20:
516:
51:
181:
511:{\displaystyle H=\sum _{n=1}^{N}\omega _{c}a_{n}^{\dagger }a_{n}+\sum _{n=1}^{N}\omega _{a}\sigma _{n}^{+}\sigma _{n}^{-}+\kappa \sum _{n=1}^{N}\left(a_{n+1}^{\dagger }a_{n}+a_{n}^{\dagger }a_{n+1}\right)+\eta \sum _{n=1}^{N}\left(a_{n}\sigma _{n}^{+}+a_{n}^{\dagger }\sigma _{n}^{-}\right)}
863:
773:
943:
551:
1404:
K. Winkler; G. Thalhammer; F. Lang; R. Grimm; J. H. Denschlag; A. J. Daley; A. Kantian; H. P. Buchler; P. Zoller (2006). "Repulsively bound atom pairs in an optical lattice".
665:
638:
1526:
173:
579:
44:
599:
117:
The JCH model was originally proposed in June 2006 in the context of Mott transitions for strongly interacting photons in coupled cavity arrays. A different
957:
bound states when the photon-atom interaction is sufficiently strong. In particular, the two polaritons associated with the bound states exhibit a strong
102:
778:
693:
66:
105:
and hence require strong-coupling theory for treatment. One method for realizing an experimental model of the system uses circularly-linked
62:
1130:
D. G. Angelakis; M. F. Santos; S. Bose (2007). "Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays".
872:
1072:
A. Nunnenkamp; Jens Koch; S. M. Girvin (2011). "Synthetic gauge fields and homodyne transmission in Jaynes-Cummings lattices".
1185:
M. J. Hartmann, F. G. S. L. Brandão and M. B. Plenio (2006). "Strongly interacting polaritons in coupled arrays of cavities".
86:
55:
1356:
78:
1598:
118:
121:
scheme was synchronically suggested, wherein four level atoms interacted with external fields, leading to
98:
1074:
106:
1240:
A. D. Greentree; C. Tahan; J. H. Cole; L. C. L. Hollenberg (2006). "Quantum phase transitions of light".
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602:
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1206:
1151:
1093:
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133:
Using mean-field theory to predict the phase diagram of the JCH model, the JCH model should exhibit
1575:
1549:
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1449:
1415:
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23:
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29:
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1042:
858:{\displaystyle {\hat {N}}_{a}\equiv \sum _{n=1}^{N}\sigma _{n}^{+}\sigma _{n}^{-}}
958:
1504:
1382:
1163:
85:. As the name suggests, the Jaynes–Cummings–Hubbard model is a variant on the
1540:
M. Valiente; D. Petrosyan (2008). "Two-particle states in the
Hubbard model".
954:
610:
122:
1445:
1050:
1420:
1256:
1201:
1146:
965:. This process is similar to the formation of a bound pair of repulsive
768:{\displaystyle {\hat {N}}_{c}\equiv \sum _{n=1}^{N}a_{n}^{\dagger }a_{n}}
1437:
667:. The cavities are treated as periodic, so that the cavity labelled by
966:
1300:
1273:
1218:
606:
59:
1467:
Javanainen, Juha and Odong, Otim and
Sanders, Jerome C. (Apr 2010).
1554:
1487:
1365:
1088:
1025:
969:
554:
82:
49:
18:
1343:"Two-polariton bound states in the Jaynes-Cummings-Hubbard model"
938:{\displaystyle \lbrack H,{\hat {N}}_{c}+{\hat {N}}_{a}\rbrack =0}
101:, Jaynes–Cummings–Hubbard dynamics depend on photonic and atomic
690:
Defining the photonic and atomic excitation number operators as
94:
1008:"Strong Coupling Theory for the Jaynes-Cummings-Hubbard Model"
1469:"Dimer of two bosons in a one-dimensional optical lattice"
581:
is the tunneling rate between neighboring cavities, and
875:
781:
696:
646:
619:
587:
567:
527:
184:
155:
89:; a one-dimensional JCH model consists of a chain of
32:
93:
coupled single-mode cavities, each with a two-level
937:
857:
767:
659:
632:
593:
573:
545:
510:
167:
38:
1320:Physics and Applications of the Josephson Effect
8:
1525:: CS1 maint: multiple names: authors list (
926:
876:
1318:Antonio Barone; Gianfranco Paternó (1982).
961:such that they stay close to each other in
77:is a many-body quantum system modeling the
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26:of photons between coupled cavities. The
1297:An Introduction to the Josephson Effects
557:operators for the two-level atom at the
1125:
1123:
998:
865:, the total number of excitations is a
609:-atom interaction strength. The cavity
156:
1518:
1341:Max T. C. Wong; C. K. Law (May 2011).
985:D. F. Walls and G. J. Milburn (1995),
1006:Schmidt, S.; Blatter, G. (Aug 2009).
149:The Hamiltonian of the JCH model is (
7:
679:= 1. Note that the model exhibits
640:and atomic transition frequency is
125:with strongly correlated dynamics.
75:Jaynes–Cummings–Hubbard (JCH) model
546:{\displaystyle \sigma _{n}^{\pm }}
46:is the tunnelling rate of photons.
14:
953:The JCH Hamiltonian supports two-
683:; this process is similar to the
1572:10.1088/0953-4075/41/16/161002
1542:J. Phys. B: At. Mol. Opt. Phys
1043:10.1103/PhysRevLett.103.086403
914:
892:
789:
704:
1:
1106:10.1088/1367-2630/13/9/095008
675:+1 corresponds to the cavity
660:{\displaystyle \omega _{a}}
633:{\displaystyle \omega _{c}}
605:which characterizes to the
1615:
1505:10.1103/PhysRevA.81.043609
1383:10.1103/PhysRevA.83.055802
1164:10.1103/physreva.76.031805
949:Two-polariton bound states
97:. Unlike in the competing
1357:American Physical Society
168:{\displaystyle \hbar =1}
79:quantum phase transition
574:{\displaystyle \kappa }
39:{\displaystyle \kappa }
16:Model in quantum optics
1075:New Journal of Physics
939:
859:
824:
769:
739:
661:
634:
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575:
547:
512:
439:
337:
270:
211:
169:
107:superconducting qubits
70:
47:
40:
1295:B. W. Petley (1971).
940:
860:
804:
770:
719:
662:
635:
603:vacuum Rabi frequency
596:
594:{\displaystyle \eta }
576:
548:
513:
419:
317:
250:
191:
170:
87:Jaynes–Cummings model
56:Jaynes–Cummings model
53:
41:
22:
873:
779:
694:
644:
617:
585:
565:
525:
182:
153:
54:Illustration of the
30:
1564:2008JPhB...41p1002V
1497:2010PhRvA..81d3609J
1438:10.1038/nature04918
1430:2006Natur.441..853W
1375:2011PhRvA..83e5802W
1266:2006NatPh...2..856G
1211:2006NatPh...2..849H
1156:2007PhRvA..76c1805A
1098:2011NJPh...13i5008N
1035:2009PhRvL.103h6403S
854:
839:
754:
542:
502:
487:
469:
391:
363:
310:
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989:, Springer-Verlag.
935:
867:conserved quantity
855:
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630:
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528:
508:
488:
473:
455:
377:
343:
296:
281:
222:
165:
103:degrees of freedom
99:Bose–Hubbard model
71:
48:
36:
1414:(7095): 853–856.
1133:Physical Review A
917:
895:
792:
707:
681:quantum tunneling
561:-th cavity. The
58:. In the circle,
1606:
1584:
1583:
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1421:cond-mat/0605196
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1332:
1331:
1315:
1309:
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1292:
1286:
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1274:10.1038/nphys466
1259:
1257:cond-mat/0609050
1237:
1231:
1230:
1219:10.1038/nphys462
1204:
1202:quant-ph/0606097
1182:
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1149:
1147:quant-ph/0606159
1127:
1118:
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1091:
1069:
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1013:Phys. Rev. Lett.
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685:Josephson effect
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1294:
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1289:
1250:(12): 856–861.
1239:
1238:
1234:
1195:(12): 849–855.
1184:
1183:
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1128:
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980:Further reading
974:optical lattice
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1599:Quantum optics
1591:
1590:
1586:
1585:
1548:(16): 161002.
1532:
1459:
1396:
1333:
1310:
1305:Mills and Boon
1287:
1243:Nature Physics
1232:
1188:Nature Physics
1177:
1140:(3): 1805(R).
1119:
1064:
997:
995:
992:
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987:Quantum Optics
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963:position space
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135:Mott insulator
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1489:
1484:
1481:(4): 043609.
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1120:
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1103:
1099:
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1085:
1082:(9): 095008.
1081:
1077:
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1065:
1060:
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1052:
1048:
1044:
1040:
1036:
1032:
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1019:(8): 086403.
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33:
25:
21:
1545:
1541:
1535:
1521:cite journal
1478:
1474:Phys. Rev. A
1472:
1462:
1411:
1405:
1399:
1352:
1348:Phys. Rev. A
1346:
1336:
1319:
1313:
1296:
1290:
1247:
1241:
1235:
1192:
1186:
1180:
1137:
1131:
1079:
1073:
1067:
1016:
1011:
1001:
986:
952:
689:
676:
672:
668:
558:
520:
148:
132:
116:
90:
74:
72:
959:correlation
145:Hamiltonian
119:interaction
1359:: 055802.
994:References
139:superfluid
129:Properties
123:polaritons
69:are shown.
67:absorption
24:Tunnelling
1580:115168045
1555:0805.1812
1488:1004.5118
1391:119200554
1366:1101.1366
1282:118903056
1114:118557639
1089:1105.1817
1026:0905.3344
955:polariton
915:^
893:^
851:−
842:σ
827:σ
806:∑
802:≡
790:^
751:†
721:∑
717:≡
705:^
649:ω
622:ω
611:frequency
589:η
569:κ
539:±
530:σ
499:−
490:σ
484:†
457:σ
421:∑
417:η
388:†
360:†
319:∑
315:κ
307:−
298:σ
283:σ
273:ω
252:∑
233:†
214:ω
193:∑
157:ℏ
34:κ
1593:Category
1513:55445588
1446:16778884
1324:New York
1172:44490741
1059:32092406
1051:19792743
869:, i.e.,
141:phases.
63:emission
1560:Bibcode
1493:Bibcode
1454:2214243
1426:Bibcode
1371:Bibcode
1262:Bibcode
1227:9122839
1207:Bibcode
1152:Bibcode
1094:Bibcode
1031:Bibcode
967:bosonic
601:is the
113:History
1578:
1511:
1452:
1444:
1407:Nature
1389:
1301:London
1280:
1225:
1170:
1112:
1057:
1049:
972:in an
607:photon
521:where
60:photon
1576:S2CID
1550:arXiv
1509:S2CID
1483:arXiv
1450:S2CID
1416:arXiv
1387:S2CID
1361:arXiv
1355:(5).
1328:Wiley
1278:S2CID
1252:arXiv
1223:S2CID
1197:arXiv
1168:S2CID
1142:arXiv
1110:S2CID
1084:arXiv
1055:S2CID
1021:arXiv
970:atoms
555:Pauli
83:light
1527:link
1442:PMID
1047:PMID
775:and
553:are
137:and
95:atom
73:The
65:and
1568:doi
1501:doi
1434:doi
1412:441
1379:doi
1270:doi
1215:doi
1160:doi
1102:doi
1039:doi
1017:103
613:is
175:):
81:of
1595::
1574:.
1566:.
1558:.
1546:41
1544:.
1523:}}
1519:{{
1507:.
1499:.
1491:.
1479:81
1477:.
1471:.
1448:.
1440:.
1432:.
1424:.
1410:.
1385:.
1377:.
1369:.
1353:83
1351:.
1345:.
1326::
1322:.
1303::
1299:.
1276:.
1268:.
1260:.
1246:.
1221:.
1213:.
1205:.
1191:.
1166:.
1158:.
1150:.
1138:76
1136:.
1122:^
1108:.
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1029:.
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1582:.
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1515:.
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1436::
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1162::
1154::
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1116:.
1104::
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1086::
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1041::
1033::
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933:0
930:=
927:]
922:a
912:N
905:+
900:c
890:N
883:,
880:H
877:[
846:n
836:+
831:n
821:N
816:1
813:=
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797:a
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761:n
757:a
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742:a
736:N
731:1
728:=
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712:c
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677:n
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669:n
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248:+
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224:a
218:c
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203:1
200:=
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189:=
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163:1
160:=
91:N
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