Density-matrix theory of the optical dynamics and transport in quantum cascade structures: The role of coherence

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 16, 2009, Pages

  Weber, C ^a   Wacker, A ^a   Knorr, A ^b  

^a LUND UNIVERSITY   (Sweden)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 66749146766     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.165322     Document Type: Article

References (63)

1. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994). 10.1126/science.264.5158.553
2. T. Elsaesser and M. Woerner, Phys. Rep. 321, 253 (1999). 10.1016/S0370-1573(99)00034-4
3. I. Waldmüller, J. Förstner, and A. Knorr, in Nonequilibrium Physics at Short Time Scales, edited by, K. Morawetz, (Springer, Berlin, 2004), pp. 251-273.
4. S. Butscher, J. Förstner, I. Waldmüller, and A. Knorr, Phys. Rev. B 72, 045314 (2005). 10.1103/PhysRevB.72.045314
5. I. Waldmueller, W. W. Chow, and A. Knorr, Phys. Rev. B 73, 035433 (2006). 10.1103/PhysRevB.73.035433
6. M. Kira and S. W. Koch, Phys. Rev. A 73, 013813 (2006). 10.1103/PhysRevA.73.013813
7. C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, Rep. Prog. Phys. 64, 1533 (2001). 10.1088/0034-4885/64/11/204
8. M. Lee and M. C. Wanke, Science 316, 64 (2007). 10.1126/science.1141012
9. B. S. Williams, Nat. Photonics 1, 517 (2007). 10.1038/nphoton.2007.166
10. P. Harrison, Appl. Phys. Lett. 75, 2800 (1999). 10.1063/1.125154
11. D. Indjin, P. Harrison, R. W. Kelsall, and Z. Ikonic, J. Appl. Phys. 91, 9019 (2002). 10.1063/1.1474613
12. R. C. Iotti and F. Rossi, Appl. Phys. Lett. 78, 2902 (2001). 10.1063/1.1370537
13. H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, Appl. Phys. Lett. 83, 207 (2003). 10.1063/1.1590749
14. O. Bonno, J.-L. Thobel, and F. Dessenne, J. Appl. Phys. 97, 043702 (2005). 10.1063/1.1840100
15. C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, J. Appl. Phys. 101, 086109 (2007). 10.1063/1.2719683
16. X. Gao, D. Botez, and I. Knezevic, J. Appl. Phys. 101, 063101 (2007). 10.1063/1.2711153
17. C. Jirauschek and P. Lugli, Phys. Status Solidi C 5, 221 (2008). 10.1002/pssc.200776566
18. S.-C. Lee and A. Wacker, Phys. Rev. B 66, 245314 (2002). 10.1103/PhysRevB.66.245314
19. F. Banit, S.-C. Lee, A. Knorr, and A. Wacker, Appl. Phys. Lett. 86, 041108 (2005). 10.1063/1.1851004
20. S.-C. Lee, F. Banit, M. Woerner, and A. Wacker, Phys. Rev. B 73, 245320 (2006). 10.1103/PhysRevB.73.245320
21. T. Kubis, C. Yeh, and P. Vogl, Phys. Status Solidi C 5, 232 (2008). 10.1002/pssc.200776591
22. T. Schmielau and M. F. Pereira, Phys. Status Solidi B 246, 329 (2009). 10.1002/pssb.200880328
23. R. C. Iotti and F. Rossi, Phys. Rev. Lett. 87, 146603 (2001). 10.1103/PhysRevLett.87.146603
24. I. Waldmueller, W. W. Chow, E. W. Young, and M. C. Wanke, IEEE J. Quantum Electron. 42, 292 (2006). 10.1109/JQE.2006.869813
25. I. Savic, N. Vukmirovic, Z. Ikonic, D. Indjin, R. W. Kelsall, P. Harrison, and V. Milanovic, Phys. Rev. B 76, 165310 (2007). 10.1103/PhysRevB.76. 165310
26. C. Weber, F. Banit, S. Butscher, A. Knorr, and A. Wacker, Appl. Phys. Lett. 89, 091112 (2006). 10.1063/1.2344844
27. H. Callebaut and Q. Hu, J. Appl. Phys. 98, 104505 (2005). 10.1063/1.2136420
28. R. C. Iotti, E. Ciancio, and F. Rossi, Phys. Rev. B 72, 125347 (2005). 10.1103/PhysRevB.72.125347
29. F. Eickemeyer, K. Reimann, M. Woerner, T. Elsaesser, S. Barbieri, C. Sirtori, G. Strasser, T. Müller, R. Bratschitsch, and K. Unterrainer, Phys. Rev. Lett. 89, 047402 (2002). 10.1103/PhysRevLett.89.047402
30. F. Eickemeyer, K. Reimann, M. Woerner, T. Elsaesser, S.-C. Lee, A. Wacker, S. Barbieri, C. Sirtori, and J. Nagle, Physica B 314, 314 (2002). 10.1016/S0921-4526(01)01452-1
31. M. Woerner, K. Reimann, and T. Elsaesser, J. Phys.: Condens. Matter 16, R25 (2004). 10.1088/0953-8984/16/4/R01
32. W. Kuehn, Appl. Phys. Lett. 93, 151106 (2008). 10.1063/1.2998648
33. J. Darmo, J. Kröll, M. Martl, D. Dietze, S. Barbieri, C. Sirtori, and K. Unterrainer, 2008 CLEO/QELS, San Jose, CA, 2008 (IEEE, New York, 2008).
34. H. Choi, L. Diehl, Z. K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, Phys. Rev. Lett. 100, 167401 (2008). 10.1103/PhysRevLett.100.167401
35. H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, Appl. Phys. Lett. 92, 122114 (2008). 10.1063/1.2898518
36. P. Y. Yu and M. Cardona, Fundamentals of Semiconductors (Springer, Berlin, 1999).
37. S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, Appl. Phys. Lett. 84, 2494 (2004). 10.1063/1.1695099
38. I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, Phys. Rev. B 69, 205307 (2004). 10.1103/PhysRevB.69.205307
39. T. Shih, K. Reimann, M. Woerner, T. Elsaesser, I. Waldmüller, A. Knorr, R. Hey, and K. H. Ploog, Phys. Rev. B 72, 195338 (2005). 10.1103/PhysRevB.72.195338
40. H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, Appl. Phys. Lett. 84, 645 (2004). 10.1063/1.1644337
41. R. Nelander and A. Wacker, Phys. Status Solidi C 6, 579 (2009). 10.1002/pssc.200880318
42. A. Vasanelli, A. Leuliet, C. Sirtori, A. Wade, G. Fedorov, D. Smirnov, G. Bastard, B. Vinter, M. Giovannini, and J. Faist, Appl. Phys. Lett. 89, 172120 (2006). 10.1063/1.2361264
43. J. Fricke, Ann. Phys. 252, 479 (1996). 10.1006/aphy.1996.0142
44. F. Rossi and T. Kuhn, Rev. Mod. Phys. 74, 895 (2002). 10.1103/RevModPhys.74.895
45. S. Butscher and A. Knorr, Phys. Rev. Lett. 97, 197401 (2006). 10.1103/PhysRevLett.97.197401
46. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).
47. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 2004).
48. J. Schilp, T. Kuhn, and G. Mahler, Phys. Rev. B 50, 5435 (1994). 10.1103/PhysRevB.50.5435
49. I. Waldmüller, M. Woerner, J. Förstner, and A. Knorr, Phys. Status Solidi B 238, 474 (2003). 10.1002/pssb.200303165
50. R. Nelander and A. Wacker, Appl. Phys. Lett. 92, 081102 (2008). 10.1063/1.2884686
51. Note that this result depends on the gauge for the exciting field which is used. In the case of the Lorenz gauge, it is necessary to take into account a phase factor when transforming the density matrix between different periods.
52. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
53. R. S. Whitney, J. Phys. A: Math. Theor. 41, 175304 (2008). 10.1088/1751-8113/41/17/175304
54. G. Schaller and T. Brandes, Phys. Rev. A 78, 022106 (2008). 10.1103/PhysRevA.78.022106
55. For the barrier widths marked by dashed lines (open circle in the current density), the inclusion of an additional low-energy scattering mechanism is necessary to achieve convergence of the current (see the discussion in the text). The value of the current density obtained in this way is approximately independent of the strength of the additional coupling when determined from the transient, in accordance with earlier results (Refs.). The resulting, unphysically large total broadening Γ does not lead to qualitatively new regimes of interest and is thus not considered further.
56. A. Wacker, Phys. Status Solidi C 5, 215 (2008). 10.1002/pssc.200776508
57. A. Wacker and A.-P. Jauho, Phys. Rev. Lett. 80, 369 (1998). 10.1103/PhysRevLett.80.369
58. M. Richter, T. Renger, and A. Knorr, Photosynth. Res. 95, 119 (2008). 10.1007/s11120-007-9256-z
59. S. W. Koch, N. Peyghambarian, and M. Lindberg, J. Phys. C 21, 5229 (1988). 10.1088/0022-3719/21/30/010
60. R. F. Kazarinov and R. A. Suris, Sov. Phys. Semicond. 6, 120 (1972).
61. R. Binder, S. W. Koch, M. Lindberg, N. Peyghambarian, and W. Schäfer, Phys. Rev. Lett. 65, 899 (1990). 10.1103/PhysRevLett.65.899
62. S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994). 10.1103/PhysRevLett.73.1178
63. S. Hughes, Phys. Rev. Lett. 81, 3363 (1998). 10.1103/PhysRevLett.81.3363