Role of phonons in Josephson oscillations of excitonic and polaritonic condensates

Physical Review B - Condensed Matter and Materials Physics

Volumn 82, Issue 19, 2010, Pages

  Magnusson, E B ^a   Flayac, H ^b,c   Malpuech, G ^b,c   Shelykh, I A ^a,d  

^a UNIVERSITY OF ICELAND   (Iceland)

^b UNIVERSITÉ CLERMONT AUVERGNE   (France)

^c UNIVERSITÉ BLAISE PASCAL   (France)

^d International Institute for Physics   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78649739827     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.82.195312     Document Type: Article

References (75)

1. B. D. Josephson, Phys. Lett. 1, 251 (1962). 10.1016/0031-9163(62)91369-0
2. See, e.g., A. Legett, Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford University Press, New York, 2006).
3. S. V. Pereverzev, A. Loshak, S. Backhaus, J. C. Davis, and R. E. Packard, Nature (London) 388, 449 (1997). 10.1038/41277
4. M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Phys. Rev. Lett. 95, 010402 (2005). 10.1103/PhysRevLett.95.010402
5. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995) 10.1126/science.269.5221.198
6. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995) 10.1103/PhysRevLett.75.3969
7. C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995) 10.1103/PhysRevLett.75.1687
8. M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 275, 637 (1997). 10.1126/science.275.5300.637
9. M. W. Jack, M. J. Collett, and D. F. Walls, Phys. Rev. A 54, R4625 (1996) 10.1103/PhysRevA.54.R4625
10. I. Zapata, F. Sols, and A. J. Leggett, Phys. Rev. A 57, R28 (1998). 10.1103/PhysRevA.57.R28
11. A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Phys. Rev. Lett. 79, 4950 (1997) 10.1103/PhysRevLett.79.4950
12. G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, Phys. Rev. A 55, 4318 (1997) 10.1103/PhysRevA.55.4318
13. S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, Phys. Rev. A 59, 620 (1999). 10.1103/PhysRevA.59.620
14. L. V. Keldysh and Yu. V. Kopaev, Sov. Phys. Solid State 6, 2219 (1965)
15. L. V. Keldysh and A. N. Kozlov, Sov. Phys. JETP 27, 521 (1968).
16. I. B. Spielman, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 87, 036803 (2001) 10.1103/PhysRevLett.87.036803
17. J. P. Eisenstein and A. H. MacDonald, Nature (London) 432, 691 (2004). 10.1038/nature03081
18. S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, Nature (London) 443, 430 (2006). 10.1038/nature05117
19. V. B. Timofeev, Phys. Usp. 48, 295 (2005). 10.1070/ PU2005v048n03ABEH002123
20. L. V. Butov, J. Phys.: Condens. Matter 19, 295202 (2007). 10.1088/0953-8984/19/29/295202
21. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymanska, R. Andre, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, Nature (London) 443, 409 (2006). 10.1038/nature05131
22. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, Science 316, 1007 (2007). 10.1126/science.1140990
23. J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Hogersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, Phys. Rev. Lett. 101, 136409 (2008). 10.1103/PhysRevLett.101.136409
24. Yu. E. Lozovik and V. I. Yudson, Zh. Eksp. Teor. Fiz. Pis'ma Red. 22, 26 (1975)
25. Yu. E. Lozovik and V. I. Yudson, [JETP Lett. 22, 26 (1975)]
26. Yu. E. Lozovik and V. I. Yudson, Zh. Eksp. Teor. Fiz. 71, 738 (1976)
27. Yu. E. Lozovik and V. I. Yudson, [Sov. Phys. JETP 44, 389 (1976)]
28. Yu. E. Lozovik and V. I. Yudson, Solid State Commun. 18, 628 (1976).
29. S. I. Shevchenko, Phys. Rev. Lett. 72, 3242 (1994). 10.1103/PhysRevLett. 72.3242
30. X. Zhu, P. B. Littlewood, M. S. Hybertsen, and T. M. Rice, Phys. Rev. Lett. 74, 1633 (1995). 10.1103/PhysRevLett.74.1633
31. O. L. Berman, Y. E. Lozovik, D. W. Snoke, and R. D. Coalson, Phys. Rev. B 70, 235310 (2004). 10.1103/PhysRevB.70.235310
32. V. Larionov, V. B. Timofeev, J. Hvam, and K. Soerensen, Zh. Eksp. Teor. Fiz. 117, 1255 (2000)
33. V. Larionov, V. B. Timofeev, J. Hvam, and K. Soerensen, [JETP 90, 1093 (2000)] 10.1134/1.559200
34. A. V. Larionov and V. B. Timofeev, Pis'ma Zh. Eksp. Teor. Fiz. 73, 342 (2001)
35. A. V. Larionov and V. B. Timofeev, [JETP Lett. 73, 301 (2001). 10.1134/1.1374266
36. D. Snoke, S. Denev, Y. Liu, L. Pfeiffer, and K. West, Nature (London) 418, 754 (2002). 10.1038/nature00940
37. L. V. Butov, C. W. Lai, A. L. Ivanov, A. C. Gossard, and D. S. Chemla, Nature (London) 417, 47 (2002) 10.1038/417047a
38. L. V. Butov, A. C. Gossard, and D. S. Chemla, Nature (London) 418, 751 (2002). 10.1038/nature00943
39. A. V. Kavokin, J. Baumberg, G. Malpuech, and F. Laussy, Microcavities (Clarendon, Oxford, 2006).
40. E. Wertz, L. Ferrier, D. D. Solnyshkov, P. Senellart, D. Bajoni, A. Miard, A. LemaÓtre, G. Malpuech, and J. Bloch, Appl. Phys. Lett. 95, 051108 (2009). 10.1063/1.3192408
41. S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, Phys. Rev. Lett. 98, 126405 (2007). 10.1103/PhysRevLett.98.126405
42. J. Kasprzak, D. D. Solnyshkov, R. Andre, Le Si Dang, and G. Malpuech, Phys. Rev. Lett. 101, 146404 (2008). 10.1103/PhysRevLett.101.146404
43. D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Pledran, M. Richard, R. Andre, and Le Si Dang, Phys. Rev. B 80, 045317 (2009). 10.1103/PhysRevB.80.045317
44. M. Maragkou, A. J. D. Grundy, E. Wertz, A. Lemaitre, I. Sagnes, P. Senellart, J. Bloch, and P. G. Lagoudakis, Phys. Rev. B 81, 081307 (2010). 10.1103/PhysRevB.81.081307
45. J. Levrat, R. Butte, E. Feltin, J. F. Carlin, Nicolas Grandjean, D. Solnyshkov, G. Malpuech, Phys. Rev. B 81, 125305 (2010). 10.1103/PhysRevB.81. 125305
46. The same is valid for indirect excitons.
47. S. Ashhab and C. Lobo, Phys. Rev. A 66, 013609 (2002). 10.1103/PhysRevA.66.013609
48. C. Ciuti, V. Savona, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Phys. Rev. B 58, 7926 (1998). 10.1103/PhysRevB.58.7926
49. M. Combescot, O. Betbeder-Matibet, and R. Combescot, Phys. Rev. Lett. 99, 176403 (2007). 10.1103/PhysRevLett.99.176403
50. T. Ostatnicky, D. Read, and A. V. Kavokin, Phys. Rev. B 80, 115328 (2009). 10.1103/PhysRevB.80.115328
51. P. Renucci, T. Amand, X. Marie, P. Senellart, J. Bloch, B. Sermage, and K. V. Kavokin, Phys. Rev. B 72, 075317 (2005). 10.1103/PhysRevB.72.075317
52. I. A. Shelykh, Yu. G. Rubo, G. Malpuech, D. D. Solnyshkov, and A. V. Kavokin, Phys. Rev. Lett. 97, 066402 (2006). 10.1103/PhysRevLett.97.066402
53. I. A. Shelykh, A. V. Kavokin, Yu. G. Rubo, T. C. H. Liew, and G. Malpuech, Semicond. Sci. Technol. 25, 013001 (2010). 10.1088/0268-1242/25/1/ 013001
54. A. T. Hammack, M. Griswold, L. V. Butov, L. E. Smallwood, A. L. Ivanov, and A. C. Gossard, Phys. Rev. Lett. 96, 227402 (2006). 10.1103/PhysRevLett.96. 227402
55. R. B. Balili, D. W. Snoke, L. Pfeiffer, and K. West, Appl. Phys. Lett. 88, 031110 (2006). 10.1063/1.2164431
56. O. El Daif, A. Baas, T. Guillet, J.-P. Brantut, R. Idrissi Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, Appl. Phys. Lett. 88, 061105 (2006) 10.1063/1.2172409
57. R. I. Kaitouni, O. El Daif, A. Baas, M. Richard, T. Paraiso, P. Lugan, T. Guillet, F. Morier-Genoud, J. D. Ganiere, J. L. Staehli, V. Savona, and B. Deveaud, Phys. Rev. B 74, 155311 (2006). 10.1103/PhysRevB.74.155311
58. E. Wertz, L. Ferrier, D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, Nat. Phys. (2010). 10.1038/nphys1750
59. M. Wouters and I. Carusotto, Phys. Rev. Lett. 99, 140402 (2007). 10.1103/PhysRevLett.99.140402
60. D. Sarchi, I. Carusotto, M. Wouters, and V. Savona, Phys. Rev. B 77, 125324 (2008). 10.1103/PhysRevB.77.125324
61. I. A. Shelykh, D. D. Solnyshkov, G. Pavlovic, G. Malpuech, Phys. Rev. B 78, 041302 (R) (2008). 10.1103/PhysRevB.78.041302
62. D. D. Solnyshkov, R. Johne, I. A. Shelykh, and G. Malpuech, Phys. Rev. B 80, 235303 (2009). 10.1103/PhysRevB.80.235303
63. D. Read, Yu. G. Rubo, and A. V. Kavokin, Phys. Rev. B 81, 235315 (2010). 10.1103/PhysRevB.81.235315
64. A. Tredicucci, Yong Chen, V. Pellegrini, Marco Borger, and F. Bassani, Phys. Rev. A 54, 3493 (1996). 10.1103/PhysRevA.54.3493
65. A. Baas, J.-Ph. Karr, M. Romanelli, A. Bramati, and E. Giacobino, Phys. Rev. B 70, 161307 (R) (2004). 10.1103/PhysRevB.70.161307
66. N. A. Gippius, S. G. Tikhodeev, V. D. Kulakovskii, D. N. Krizhanovskii, and A. I. Tartakovskii, Europhys. Lett. 67, 997 (2004). 10.1209/epl/i2004-10133- 6
67. N. A. Gippius, I. A. Shelykh, D. D. Solnyshkov, S. S. Gavrilov, Yu. G. Rubo, A. V. Kavokin, S. G. Tikhodeev, and G. Malpuech, Phys. Rev. Lett. 98, 236401 (2007). 10.1103/PhysRevLett.98.236401
68. T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. Lett. 101, 016402 (2008). 10.1103/PhysRevLett.101.016402
69. T. K. Paraïso, M. Wouters, Y. Léger, F. Morier-Genoud, and B. Deveaud-Plédran, Nature Mater. 9, 655 (2010). 10.1038/NMAT2787
70. A. O. Caldeira and A. J. Leggett, Phys. Rev. Lett. 46, 211 (1981). 10.1103/PhysRevLett.46.211
71. I. L. Aleiner and E. L. Ivchenko, JETP Lett. 55, 692 (1992).
72. L. Klopotowski, A. Amo, M. D. Martin, L. Vina, I. A. Shelykh, M. M. Glazov, G. Malpuech, A. V. Kavokin, and R. Andre, Solid State Commun. 139, 511 (2006) 10.1016/j.ssc.2006.07.016
73. J. Kasprzak, R. Andre, L. S. Dang, I. A. Shelykh, A. V. Kavokin, Yu. G. Rubo, K. V. Kavokin, and G. Malpuech, Phys. Rev. B 75, 045326 (2007). 10.1103/PhysRevB.75.045326
74. M. Trujillo-Martinez, A. Posazhennikova, and J. Kroha, Phys. Rev. Lett. 103, 105302 (2009). 10.1103/PhysRevLett.103.105302
75. For details of the derivation of dissipative master equations in quantum optics see, e.g., H. Carmichael, Quantum Optics 1: Master Equations And Fokker-Planck Equations (Springer, New York, 2007).