Generalized nonlinear Schrödinger equation and ultraslow optical solitons in a cold four-state atomic system

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 3, 2006, Pages

  Hang, Chao ^a   Huang, Guoxiang ^a   Deng, L ^b  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FOUR-STATE ATOMIC SYSTEM; GENERALIZED NONLINEAR SCHRÖDINGER EQUATION; NUMERICAL SIMULATIONS; ULTRASLOW OPTICAL SOLITONS;

COMPUTER SIMULATION; LIGHT PROPAGATION; PERTURBATION TECHNIQUES; REFRACTIVE INDEX; SOLITONS;

NONLINEAR EQUATIONS;

EID: 33644908206     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.036607     Document Type: Article

References (62)

1. S. L. McCall and E. L. Hahn, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.18.908 18, 908 (1967).
2. L. Allen and E. L. Eberly, Optical Resonance and Two-Level Atoms (Dover Publications, New York, 1987).
3. M. J. Konopnicki and J. H. Eberly, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.24.2567 24, 2567 (1981);
4. R. Grobe, F. T. Hioe, and J. H. Eberly, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.3183 73, 3183 (1994);
5. M. Fleischhauer and A. S. Manka, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.794 54, 794 (1996);
6. G. Vemuri, G. S. Agarwal, and K. V. Vasavada, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3889 79, 3889 (1997);
7. Q. Han Park and H. J. Shin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.4643 57, 4643 (1998);
8. A. V. Rybin, J. Opt. B: Quantum Semiclassical Opt. JOBOFD 1464-4266 10.1088/1464-4266/6/10/006 6, 416 (2004).
9. F. T. Hioe and R. Grobe, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.2559 73, 2559 (1994);
10. J. L. Eberly, Quantum Semiclassic. Opt. QUSOEC 1355-5111 10.1088/1355-5111/7/3/013 7, 373 (1995);
11. A. Rahman and J. H. Eberly, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.R805 58, R805 (1998);
12. G. S. Agarwal and J. H. Eberly, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.013404 61, 013404 (1999).
13. O. A. Kocharovskaya and Ya. I. Khanin, JETP Lett. JTPLA2 0021-3640 48, 630 (1988);
14. O. Kocharovskaya, P. Mandel, and Y. V. Radeonychev, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.1997 45, 1997 (1992);
15. J. H. Chen, M. E. Fisher, and B. G. Nickel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.48.630 48, 630 (1982);
16. M. O. Scully, S. Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.2813 62, 2813 (1989).
17. M. O. Scully, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67. 1855 67, 1855 (1991);
18. M. O. Scully, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(92)90136-N 219, 191 (1992);
19. M. O. Scully, Quantum Opt. QUOPET 0954-8998 6, 201 (1994);
20. J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.3687 76, 3687 (1996).
21. S. E. Harris, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.52 72, 52 (1994).
22. S. E. Harris, Phys. Today PHTOAD 0031-9228 10.1063/1.881886 50, 36 (1997);
23. J. P. Marangos, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003498151771 45, 471 (1998);
24. M. Fleischhauer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.77. 633 77, 633 (2005).
25. H. Schmidt and A. Imamoglu, Opt. Lett. OPLEDP 0146-9592 10.1103/PhysRevLett.64.1107 21, 1936 (1996).
26. S. E. Harris and L. V. Hau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.4611 82, 4611 (1999).
27. M. D. Lukin and A. Imamoglu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.1419 84, 1419 (2000).
28. M. D. Lukin, Adv. At., Mol., Opt. Phys. AAMPE9 1049-250X 42, 347 (2000);
29. M. D. Lukin, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.75.457 75, 457 (2003).
30. M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5094 84, 5094 (2000);
31. C. Liu, Nature (London) NATUAS 0028-0836 10.1038/35054017 409, 490 (2001);
32. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.783 86, 783 (2001).
33. D. Petrosyan and G. Kurizki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.033833 65, 033833 (2002).
34. A. B. Matsko, Opt. Lett. OPLEDP 0146-9592 28, 96 (2003).
35. L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.143902 88, 143902 (2002).
36. L. V. Hau, Nature (London) NATUAS 0028-0836 10.1038/17561 397, 594 (1999).
37. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Walch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.5229 82, 5229 (1999).
38. J. E. Heebner, R. W. Boyd, and Q. Han Park, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.036619 65, 036619 (2002).
39. M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.666 74, 666 (1995);
40. M. Xiao, Opt. Photonics News OPPHEL 1047-6938 13, 44 (2002).
41. H. Kang and Y. Zhu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.093601 91, 093601 (2003).
42. Y. Wu and L. Deng, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 93.143904 93, 143904 (2004).
43. Y. Wu and L. Deng, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.29.002064 29, 2064 (2004).
44. G. Huang, L. Deng, and M. G. Payne, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.016617 72, 016617 (2005);
45. L. Deng, M. G. Payne, G. Huang, and E. W. Hagley, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.055601 72, 055601 (2005).
46. M. G. Payne and L. Deng, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.031802 64, 031802 (R) (2001);
47. L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.051805 65, 051805 (R) (2002).
48. For an excellent description on the method of multiple-scales, see A. Jeffery and T. Kawahara, Asymptotic Methods in Nonlinear Wave Theory (Pitman, London, 1982).
49. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001);
50. A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer, Berlin, 2003). Note that for optical soliton propagation in fibers, the NLS equation [i.e., the last three terms in Eq. 9 are omitted] is valid for ps (10-12 s) optical pulses. The generalized NLS with the form of Eq. 9 describes femtosecond optical pulses with width shorter than 100 fs (10-13 s).
51. K. Porsezian and K. Nakkeeran, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.3955 76, 3955 (1996);
52. D. Mihalache, N. Truta, and L. C. Crasovan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.56.1064 56, 1064 (1997);
53. A. Mahalingam and K. Porsezian, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.046608 64, 046608 (2001);
54. Z. H. Li, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.4096 84, 4096 (2000).
55. Z. Xu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.026603 67, 026603 (2003).
56. K. Nakkeeran, K. Porsezian, P. S. Sundaram, and A. Mahalingam, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.1425 80, 1425 (1998).
57. M. Gedalin, T. C. Scott, and Y. B. Band, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.448 78, 448 (1997).
58. S. L. Palacios, A. Guinea, J. M. Fernandez-Diaz, and R. D. Crespo, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.R45 60, R45 (1999).
59. T. R. Taha and M. J. Ablowitz, J. Comput. Phys. JCTPAH 0021-9991 10.1016/0021-9991(84)90003-2 55, 203 (1984).
60. A. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Redwood City, 1992).
61. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, 1995).
62. In a recent work, J. Cheng [Opt. Lett. OPLEDP 0146-9592 30, 2638 (2005)] proposed an equation for the nonlinear propagation of optical pulses in a three-state atomic system when noninstantaneous Kerr nonlinearity is taken into account. However, the equation obtained cannot be taken as a standard model equation from the point of view of the method of multiple-scales.