidence for a Bose–Einstein condensate of excitons".
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Berman, OL; Kezerashvili, RY; Lozovik, YE; Snoke, DW (1 November 2010). "Bose–Einstein condensation and superfluidity of trapped polaritons in graphene and quantum wells embedded in a microcavity".
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Demokritov, S.O.; Demidov, VE; Dzyapko, O; Melkov, GA; Serga, AA; Hillebrands, B; Slavin, AN (2006). "Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping".
1050:, at temperatures as large as 14 K. The high transition temperature (relative to atomic gases) is due to the small mass (near an electron) and greater density. In 2006, condensation in a
902:, preventing a high density paraexciton BEC. A potential well limits diffusion, damps exciton decay, and lowers the critical number, yielding an improved critical temperature versus the
110:
338:
1267:
Bugrij, A. I.; Loktev, V. M. (2007). "On the theory of Bose–Einstein condensation of quasiparticles: On the possibility of condensation of ferromagnons at high temperatures".
758:
1054:
Yttrium-iron-garnet thin film was seen even at room temperature with optical pumping. Condensation was reported in gadolinium in 2011. Magnon BECs have been considered as
900:
531:
1816:
Stolz, H.; Semkat, D. (2010). "Unique signatures for Bose-Einstein condensation in the decay luminescence lineshape of weakly interacting excitons in a potential trap".
1501:
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484:
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2398:
Plumhof, JD; Stöferle, T; Mai, L; Scherf, U; Mahrt, RF (8 December 2013). "Room-temperature Bose–Einstein condensation of cavity exciton–polaritons in a polymer".
1018:= 10s. For an achievable T = 0.01K, a manageable optical pumping rate of 10/s should produce a condensate. More detailed calculations by J. Keldysh and later by
818:
798:
731:
346:
490:
and will not interact with phonons. While the normal exciton absorption is broadened by phonons, in the superfluid absorption degenerates to a line.
1312:
Butov, L. V.; Lai, C. W.; Ivanov, A. L.; Gossard, A. C.; Chemla, D. S. (2002). "Towards Bose–Einstein condensation of excitons in potential traps".
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Utsunomiya, S; Tian, L; Roumpos, G; Lai, C. W; Kumada, N; Fujisawa, T; Kuwata-Gonokami, M; Löffler, A; Höfling, S; Forchel, A; Yamamoto, Y (2008).
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2611:
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2312:"Polariton Bose–Einstein condensate at room temperature in an Al(Ga)N nanowire–dielectric microcavity with a spatial potential trap"
1781:
Joshioka, K.; Ideguchi, T.; Mysyrovicz, A; Kuwata-Gonokami, M. (2010). "Quantum inelastic collisions between paraexcitons inCu2O".
1107:
1074:
694:{\displaystyle n^{1/3}=\hbar ^{-1}(m_{\text{eff}}kT_{cr})^{1/2}\longrightarrow T_{c}={\frac {n^{2/3}\hbar ^{2}}{km_{\text{eff}}}}}
204:
2128:
Mathew, SP; Kaul, SN (Jul 6, 2011). "Bose–Einstein condensation of magnons in polycrystalline gadolinium with nano-size grains".
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1746:
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1102:
1871:"Transition to a Bose–Einstein condensate and relaxation explosion of excitons at sub-Kelvin temperatures"
290:
2467:
2381:"SCIENTIFIC METHOD / SCIENCE & EXPLORATION Bose–Einstein condensate created at room temperature"
1969:
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transitions when inter-particle spacing approaches the thermal De-Broglie wavelength:
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284:. The particles obey the Bose–Einstein distribution and all occupy the ground state:
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1978:
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1239:
1184:
1137:
800:
are the Planck and
Boltzmann constants. Density depends on the optical generation
2523:
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2255:
1767:
2035:
437:{\displaystyle f(0)={\frac {N_{0}(t)}{N}}=1-\left({\frac {T}{T_{c}}}\right)^{3}}
2695:
2642:
2589:
2200:
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1251:
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463:
2346:
849:. Tuned lasers create excitons which efficiently self-annihilate at a rate:
2509:
2427:
2365:
2247:
2157:
2094:
2043:
1469:
1461:
1418:
1349:
979:{\displaystyle N_{c}=\zeta (3)\left({\frac {kT}{\hbar \omega }}\right)^{3}}
2558:
L. A. Melnikovsky (22 July 2011). "Bose–Einstein condensation of rotons".
2310:
Das, A; Bhattacharya, P; Heo, J; Banerjee, A; Guo, W (February 19, 2013).
1732:
2018:
1780:
1700:
1393:
1171:
1019:
340:, with the ground state occupancy fraction as a function of temperature:
2271:"Observation of Bogoliubov excitations in exciton-polariton condensates"
2239:
2086:
1410:
1904:
1869:
Yoshioka, Kosuke; Chae, Eunmi; Kuwata-Gonokami, Makoto (May 31, 2011).
1070:
487:
2295:
2270:
1288:
1073:, caused by light coupling to excitons, occur in optical cavities and
2419:
1581:
1556:
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1038:
460:
456:
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1951:
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1226:
1156:
1079:
1041:
1031:
733:
is the exciton density, effective mass(of electron mass order)
2064:
1439:
2216:
1503:-Point of Liquid Helium and the Bose–Einstein Condensation".
1090:
1055:
1935:
277:{\displaystyle T_{c}<32\pi ^{3}\hbar ^{6}V^{2}u_{0}P^{2}}
2716:
1868:
1082:
energy semiconductor device and in a polymer microcavity.
1037:
In 1999 condensation was demonstrated in antiferromagnetic
2309:
1999:
194:{\displaystyle N\propto (T/2\pi )^{3}u^{1/2}P/v\hbar ^{3}}
2397:
2268:
1607:
1605:
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1004:
915:
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472:
349:
293:
207:
118:
46:
2522:
1699:
1602:
1211:
2610:
1378:
287:The Bose gas can be considered in a harmonic trap,
1495:
1010:
978:
894:
841:
812:
792:
772:
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478:
436:
332:
276:
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104:
2557:
1442:Philosophical Transactions of the Royal Society A
2750:
2663:
2178:
1676:"Diagram Technique for Nonequilibrium Processes"
2316:Proceedings of the National Academy of Sciences
1664:Aurora, C.P. (2001) Thermodynamics, McGraw-Hill
1165:(3). American Physical Society (APS): 463–512.
1128:(2). American Physical Society (APS): 437–672.
1119:
26:, particles that are effective descriptions of
1611:
1557:"Viscosity of Liquid Helium below the λ-Point"
1545:Einstein, A. (1920) Proc. Berlin Acad. Science
2212:
2210:
1745:
1266:
1815:
105:{\displaystyle k_{B}T=~\hbar ^{2}n^{2/3}/M}
2207:
2127:
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2440:
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2017:
1968:
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1108:Bose-Einstein condensation of polaritons
2480:
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1673:
1085:
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1554:
1482:
112:. The critical concentration is then
459:are electron-hole pairs. Similar to
201:, leading to a critical temperature:
535:
16:Occurrence in collective excitations
2058:
333:{\displaystyle V(r)=M\omega ^{2}/2}
13:
1075:condensation of exciton-polaritons
14:
2775:
2116:Magnon Bose Einstein Condensation
2379:Francis, Matthew (Feb 6, 2013).
1320:(6884). Springer Nature: 47–52.
2710:
2657:
2604:
2551:
2545:10.1070/PU1980v023n06ABEH004937
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2739:10.1016/j.physleta.2003.11.063
2150:10.1088/0953-8984/23/26/266003
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1644:10.1088/1367-2630/14/10/105007
1589:
1548:
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989:
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753:{\displaystyle m_{\text{eff}}}
626:
609:
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384:
378:
359:
353:
303:
297:
143:
125:
1:
1365:
1065:
895:{\displaystyle dn/dt=-an^{2}}
526:{\displaystyle \lambda _{dB}}
34:
1768:10.1016/j.jlumin.2004.09.035
1275:(1). AIP Publishing: 37–50.
7:
2036:10.1103/PhysRevLett.84.5868
1979:10.1209/0295-5075/107/10012
1096:
906:scaling of free particles:
451:
10:
2780:
2696:10.1103/PhysRevB.89.224516
2643:10.1103/PhysRevA.86.021604
2590:10.1103/PhysRevB.84.024525
2201:10.1103/PhysRevA.90.042303
1848:10.1103/physrevb.81.081302
1803:10.1103/physrevb.82.041201
1026:
20:Bose–Einstein condensation
2759:Bose–Einstein condensates
1725:10.1103/physrevb.41.11171
1244:10.1103/revmodphys.80.885
1214:Reviews of Modern Physics
1189:10.1103/revmodphys.71.463
1159:Reviews of Modern Physics
1142:10.1103/revmodphys.54.437
1122:Reviews of Modern Physics
493:
1496:{\displaystyle \lambda }
1103:Bose–Einstein condensate
842:{\displaystyle n=g\tau }
479:{\displaystyle \lambda }
2347:10.1073/pnas.1210842110
2006:Physical Review Letters
1748:Journal of Luminescence
1483:London, F (1938). "The
1269:Low Temperature Physics
2525:Soviet Physics Uspekhi
2510:10.1103/PhysRev.94.262
2481:Feynman, R. P (1954).
1674:Keldysh, L.V. (1965).
1614:New Journal of Physics
1497:
1462:10.1098/rsta.2010.0208
1114:Important publications
1012:
980:
896:
843:
814:
794:
774:
773:{\displaystyle \hbar }
754:
727:
695:
527:
480:
438:
334:
278:
195:
106:
28:collective excitations
2130:J Phys Condens Matter
1875:Nature Communications
1498:
1013:
1011:{\displaystyle \tau }
981:
897:
844:
815:
795:
775:
755:
728:
696:
528:
501:de Broglie wavelength
481:
439:
335:
279:
196:
107:
1487:
1086:Other quasiparticles
1002:
913:
853:
824:
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784:
764:
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542:
507:
470:
347:
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205:
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44:
2731:2004PhLA..321..381M
2688:2014PhRvB..89v4516G
2635:2012PhRvA..86b1604B
2582:2011PhRvB..84b4525M
2537:1980SvPhU..23..317I
2502:1954PhRv...94..262F
2412:2014NatMa..13..247P
2338:2013PNAS..110.2735D
2287:2008NatPh...4..673U
2240:10.1038/nature05131
2232:2006Natur.443..409K
2193:2014PhRvA..90d2303A
2142:2011JPCM...23z6003M
2087:10.1038/nature05117
2079:2006Natur.443..430D
2028:2000PhRvL..84.5868N
1961:2014EL....10710012A
1897:2011NatCo...2..328Y
1840:2010PhRvB..81h1302S
1795:2010PhRvB..82d1201Y
1760:2005JLum..112...11N
1717:1990PhRvB..4111171S
1711:(16): 11171–11184.
1636:2012NJPh...14j5007S
1573:1938Natur.141...74K
1517:1938Natur.141..643L
1454:2010RSPTA.368.5459B
1411:10.1038/nature03081
1403:2004Natur.432..691E
1326:2002Natur.417...47B
1281:2007LTP....33...37B
1236:2008RvMP...80..885B
1181:1999RvMP...71..463D
1134:1982RvMP...54..437A
2441:L. Landau (1941).
1905:10.1038/ncomms1335
1555:Kapiza, P (1938).
1493:
1008:
994:In an ultrapure Cu
976:
892:
839:
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2719:Physics Letters A
2462:Missing or empty
2296:10.1038/nphys1034
2226:(7110): 409–414.
2073:(7110): 430–433.
1511:(3571): 643–644.
1448:(1932): 5459–82.
1387:(7018): 691–694.
1289:10.1063/1.2409633
1060:quantum computing
964:
820:and lifetime as:
813:{\displaystyle g}
793:{\displaystyle k}
747:
726:{\displaystyle n}
711:
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391:
65:
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2725:(5–6): 381–387.
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2400:Nature Materials
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2322:(8): 2735–2740.
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2019:cond-mat/9908118
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488:superfluid
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