光晶格中旋量玻色—爱因斯坦凝聚体的自旋动力学研究
摘要
Bose-Einstein condensation (BEC) is a phenomenon that condensation into a single quantum state occurs for identical bosons when the inter-particle separation is less than the thermal de Broglie wavelength of the particles. In this work report, the modulational instability and intrinsic localized mode of spin wave in atomic chain of spinor BEC are investigated. Compared with the solid-state spin systems in which the Heisenberg-like short-range exchange interaction plays the dominate role, the atomic spin chain where the long-range dipole-dipole interaction between different spin sites is dominant. As a result, an analogy of atomic chains of spinor BECs can be made to the spin chains in the solid magnetic systems. However a key difference of the atomic spin chain from solid-state one is that we are facing a completely new spin system in atomic physics where the long-range interactions play a dominant role in the spin dynamics.
引文
1 S. Bose, Z. Phys. 26, 178 (1924).
2 A. Einstein, Sitzungsber, K. Preuss. Akad. Wiss., Phys. Math. Kl. 3. 1925.
3 M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269,198 (1995).
4 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).
5 C. C. Bradely, C. A. Sackett, J. J. Tollett, and R. G. Hullet, Phys. Rev. Lett. 75,1687 (1995); ibid, 78, 985 (1997).
6 R.D. Etters, J.V. Dugan, Jr., and R. Palmer, Rev. Mod. Phys., 62, 313 (1975).
7 I.F.Silvera, and J.T. Walraven, Applied Physics B 71, 475 (2000).
8 R.A. Cline, D.A. Smith, T.J. Greytak, and D. Kleppner, Phys. Rev. Lett., 45, 2117 (1980).
9 H. Hess, G.P. Kochansky, J.M. Doyle, N. Masuhara, D. Kleppner, and T.J. Greytak, Phys. Rev. Lett. 59,672(1987).
10 R. van Roijen, J.J. Berkhout, S. Jaakkola, and J. Walraven, Phys. Rev. Lett. 62, 931 (1988).
11 H.F. Hess, Phys. Rev. B 34, 3476 (1986).
12 O.J. Luiten, M.W. Reynolds, and J.T.M. Walraven, Phys. Rev. A 53, 3 81 (1996).
13 W.D. Phillips, Rev. Mod. Phys., 70, 721 (1998).
14 W. Ketterle, D.S. Durfee, and D.M. Stamper-Kurn, Making probing and understanding Bose-Einstein condensates. In M. Inguscio, S. Stringari, and C.E. Wieman, editors, Bose-Einstein Condensation in Atomic Gases, Proceedings of the alnternational School of Physics 'Enrico Fermi', Course CXL. IOS Press Ohmsha, 1999.
15 E. A. Cornell, J.R. Ensher, and C.E. Wieman, Experiments in dilute atomic Bose-Einstein Condensates. In M. Inguscio, S. Stringari, and C.E. Wieman, editors, Bose-Einstein Condensation in Atomic Gases, Proceedings of the alnternational School of Physics 'Enrico Fermi', Course CXL. IOS Press Ohmsha, 1999
16 F. Dalfovo, S. Giorgini, L.P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
17 J. Ruostekoski, M.J. Collett, R. Graham, and D.F. Walls, Phys. Rev. A 57, 511 (1998).
18 E.V. Goldstin, M.G. Moore, and P. Meystre,, Laser Phys. 10, 8 (2000).
19 J. Heurich, M.G. Moore, and P. Meystre, Opt. Commun. 179, 549 (2000).
20 G. Baym and C. J. Pethick, Phys. Rev. Lett. 76, 6 (1996).
21 F. Dalfovo and S. Stringari, Phys. Rev. A 53,2477 (1996).
22 C. C. Bradley, C. A. Sackett, and R. G. Hulet, Phys. Rev. Lett. 78, 985 (1997).
23 E. A. Donley et al, Nature 412, 295 (2001).
24 C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, UK, 2002).
25 M. R. Matthews et al., Phys. Rev. Lett. 83, 2498 (1999).
26 K. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84, 806 (2000),
27 M. R. Andrews et al., Phys.Rev. Lett. 79, 553 (1997).
28 S. Burger et al., Phys. Rev. Lett. 83, 5198 (1999).
29 J. Denschlag et al., Science 287, 97 (2000).
30 T. L. Ho, Phys. Rev. Lett. 81, 742 (1998).
31 T. Ohmi and K. Machida, J. Phys. Soc. Jpn. 67, 1822 (1998).
32 J. Stenger et al., Nature 396, 345 (1998).
33 A. J. Leggett, Rev. Mod.Phys. 47, 331 (1975).
34 J. C. Wheatley, Rev. Mod. Phys. 47, 415 (1975).
35 A. P. M. Maeno and Y., Rev. Mod. Phys. 75, 657 (2003).
36 C. V. Ciobanu, S. K. Yip, and T. L. Ho, Phys. Rev. A 61, 033607 (2000).
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38 H. J. Miesner et al., Phys. Rev. Lett. 82, 2228 (1999).
39 D. M. Stamper-Kurn et al., Phys. Rev. Lett. 83, 661 (1999).
40 M. Koashi and M. Ueda, Phys. Rev. Lett. 84, 1066 (2000).
41 W. X. Zhang, S. Yi, and L. You, New J. Phys. 5, 77 (2003).
42 E. V. Goldstein and P. Meystre, Phys. Rev. A 59, 3896 (1999).
43 H. Pu, C. K. Law, S. Raghavan, J. H. Eberly, and N. P. Bigelow, Phys. Rev. A 60, 1463 (1999).
44 J. P. Burke, P. S. Julienne, C. J. Williams, Y. B. Band, and M. Trippenbach, Phys. Rev. A 70, 033606(2004).
45 A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 90, 140403(2003).
46 T. Isoshima, K. Machida, and T. Ohmi, Phys. Rev. A 60, 4857 (1999).
47 L. M. Duan, J. I. Cirac, and P. Zoller, Phys. Rev. A 65, 033619 (2002).
48 N. N. Klausen, J. L. Bohn, and C. H. Greene, Phys. Rev. A 64, 053602 (2001).
49 E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Ver-haar, Phys. Rev. Lett 88, 093201 (2002).
50 J. P. Burke, C. H. Greene, and J. L. Bohn, Phys. Rev. Lett. 81, 3355 (1998).
51 Grimm, R., M. Weidemuller, and Y. B. Ovchinnikov, Adv. At., Mol., Opt. Phys. 42, 95 (2000).
52 P. S. Jessen, I. H. Deutsch, Adv. AMO phys. 37, 95 (1996).
53 F. Bloch, Z. Phys. 52, 555 (1929).
54 M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
55 S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, M. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
56 B. P. Aderson and M. A. Kasevich, Science 282, 1686 (1998).
57 D. M. Stamper-Kurn et. al. Phys. Rev. Lett. 80, 2227 (1998).
58 F. S. Cataliotti et. al. Science 293, 843 (2001).
59 O. Morsch, J. H. Muller, M. Christiani, D. Ciampini, E. Arimpmdo, Phys. Rev. Lett. 87, 140402 (2001).
60 J. Denschlag et. al, J. Phys. B 35, 3095 (2002).
61 C. Orzel, et. al., Science 291, 2386 (2001).
62 M. Greiner, O. Mandel, T. Esslinger, T. Hansch, I. Bloch, Nature 415, 39 (2002).
63 T. Stoferle, H. Moritz, C. Schori, M. Kohl, T. Esslinger, Cond-mat/ 0312440 (2003).
[1] J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur and W. Ketterle, Nature 396, 345.
[2] H. J. Miesner, D. M. Stamper-Kurn, J. Stenger, S. Inouye, A. P. Chikkatur, and W. Ketterle, Phys. Rev. Lett. 82,2228 (1999).
[3J D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, S.Inouye, J. Stenger, and W. Ketterle, Phys. Rev. Lett. 83, 661 (1999).
[4] M. S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, Phys. Rev. Lett. 92, 140403 (2004).
[5] A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 90, 140403 (2003).
[6] M. S. Chang, Q. Qin, W. Z. Zhang, L. You and M. S. Chapman, Nature Physics 1,111 (2005).
[7] Nichilas P Robins, Weiping Zhang, Elena A, Ostrovskaya, and Yuri S. Kivshar, Phys. Rev. A 64, 021601 (2001).
[8] Lu Li, Zaidong Li, Boris A. Malomed, Dumitru Mihalache, and W. M. Liu, Phys. Rev. A 72, 033611(2005).
[9] J. Ieda, T. Miyakawa, and M. Wadati, Phys. Rev. Lett. 93,194102 (2004).
[10] Weiping Zhang, Han Pu, Chris Search, and Pierre Meystre, Phys. Rev. Lett. 88,060401 (2002).
[11] H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87,140405 (2001).
[12] David Carpentier and Leon Balents, Phys. Rev. B 65, 024427 (2002).
[13] V. Yu. Irkhin and M. I. Katsnelson, Phys. Rev. B 56, 8109 (1997).
[14] L. J. Azevedo, A. Narath, Peter M. Richards, and Z. G. Soos,Phys. Rev. Lett. 43, 875 (1979).
[15] R. Lai and A. J. Sievers, Phys. Rev. B 57,3433 (1998).
[16] Jean-Pierre Nguenang, et al., J. Phys 17, 3083 (2005).
[17] I. Daumont, T. Dauxbis, and M. Peyrard, Nonlinearity 10,617 (1997).
[18] V.M. Burlakov, S.A. Kiselev, Sov. Phys. JETP 72, 854 (1991).
[19] Y. S. Kivshar and M. Salerno, Phys. Rev. E 49, 3543 (1994).
[20] K.W. Sandusky and J.B. Page, Phys. Rev. B 50, 866 (1994).
[21] Kevin Gross, Chris P. Search, Han Pu, Weiping Zhang, and Pierre Meystre, Phys. Rev. A 66, 033603 (2002).
[22] J.Javanainen, Phys. Rev. Lett. 72, 2375 (1994).
[23] J. Callaway, Quantum theory of the solid state (Academic Press, New York, 1991).
[24] Zhang W M, Feng D H and Glimore R. Rev. Mod. Phys. 62, 867 (1991).
[25] J.Ford, Phys. Rep. 213, 271 (1992).
[26] Jean-Pierre Nguenang, Michel Peyrard, Aurelien J Kenfaek and Timoleon C Kofane, J. Phys. Condens. Matter 17, 3083
[1] A. S. Davydov, Solitons in Molecular Systems (Reidel, Boston, 1985).
[2] A. M. Kosevich, B. A. Ivanov, A. S. Kovalev, Phys. Rep. 194,117 (1990).
[3] A. Newell, Solitons in Mathematics and physics (SIAM Philadelphia, 1985).
[4] A. R. Bishop, T. Schneider, in: M. Cardona, P. Fulde, H. -J. Queisser (Eds.), Springer Series in Solid-State Sciences (Springer, Berlin, 1978).
[5] S. Flach, C.R. Willis, Phys. Rep. 295,181 (1998).
[6] R. Lai, A. J. Sievers, Phys. Rep. 314,147 (1999).
[7] S. A. Kiselev, S.R. Bickham, A.J. Sievers, Comments Cond. Mater. Phys. 17, 135(1995).
[8] R. F. Wallis and D. L. Mills, Phys. Rev. B 52, R3828 (1995).
[9] R. Lai and A. J. Sievers, Phys. Rev. B 57, 3433 (1998).
[10] Weiping Zhang, Han Pu, Chris Search,and Pierre Meystre, Phys. Rev. Lett. 88, 060401 (2002).
[11] H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87,140405 (2001).
[12] Kevin Gross, Chris P. Search, Han Pu, Weiping Zhang, and Pierre Meystre, Phys. Rev. A 66, 033603 (2002).
[13] Nicholas P. Robins, Weiping Zhang, Elena A. Ostrovskaya and Yuri S. Kivshar, Phys. Rev. A64, 021601 (2001).
[14] Matlab 6.5 R13, optimization toolbox, function lsqnonlin.
[15] Xing-Dong Zhao, Zhang Wei Xie, and Weiping Zhang, unpublished.
2 A. Einstein, Sitzungsber, K. Preuss. Akad. Wiss., Phys. Math. Kl. 3. 1925.
3 M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269,198 (1995).
4 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).
5 C. C. Bradely, C. A. Sackett, J. J. Tollett, and R. G. Hullet, Phys. Rev. Lett. 75,1687 (1995); ibid, 78, 985 (1997).
6 R.D. Etters, J.V. Dugan, Jr., and R. Palmer, Rev. Mod. Phys., 62, 313 (1975).
7 I.F.Silvera, and J.T. Walraven, Applied Physics B 71, 475 (2000).
8 R.A. Cline, D.A. Smith, T.J. Greytak, and D. Kleppner, Phys. Rev. Lett., 45, 2117 (1980).
9 H. Hess, G.P. Kochansky, J.M. Doyle, N. Masuhara, D. Kleppner, and T.J. Greytak, Phys. Rev. Lett. 59,672(1987).
10 R. van Roijen, J.J. Berkhout, S. Jaakkola, and J. Walraven, Phys. Rev. Lett. 62, 931 (1988).
11 H.F. Hess, Phys. Rev. B 34, 3476 (1986).
12 O.J. Luiten, M.W. Reynolds, and J.T.M. Walraven, Phys. Rev. A 53, 3 81 (1996).
13 W.D. Phillips, Rev. Mod. Phys., 70, 721 (1998).
14 W. Ketterle, D.S. Durfee, and D.M. Stamper-Kurn, Making probing and understanding Bose-Einstein condensates. In M. Inguscio, S. Stringari, and C.E. Wieman, editors, Bose-Einstein Condensation in Atomic Gases, Proceedings of the alnternational School of Physics 'Enrico Fermi', Course CXL. IOS Press Ohmsha, 1999.
15 E. A. Cornell, J.R. Ensher, and C.E. Wieman, Experiments in dilute atomic Bose-Einstein Condensates. In M. Inguscio, S. Stringari, and C.E. Wieman, editors, Bose-Einstein Condensation in Atomic Gases, Proceedings of the alnternational School of Physics 'Enrico Fermi', Course CXL. IOS Press Ohmsha, 1999
16 F. Dalfovo, S. Giorgini, L.P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
17 J. Ruostekoski, M.J. Collett, R. Graham, and D.F. Walls, Phys. Rev. A 57, 511 (1998).
18 E.V. Goldstin, M.G. Moore, and P. Meystre,, Laser Phys. 10, 8 (2000).
19 J. Heurich, M.G. Moore, and P. Meystre, Opt. Commun. 179, 549 (2000).
20 G. Baym and C. J. Pethick, Phys. Rev. Lett. 76, 6 (1996).
21 F. Dalfovo and S. Stringari, Phys. Rev. A 53,2477 (1996).
22 C. C. Bradley, C. A. Sackett, and R. G. Hulet, Phys. Rev. Lett. 78, 985 (1997).
23 E. A. Donley et al, Nature 412, 295 (2001).
24 C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, UK, 2002).
25 M. R. Matthews et al., Phys. Rev. Lett. 83, 2498 (1999).
26 K. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84, 806 (2000),
27 M. R. Andrews et al., Phys.Rev. Lett. 79, 553 (1997).
28 S. Burger et al., Phys. Rev. Lett. 83, 5198 (1999).
29 J. Denschlag et al., Science 287, 97 (2000).
30 T. L. Ho, Phys. Rev. Lett. 81, 742 (1998).
31 T. Ohmi and K. Machida, J. Phys. Soc. Jpn. 67, 1822 (1998).
32 J. Stenger et al., Nature 396, 345 (1998).
33 A. J. Leggett, Rev. Mod.Phys. 47, 331 (1975).
34 J. C. Wheatley, Rev. Mod. Phys. 47, 415 (1975).
35 A. P. M. Maeno and Y., Rev. Mod. Phys. 75, 657 (2003).
36 C. V. Ciobanu, S. K. Yip, and T. L. Ho, Phys. Rev. A 61, 033607 (2000).
37 C. K. Law, H. Pu, and N. P. Bigelow, Phys. Rev. Lett. 81, 5257 (1998).
38 H. J. Miesner et al., Phys. Rev. Lett. 82, 2228 (1999).
39 D. M. Stamper-Kurn et al., Phys. Rev. Lett. 83, 661 (1999).
40 M. Koashi and M. Ueda, Phys. Rev. Lett. 84, 1066 (2000).
41 W. X. Zhang, S. Yi, and L. You, New J. Phys. 5, 77 (2003).
42 E. V. Goldstein and P. Meystre, Phys. Rev. A 59, 3896 (1999).
43 H. Pu, C. K. Law, S. Raghavan, J. H. Eberly, and N. P. Bigelow, Phys. Rev. A 60, 1463 (1999).
44 J. P. Burke, P. S. Julienne, C. J. Williams, Y. B. Band, and M. Trippenbach, Phys. Rev. A 70, 033606(2004).
45 A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 90, 140403(2003).
46 T. Isoshima, K. Machida, and T. Ohmi, Phys. Rev. A 60, 4857 (1999).
47 L. M. Duan, J. I. Cirac, and P. Zoller, Phys. Rev. A 65, 033619 (2002).
48 N. N. Klausen, J. L. Bohn, and C. H. Greene, Phys. Rev. A 64, 053602 (2001).
49 E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Ver-haar, Phys. Rev. Lett 88, 093201 (2002).
50 J. P. Burke, C. H. Greene, and J. L. Bohn, Phys. Rev. Lett. 81, 3355 (1998).
51 Grimm, R., M. Weidemuller, and Y. B. Ovchinnikov, Adv. At., Mol., Opt. Phys. 42, 95 (2000).
52 P. S. Jessen, I. H. Deutsch, Adv. AMO phys. 37, 95 (1996).
53 F. Bloch, Z. Phys. 52, 555 (1929).
54 M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
55 S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, M. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
56 B. P. Aderson and M. A. Kasevich, Science 282, 1686 (1998).
57 D. M. Stamper-Kurn et. al. Phys. Rev. Lett. 80, 2227 (1998).
58 F. S. Cataliotti et. al. Science 293, 843 (2001).
59 O. Morsch, J. H. Muller, M. Christiani, D. Ciampini, E. Arimpmdo, Phys. Rev. Lett. 87, 140402 (2001).
60 J. Denschlag et. al, J. Phys. B 35, 3095 (2002).
61 C. Orzel, et. al., Science 291, 2386 (2001).
62 M. Greiner, O. Mandel, T. Esslinger, T. Hansch, I. Bloch, Nature 415, 39 (2002).
63 T. Stoferle, H. Moritz, C. Schori, M. Kohl, T. Esslinger, Cond-mat/ 0312440 (2003).
[1] J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur and W. Ketterle, Nature 396, 345.
[2] H. J. Miesner, D. M. Stamper-Kurn, J. Stenger, S. Inouye, A. P. Chikkatur, and W. Ketterle, Phys. Rev. Lett. 82,2228 (1999).
[3J D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, S.Inouye, J. Stenger, and W. Ketterle, Phys. Rev. Lett. 83, 661 (1999).
[4] M. S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, Phys. Rev. Lett. 92, 140403 (2004).
[5] A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 90, 140403 (2003).
[6] M. S. Chang, Q. Qin, W. Z. Zhang, L. You and M. S. Chapman, Nature Physics 1,111 (2005).
[7] Nichilas P Robins, Weiping Zhang, Elena A, Ostrovskaya, and Yuri S. Kivshar, Phys. Rev. A 64, 021601 (2001).
[8] Lu Li, Zaidong Li, Boris A. Malomed, Dumitru Mihalache, and W. M. Liu, Phys. Rev. A 72, 033611(2005).
[9] J. Ieda, T. Miyakawa, and M. Wadati, Phys. Rev. Lett. 93,194102 (2004).
[10] Weiping Zhang, Han Pu, Chris Search, and Pierre Meystre, Phys. Rev. Lett. 88,060401 (2002).
[11] H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87,140405 (2001).
[12] David Carpentier and Leon Balents, Phys. Rev. B 65, 024427 (2002).
[13] V. Yu. Irkhin and M. I. Katsnelson, Phys. Rev. B 56, 8109 (1997).
[14] L. J. Azevedo, A. Narath, Peter M. Richards, and Z. G. Soos,Phys. Rev. Lett. 43, 875 (1979).
[15] R. Lai and A. J. Sievers, Phys. Rev. B 57,3433 (1998).
[16] Jean-Pierre Nguenang, et al., J. Phys 17, 3083 (2005).
[17] I. Daumont, T. Dauxbis, and M. Peyrard, Nonlinearity 10,617 (1997).
[18] V.M. Burlakov, S.A. Kiselev, Sov. Phys. JETP 72, 854 (1991).
[19] Y. S. Kivshar and M. Salerno, Phys. Rev. E 49, 3543 (1994).
[20] K.W. Sandusky and J.B. Page, Phys. Rev. B 50, 866 (1994).
[21] Kevin Gross, Chris P. Search, Han Pu, Weiping Zhang, and Pierre Meystre, Phys. Rev. A 66, 033603 (2002).
[22] J.Javanainen, Phys. Rev. Lett. 72, 2375 (1994).
[23] J. Callaway, Quantum theory of the solid state (Academic Press, New York, 1991).
[24] Zhang W M, Feng D H and Glimore R. Rev. Mod. Phys. 62, 867 (1991).
[25] J.Ford, Phys. Rep. 213, 271 (1992).
[26] Jean-Pierre Nguenang, Michel Peyrard, Aurelien J Kenfaek and Timoleon C Kofane, J. Phys. Condens. Matter 17, 3083
[1] A. S. Davydov, Solitons in Molecular Systems (Reidel, Boston, 1985).
[2] A. M. Kosevich, B. A. Ivanov, A. S. Kovalev, Phys. Rep. 194,117 (1990).
[3] A. Newell, Solitons in Mathematics and physics (SIAM Philadelphia, 1985).
[4] A. R. Bishop, T. Schneider, in: M. Cardona, P. Fulde, H. -J. Queisser (Eds.), Springer Series in Solid-State Sciences (Springer, Berlin, 1978).
[5] S. Flach, C.R. Willis, Phys. Rep. 295,181 (1998).
[6] R. Lai, A. J. Sievers, Phys. Rep. 314,147 (1999).
[7] S. A. Kiselev, S.R. Bickham, A.J. Sievers, Comments Cond. Mater. Phys. 17, 135(1995).
[8] R. F. Wallis and D. L. Mills, Phys. Rev. B 52, R3828 (1995).
[9] R. Lai and A. J. Sievers, Phys. Rev. B 57, 3433 (1998).
[10] Weiping Zhang, Han Pu, Chris Search,and Pierre Meystre, Phys. Rev. Lett. 88, 060401 (2002).
[11] H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87,140405 (2001).
[12] Kevin Gross, Chris P. Search, Han Pu, Weiping Zhang, and Pierre Meystre, Phys. Rev. A 66, 033603 (2002).
[13] Nicholas P. Robins, Weiping Zhang, Elena A. Ostrovskaya and Yuri S. Kivshar, Phys. Rev. A64, 021601 (2001).
[14] Matlab 6.5 R13, optimization toolbox, function lsqnonlin.
[15] Xing-Dong Zhao, Zhang Wei Xie, and Weiping Zhang, unpublished.