33:
1380:
in eq. (2) can be regarded as the number of photons absorbed from (or emitted to) the laser field. In order to prove this statement, we clarify the correspondence between the solution (2), which is derived from the classical expression of the electromagnetic field where there is no concept of
833:
1252:
317:
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1076:
435:
707:
719:
1090:
1312:
516:
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650:
381:
355:
1314:
is the frequency of the laser field. This expression (2) reveals that a quantum state of the system governed by the
Hamiltonian (1) can be specified by a real number
1431:
981:
572:
544:
1452:
1404:
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1333:
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Guérin, S; Monti, F; Dupont, J-M; Jauslin, H R (1997). "On the relation between cavity-dressed states, Floquet states, RWA and semiclassical models".
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is the speed of light. By virtue of this time-periodicity of the laser field, the total
Hamiltonian is also periodic in time as
1673:
145:
386:
828:{\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi (\{\mathbf {r} _{i}\},t)=H(t)\psi (\{\mathbf {r} _{i}\},t)}
47:
41:
662:
1247:{\displaystyle \psi (\{\mathbf {r} _{i}\},t)=\exp\sum _{n=-\infty }^{\infty }\exp\phi _{n}(\{\mathbf {r} _{i}\})}
58:
1501:
Sambe, Hideo (1973). "Steady States and
Quasienergies of a Quantum-Mechanical System in an Oscillating Field".
1693:
1688:
1612:
Guérin, S.; Jauslin, H. R. (2003). "Control of
Quantum Dynamics by Laser Pulses: Adiabatic Floquet Theory".
710:
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491:
461:
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117:
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Shirley, Jon H. (1965). "Solution of the Schrödinger
Equation with a Hamiltonian Periodic in Time".
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440:
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Cardoso, G.C.; Tabosa, J.W.R. (2000). "Four-wave mixing in dressed cold cesium atoms".
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of a system of charged particles interacting with a laser light can be expressed as
1406:
is equal to the expectation value of the absorbed photon number at the limit of
312:{\displaystyle H=\sum _{i}{\frac {1}{2m_{i}}}\left^{2}+V(\{\mathbf {r} _{i}\}),}
952:{\displaystyle \psi (\{\mathbf {r} _{i}\},t)=\exp\phi (\{\mathbf {r} _{i}\},t)}
1381:
photons, and one which is derived from a quantized electromagnetic field (see
1071:{\displaystyle \phi (\{\mathbf {r} _{i}\},t+T)=\phi (\{\mathbf {r} _{i}\},t).}
17:
1639:
1604:
1567:
1530:
1493:
1485:
1522:
1621:
125:
129:
98:
113:
110:
121:
26:
518:, respectively, while its mass and charge are symbolized as
136:
in differential equations with periodic coefficients.
1439:
1412:
1391:
1365:
1341:
1320:
1276:
1093:
989:
968:
847:
722:
665:
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580:
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524:
494:
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443:
389:
367:
341:
159:
109:
of an atomic or molecular system interacting with a
1446:
1425:
1398:
1372:
1348:
1327:
1306:
1246:
1070:
983:has the same time-periodicity as the Hamiltonian,
975:
951:
827:
701:
644:
587:
566:
538:
510:
480:
450:
429:
375:
349:
311:
430:{\displaystyle \mathbf {A} (t+T)=\mathbf {A} (t)}
261:
240:
1540:Journal of Physics A: Mathematical and General
702:{\displaystyle \psi (\{\mathbf {r} _{i}\},t)}
8:
1238:
1223:
1115:
1100:
1053:
1038:
1011:
996:
937:
922:
869:
854:
813:
798:
765:
750:
687:
672:
300:
285:
361:of the electromagnetic field of the laser;
1078:Therefore, this part can be expanded in a
1454:is the initial number of total photons.)
1443:
1438:
1422:
1411:
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1005:
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729:
721:
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603:
584:
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176:
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77:Learn how and when to remove this message
40:This article includes a list of general
1156:
910:
726:
132:. The Floquet picture is based on the
7:
1084:
150:
1307:{\displaystyle \omega (=2\pi /T)\,}
437:. The position and momentum of the
1181:
1176:
735:
731:
511:{\displaystyle \mathbf {p} _{i}\,}
481:{\displaystyle \mathbf {r} _{i}\,}
46:it lacks sufficient corresponding
25:
1648:Theory of Multiphoton Processes,
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1674:Hamiltonian (quantum mechanics)
713:with this type of Hamiltonian,
1300:
1280:
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1220:
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1035:
1026:
993:
946:
919:
913:
890:
878:
851:
822:
795:
789:
783:
774:
747:
696:
669:
645:{\displaystyle H(t+T)=H(t)\,.}
635:
629:
620:
608:
424:
418:
407:
395:
303:
282:
1:
1597:10.1016/S0030-4018(00)01033-6
1385:). (It can be verified that
838:can be expressed in the form
659:guarantees that any solution
458:-th particle are denoted as
1614:Advances in Chemical Physics
376:{\displaystyle \mathbf {A} }
350:{\displaystyle \mathbf {A} }
1560:10.1088/0305-4470/30/20/020
1710:
1486:10.1103/PhysRev.138.B979
1426:{\displaystyle n\ll N\,}
140:Mathematical formulation
1650:Plenum (New York) 1987
1523:10.1103/PhysRevA.7.2203
976:{\displaystyle \phi \,}
567:{\displaystyle z_{i}\,}
539:{\displaystyle m_{i}\,}
383:is periodic in time as
120:, i.e. roughly like an
61:more precise citations.
1622:10.1002/0471428027.ch3
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1577:Optics Communications
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1616:. pp. 147–267.
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1410:
1389:
1383:quantum field theory
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1318:
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1091:
987:
966:
845:
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711:Schrödinger equation
663:
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339:
157:
1589:2000OptCo.185..353C
1552:1997JPhA...30.7193G
1515:1973PhRvA...7.2203S
1478:1965PhRv..138..979S
1447:{\displaystyle N\,}
1399:{\displaystyle n\,}
1373:{\displaystyle n\,}
1349:{\displaystyle n\,}
1328:{\displaystyle E\,}
588:{\displaystyle c\,}
451:{\displaystyle i\,}
103:light dressed state
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101:science, the term
1546:(20): 7193–7215.
1503:Physical Review A
1472:(4B): B979–B987.
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1267:
742:
574:, respectively.
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332:
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196:
166:
89:In the fields of
87:
86:
79:
16:(Redirected from
1701:
1643:
1608:
1583:(4–6): 353–358.
1571:
1534:
1509:(6): 2203–2213.
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1453:
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1334:
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1305:
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1236:
1231:
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1218:
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832:
831:
826:
812:
811:
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743:
741:
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685:
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651:
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533:
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436:
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417:
394:
382:
380:
379:
374:
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359:vector potential
356:
354:
353:
348:
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235:
230:
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197:
195:
194:
193:
177:
174:
151:
116:in terms of the
82:
75:
71:
68:
62:
57:this article by
48:inline citations
35:
34:
27:
21:
1709:
1708:
1704:
1703:
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1679:
1678:
1665:
1646:F.H.M. Faisal,
1632:
1611:
1574:
1537:
1500:
1466:Physical Review
1463:
1460:
1435:
1434:
1408:
1407:
1387:
1386:
1361:
1360:
1337:
1336:
1335:and an integer
1316:
1315:
1272:
1271:
1260:
1226:
1210:
1103:
1089:
1088:
1041:
999:
985:
984:
964:
963:
925:
857:
843:
842:
801:
753:
734:
718:
717:
675:
661:
660:
657:Floquet theorem
600:
599:
576:
575:
553:
548:
547:
525:
520:
519:
495:
490:
489:
465:
460:
459:
439:
438:
385:
384:
363:
362:
337:
336:
325:
288:
243:
221:
204:
203:
199:
198:
185:
181:
155:
154:
142:
134:Floquet theorem
118:Floquet picture
83:
72:
66:
63:
53:Please help to
52:
36:
32:
23:
22:
15:
12:
11:
5:
1707:
1705:
1697:
1696:
1694:Quantum states
1691:
1689:Quantum optics
1681:
1680:
1677:
1676:
1671:
1669:Quantum optics
1664:
1661:
1660:
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1630:
1609:
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1456:
1442:
1421:
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1368:
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1302:
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1213:
1209:
1206:
1203:
1200:
1197:
1194:
1191:
1188:
1183:
1178:
1175:
1172:
1169:
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1158:
1154:
1150:
1147:
1144:
1141:
1138:
1135:
1132:
1129:
1126:
1123:
1120:
1117:
1112:
1107:
1102:
1099:
1096:
1080:Fourier series
1067:
1064:
1061:
1058:
1055:
1050:
1045:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
1019:
1016:
1013:
1008:
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998:
995:
992:
971:
960:
959:
948:
945:
942:
939:
934:
929:
924:
921:
918:
915:
912:
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904:
901:
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895:
892:
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883:
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877:
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871:
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856:
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850:
836:
835:
824:
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815:
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805:
800:
797:
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791:
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779:
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631:
628:
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619:
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607:
583:
560:
556:
532:
528:
504:
499:
474:
469:
446:
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423:
420:
416:
412:
409:
406:
403:
400:
397:
393:
371:
345:
331:
330:
321:
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308:
305:
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297:
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287:
284:
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138:
85:
84:
39:
37:
30:
24:
18:Dressed states
14:
13:
10:
9:
6:
4:
3:
2:
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1692:
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1687:
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1662:
1657:
1656:0-306-42317-0
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1637:
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1631:9780471214526
1627:
1623:
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1615:
1610:
1606:
1602:
1598:
1594:
1590:
1586:
1582:
1578:
1573:
1569:
1565:
1561:
1557:
1553:
1549:
1545:
1541:
1536:
1532:
1528:
1524:
1520:
1516:
1512:
1508:
1504:
1499:
1495:
1491:
1487:
1483:
1479:
1475:
1471:
1467:
1462:
1461:
1457:
1455:
1440:
1419:
1416:
1413:
1392:
1384:
1366:
1357:
1342:
1321:
1297:
1293:
1289:
1286:
1283:
1277:
1264:
1257:
1255:
1233:
1215:
1211:
1204:
1201:
1198:
1195:
1189:
1186:
1173:
1170:
1167:
1163:
1152:
1148:
1145:
1142:
1139:
1133:
1130:
1127:
1121:
1118:
1110:
1094:
1087:
1086:
1083:
1081:
1065:
1059:
1056:
1048:
1032:
1029:
1023:
1020:
1017:
1014:
1006:
990:
969:
943:
940:
932:
916:
906:
902:
899:
896:
893:
887:
884:
881:
875:
872:
864:
848:
841:
840:
839:
819:
816:
808:
792:
786:
780:
777:
771:
768:
760:
744:
738:
723:
716:
715:
714:
712:
693:
690:
682:
666:
658:
639:
632:
626:
623:
617:
614:
611:
605:
598:
597:
596:
581:
558:
554:
530:
526:
502:
472:
444:
421:
410:
404:
401:
398:
360:
329:
322:
320:
306:
295:
279:
276:
271:
266:
231:
226:
222:
216:
211:
200:
190:
186:
182:
178:
171:
167:
163:
160:
153:
152:
149:
147:
139:
137:
135:
131:
127:
123:
119:
115:
112:
108:
107:quantum state
104:
100:
96:
92:
81:
78:
70:
60:
56:
50:
49:
43:
38:
29:
28:
19:
1647:
1613:
1580:
1576:
1543:
1539:
1506:
1502:
1469:
1465:
1359:The integer
1358:
1269:
1258:
1082:, obtaining
961:
837:
654:
334:
323:
143:
105:refers to a
102:
88:
73:
64:
45:
146:Hamiltonian
59:introducing
1683:Categories
1458:References
67:April 2021
42:references
1640:1934-4791
1605:0030-4018
1568:0305-4470
1531:0556-2791
1494:0031-899X
1417:≪
1290:π
1278:ω
1212:ϕ
1202:ω
1190:
1182:∞
1177:∞
1174:−
1164:∑
1157:ℏ
1140:−
1134:
1095:ψ
1033:ϕ
991:ϕ
970:ϕ
917:ϕ
911:ℏ
894:−
888:
849:ψ
793:ψ
745:ψ
736:∂
732:∂
727:ℏ
667:ψ
217:−
168:∑
95:molecular
1663:See also
1433:, where
709:of the
126:molecule
1585:Bibcode
1548:Bibcode
1511:Bibcode
1474:Bibcode
357:is the
128:plus a
99:optical
55:improve
1654:
1638:
1628:
1603:
1566:
1529:
1492:
1270:where
962:where
335:where
130:photon
97:, and
91:atomic
44:, but
124:or a
114:light
111:laser
1652:ISBN
1636:ISSN
1626:ISBN
1601:ISSN
1564:ISSN
1527:ISSN
1490:ISSN
655:The
546:and
488:and
144:The
122:atom
1618:doi
1593:doi
1581:185
1556:doi
1519:doi
1482:doi
1470:138
1187:exp
1131:exp
885:exp
1685::
1634:.
1624:.
1599:.
1591:.
1579:.
1562:.
1554:.
1544:30
1542:.
1525:.
1517:.
1505:.
1488:.
1480:.
1468:.
1356:.
93:,
1658:.
1642:.
1620::
1607:.
1595::
1587::
1570:.
1558::
1550::
1533:.
1521::
1513::
1507:7
1496:.
1484::
1476::
1441:N
1420:N
1414:n
1393:n
1367:n
1343:n
1322:E
1301:)
1298:T
1294:/
1287:2
1284:=
1281:(
1263:)
1261:2
1259:(
1242:)
1239:}
1234:i
1229:r
1224:{
1221:(
1216:n
1208:]
1205:t
1199:n
1196:i
1193:[
1171:=
1168:n
1160:]
1153:/
1149:t
1146:E
1143:i
1137:[
1128:=
1125:)
1122:t
1119:,
1116:}
1111:i
1106:r
1101:{
1098:(
1066:.
1063:)
1060:t
1057:,
1054:}
1049:i
1044:r
1039:{
1036:(
1030:=
1027:)
1024:T
1021:+
1018:t
1015:,
1012:}
1007:i
1002:r
997:{
994:(
947:)
944:t
941:,
938:}
933:i
928:r
923:{
920:(
914:]
907:/
903:t
900:E
897:i
891:[
882:=
879:)
876:t
873:,
870:}
865:i
860:r
855:{
852:(
823:)
820:t
817:,
814:}
809:i
804:r
799:{
796:(
790:)
787:t
784:(
781:H
778:=
775:)
772:t
769:,
766:}
761:i
756:r
751:{
748:(
739:t
724:i
697:)
694:t
691:,
688:}
683:i
678:r
673:{
670:(
640:.
636:)
633:t
630:(
627:H
624:=
621:)
618:T
615:+
612:t
609:(
606:H
582:c
559:i
555:z
531:i
527:m
503:i
498:p
473:i
468:r
445:i
425:)
422:t
419:(
415:A
411:=
408:)
405:T
402:+
399:t
396:(
392:A
370:A
344:A
328:)
326:1
324:(
307:,
304:)
301:}
296:i
291:r
286:{
283:(
280:V
277:+
272:2
267:]
262:)
259:t
256:,
251:i
246:r
241:(
238:A
232:c
227:i
223:z
212:i
207:p
201:[
191:i
187:m
183:2
179:1
172:i
164:=
161:H
80:)
74:(
69:)
65:(
51:.
20:)
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