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Multiple dark solitons in Bose-Einstein condensates at finite temperatures
1. | University of Massachusetts, Lederle Graduate Research Tower, Department of Mathematics and Statistics, Amherst, MA 01003 |
2. | Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece |
References:
[1] |
B. P. Anderson, P. C. Haljan, C. A. Regal, D. L. Feder, L. A. Collins, C. W. Clark and E. A. Cornell, Watching dark solitons decay into vortex rings in a Bose-Einstein condensate, Phys. Rev. Lett., 86 (2001), 2926-2929.
doi: 10.1103/PhysRevLett.86.2926. |
[2] |
I. Aranson and V. Steinberg, Stability of multicharged vortices in a model of superflow, Phys. Rev. B, 53 (1996), 75-78.
doi: 10.1103/PhysRevB.53.75. |
[3] |
C. Becker, S. Stellmer, P. Soltan-Panahi, S. Dörscher, M. Baumert, E.-M. Richter, J. Kronjäger, K. Bongs and K. Sengstock, Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates, Nature Phys., 4 (2008), 496-501.
doi: 10.1038/nphys962. |
[4] |
K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer and K. Sengstock, Coherent manipulation and guiding of Bose-Einstein condensates by optical dipole potentials, C. R. Acad. Sci. Paris, 2 (2001), 671-680. |
[5] |
S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A. Sanpera, G. V. Shlyapnikov and M. Lewenstein, Dark solitons in Bose-Einstein condensates, Phys. Rev. Lett., 83 (1999), 5198-5201.
doi: 10.1103/PhysRevLett.83.5198. |
[6] |
Th. Busch and J. R. Anglin, Motion of dark solitons in trapped Bose-Einstein Condensates, Phys. Rev. Lett., 84 (2000), 2298-2301.
doi: 10.1103/PhysRevLett.84.2298. |
[7] |
R. Carretero-González, B. P. Anderson, P. G. Kevrekidis, D. J. Frantzeskakis and C. N. Weiler, Dynamics of vortex formation in merging Bose-Einstein condensate fragments, Phys. Rev. A, 77 (2008), 033625. |
[8] |
R. Carretero-González, P. G. Kevrekidis and D. J. Frantzeskakis, Nonlinear waves in Bose-Einstein condensates: Physical relevance and mathematical techniques, Nonlinearity, 21 (2008), R139-R202. |
[9] |
R. Carretero-González, N. Whitaker, P. G. Kevrekidis and D. J. Frantzeskakis, Vortex structures formed by the interference of sliced condensates, Phys. Rev. A, 77 (2008), 023605. |
[10] |
S. Choi, S. A. Morgan and K. Burnett, Phenomenological damping in trapped atomic Bose-Einstein condensates, Phys. Rev. A, 57 (1998), 4057-4060.
doi: 10.1103/PhysRevA.57.4057. |
[11] |
S. P. Cockburn, H. E. Nistazakis, T. P. Horikis, P. G. Kevrekidis, N. P. Proukakis and D. J. Frantzeskakis, Matter-wave dark solitons: Stochastic vs. analytical results, Phys. Rev. Lett, 104 (2010), 174101.
doi: 10.1103/PhysRevLett.104.174101. |
[12] |
S. P. Cockburn and N. P. Proukakis, The stochastic Gross-Pitaevskii equation and some applications, Laser Phys., 19 (2009), 558-570.
doi: 10.1134/S1054660X09040057. |
[13] |
J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark, L. A. Collins, J. Cubizolles, L. Deng, E. W. Hagley, K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider and W. D. Phillips, Generating solitons by phase engineering of a Bose-Einstein condensate, Science, 287 (2000), 97-101.
doi: 10.1126/science.287.5450.97. |
[14] |
Z. Dutton, M. Budde, C. Slowe and L. V. Hau, Observation of quantum shock waves created with ultra-compressed slow light pulses in a Bose-Einstein Condensate, Science, 293 (2001), 663-668.
doi: 10.1126/science.1062527. |
[15] |
P. Engels and C. Atherton, Stationary and nonstationary fluid flow of a Bose-Einstein condensate through a penetrable barrier, Phys. Rev. Lett., 99 (2007), 160405.
doi: 10.1103/PhysRevLett.99.160405. |
[16] |
P. O. Fedichev, A. E. Muryshev and G. V. Shlyapnikov, Dissipative dynamics of a kink state in a Bose-condensed gas, Phys. Rev. A, 60 (1999), 3220-3224.
doi: 10.1103/PhysRevA.60.3220. |
[17] |
D. J. Frantzeskakis, Dark solitons in atomic Bose-Einstein condensates: from theory to experiments, J. Phys. A: Math. Theor., 43 (2010), 213001.
doi: 10.1088/1751-8113/43/21/213001. |
[18] |
D. J. Frantzeskakis, G. Theocharis, F. K. Diakonos, P. Schmelcher and Yu. S. Kivshar, Interaction of dark solitons with localized impurities in Bose-Einstein condensates, Phys. Rev. A, 66 (2002), 053608.
doi: 10.1103/PhysRevA.66.053608. |
[19] |
R. Graham, Decoherence of Bose-Einstein condensates in traps at finite temperature, Phys. Rev. Lett., 81 (1998), 5262-5265.
doi: 10.1103/PhysRevLett.81.5262. |
[20] |
B. Jackson and N. P. Proukakis, Finite-temperature models of Bose-Einstein condensation, J. Phys. B: At. Mol. Opt. Phys., 41 (2008), 203002.
doi: 10.1088/0953-4075/41/20/203002. |
[21] |
B. Jackson, C. F. Barenghi and N. P. Proukakis, Matter wave solitons at finite temperatures, J. Low Temp. Phys., 148 (2007), 387-391.
doi: 10.1007/s10909-007-9410-1. |
[22] |
B. Jackson, N. P. Proukakis and C. F. Barenghi, Dark-soliton dynamics in Bose-Einstein condensates at finite temperature, Phys., Rev. A, 75 (2007), 051601.
doi: 10.1103/PhysRevA.75.051601. |
[23] |
T. Kapitula and P. G. Kevrekidis, Bose-Einstein condensates in the presence of a magnetic trap and optical lattice, Chaos, 15 (2005), 037114.
doi: 10.1063/1.1993867. |
[24] |
T. Kapitula, P. G. Kevrekidis and B. Sandstede, Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian system, Physica D, 195 (2004), 263-282.
doi: 10.1016/j.physd.2004.03.018. |
[25] |
P. G. Kevrekidis, D. J. Frantzeskakis and R. Carretero-González R (eds.), "Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment," Springer, Berlin, 2007. |
[26] |
Yu. S. Kivshar and W. Królikowski, Lagrangian approach for dark solitons, Opt. Commun., 114 (1995), 353-362.
doi: 10.1016/0030-4018(94)00644-A. |
[27] |
Yu. S. Kivshar and X. Yang, Perturbation-induced dynamics of dark solitons, Phys. Rev. E, 49 (1994), 1657-1670.
doi: 10.1103/PhysRevE.49.1657. |
[28] |
C. K. Law, P. T. Leung and M.-C. Chu, Quantum fluctuations of coupled dark solitons in a trapped Bose-Einstein condensate, J. Phys. B: At. Mol. Opt. Phys., 35 (2002), 3583-3590.
doi: 10.1088/0953-4075/35/16/316. |
[29] |
M. D. Lee and C. W. Gardiner, Quantum kinetic theory. VI. The growth of a Bose-Einstein condensate, Phys. Rev. A, 62 (2000), 033606.
doi: 10.1103/PhysRevA.62.033606. |
[30] |
E. J. M. Madarassy and C. F. Barenghi, Vortex dynamics in trapped Bose-Einstein condensate, J. Low Temp. Phys., 152 (2008), 122-135.
doi: 10.1007/s10909-008-9811-9. |
[31] |
A. A. Penckwitt, R. J. Ballagh and C. W. Gardiner, Nucleation, growth and stabilization of Bose-Einstein condensate vortex lattices, Phys. Rev. Lett., 89 (2002), 260402.
doi: 10.1103/PhysRevLett.89.260402. |
[32] |
L. P. Pitaevskii, , Zh. Eksp. Teor. Fiz., 35 (1958), 408; [Sov. Phys. JETP, 35 (1959), 282]. |
[33] |
L. P. Pitaevskii and S. Stringari, "Bose-Einstein Condensation," Oxford University Press, Oxford, 2003. |
[34] |
N. P. Proukakis, N. G. Parker, C. F. Barenghi and C. S. Adams, Parametric driving of dark solitons in atomic Bose-Einstein condensates, Phys. Rev. Lett., 93 (2004), 130408.
doi: 10.1103/PhysRevLett.93.130408. |
[35] |
R. Sásik, L. M. A. Bettencourt and S. Habib, Thermal vortex dynamics in a two-dimensional condensate, Phys. Rev. B, 62 (2000), 1238-1243.
doi: 10.1103/PhysRevB.62.1238. |
[36] |
D. V. Skryabin, Energy of internal modes of nonlinear waves and complex frequencies due to symmetry breaking, Phys. Rev. E, 64 (2001), 055601.
doi: 10.1103/PhysRevE.64.055601. |
[37] |
S. Stellmer, C. Becker, P. Soltan-Panahi, E.-M. Richter, S. Dörscher, M. Baumert, J. Kronjäger, K. Bongs and K. Sengstock, Collisions of dark solitons in elongated Bose-Einstein condensates, Phys. Rev. Lett., 101 (2008), 120406.
doi: 10.1103/PhysRevLett.101.120406. |
[38] |
G. Theocharis, P. G. Kevrekidis, M. K. Oberthaler and D. J. Frantzeskakis, Dark matter-wave solitons in the dimensionality crossover, Phys. Rev. A, 76 (2007), 045601.
doi: 10.1103/PhysRevA.76.045601. |
[39] |
G. Theocharis, A. Weller, J. P. Ronzheimer, C. Gross, M. K. Oberthaler, P. G. Kevrekidis and D. J. Frantzeskakis, Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates, Phys. Rev. A, 81 (2009), 063604.
doi: 10.1103/PhysRevA.81.063604. |
[40] |
M. Tsubota, K. Kasamatsu and M. Ueda, Vortex lattice formation in a rotating Bose-Einstein condensate, Phys. Rev. A, 65 (2002), 023603; ibid Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate, 67 (2003), 033610. |
[41] |
A. Weller, J. P. Ronzheimer, C. Gross, J. Esteve, M. K. Oberthaler, D. J. Frantzeskakis, G. Theocharis and P. G. Kevrekidis, Experimental observation of oscillating and interacting matter-wave dark solitons, Phys. Rev. Lett., 101 (2008), 130401.
doi: 10.1103/PhysRevLett.101.130401. |
show all references
References:
[1] |
B. P. Anderson, P. C. Haljan, C. A. Regal, D. L. Feder, L. A. Collins, C. W. Clark and E. A. Cornell, Watching dark solitons decay into vortex rings in a Bose-Einstein condensate, Phys. Rev. Lett., 86 (2001), 2926-2929.
doi: 10.1103/PhysRevLett.86.2926. |
[2] |
I. Aranson and V. Steinberg, Stability of multicharged vortices in a model of superflow, Phys. Rev. B, 53 (1996), 75-78.
doi: 10.1103/PhysRevB.53.75. |
[3] |
C. Becker, S. Stellmer, P. Soltan-Panahi, S. Dörscher, M. Baumert, E.-M. Richter, J. Kronjäger, K. Bongs and K. Sengstock, Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates, Nature Phys., 4 (2008), 496-501.
doi: 10.1038/nphys962. |
[4] |
K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer and K. Sengstock, Coherent manipulation and guiding of Bose-Einstein condensates by optical dipole potentials, C. R. Acad. Sci. Paris, 2 (2001), 671-680. |
[5] |
S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A. Sanpera, G. V. Shlyapnikov and M. Lewenstein, Dark solitons in Bose-Einstein condensates, Phys. Rev. Lett., 83 (1999), 5198-5201.
doi: 10.1103/PhysRevLett.83.5198. |
[6] |
Th. Busch and J. R. Anglin, Motion of dark solitons in trapped Bose-Einstein Condensates, Phys. Rev. Lett., 84 (2000), 2298-2301.
doi: 10.1103/PhysRevLett.84.2298. |
[7] |
R. Carretero-González, B. P. Anderson, P. G. Kevrekidis, D. J. Frantzeskakis and C. N. Weiler, Dynamics of vortex formation in merging Bose-Einstein condensate fragments, Phys. Rev. A, 77 (2008), 033625. |
[8] |
R. Carretero-González, P. G. Kevrekidis and D. J. Frantzeskakis, Nonlinear waves in Bose-Einstein condensates: Physical relevance and mathematical techniques, Nonlinearity, 21 (2008), R139-R202. |
[9] |
R. Carretero-González, N. Whitaker, P. G. Kevrekidis and D. J. Frantzeskakis, Vortex structures formed by the interference of sliced condensates, Phys. Rev. A, 77 (2008), 023605. |
[10] |
S. Choi, S. A. Morgan and K. Burnett, Phenomenological damping in trapped atomic Bose-Einstein condensates, Phys. Rev. A, 57 (1998), 4057-4060.
doi: 10.1103/PhysRevA.57.4057. |
[11] |
S. P. Cockburn, H. E. Nistazakis, T. P. Horikis, P. G. Kevrekidis, N. P. Proukakis and D. J. Frantzeskakis, Matter-wave dark solitons: Stochastic vs. analytical results, Phys. Rev. Lett, 104 (2010), 174101.
doi: 10.1103/PhysRevLett.104.174101. |
[12] |
S. P. Cockburn and N. P. Proukakis, The stochastic Gross-Pitaevskii equation and some applications, Laser Phys., 19 (2009), 558-570.
doi: 10.1134/S1054660X09040057. |
[13] |
J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark, L. A. Collins, J. Cubizolles, L. Deng, E. W. Hagley, K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider and W. D. Phillips, Generating solitons by phase engineering of a Bose-Einstein condensate, Science, 287 (2000), 97-101.
doi: 10.1126/science.287.5450.97. |
[14] |
Z. Dutton, M. Budde, C. Slowe and L. V. Hau, Observation of quantum shock waves created with ultra-compressed slow light pulses in a Bose-Einstein Condensate, Science, 293 (2001), 663-668.
doi: 10.1126/science.1062527. |
[15] |
P. Engels and C. Atherton, Stationary and nonstationary fluid flow of a Bose-Einstein condensate through a penetrable barrier, Phys. Rev. Lett., 99 (2007), 160405.
doi: 10.1103/PhysRevLett.99.160405. |
[16] |
P. O. Fedichev, A. E. Muryshev and G. V. Shlyapnikov, Dissipative dynamics of a kink state in a Bose-condensed gas, Phys. Rev. A, 60 (1999), 3220-3224.
doi: 10.1103/PhysRevA.60.3220. |
[17] |
D. J. Frantzeskakis, Dark solitons in atomic Bose-Einstein condensates: from theory to experiments, J. Phys. A: Math. Theor., 43 (2010), 213001.
doi: 10.1088/1751-8113/43/21/213001. |
[18] |
D. J. Frantzeskakis, G. Theocharis, F. K. Diakonos, P. Schmelcher and Yu. S. Kivshar, Interaction of dark solitons with localized impurities in Bose-Einstein condensates, Phys. Rev. A, 66 (2002), 053608.
doi: 10.1103/PhysRevA.66.053608. |
[19] |
R. Graham, Decoherence of Bose-Einstein condensates in traps at finite temperature, Phys. Rev. Lett., 81 (1998), 5262-5265.
doi: 10.1103/PhysRevLett.81.5262. |
[20] |
B. Jackson and N. P. Proukakis, Finite-temperature models of Bose-Einstein condensation, J. Phys. B: At. Mol. Opt. Phys., 41 (2008), 203002.
doi: 10.1088/0953-4075/41/20/203002. |
[21] |
B. Jackson, C. F. Barenghi and N. P. Proukakis, Matter wave solitons at finite temperatures, J. Low Temp. Phys., 148 (2007), 387-391.
doi: 10.1007/s10909-007-9410-1. |
[22] |
B. Jackson, N. P. Proukakis and C. F. Barenghi, Dark-soliton dynamics in Bose-Einstein condensates at finite temperature, Phys., Rev. A, 75 (2007), 051601.
doi: 10.1103/PhysRevA.75.051601. |
[23] |
T. Kapitula and P. G. Kevrekidis, Bose-Einstein condensates in the presence of a magnetic trap and optical lattice, Chaos, 15 (2005), 037114.
doi: 10.1063/1.1993867. |
[24] |
T. Kapitula, P. G. Kevrekidis and B. Sandstede, Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian system, Physica D, 195 (2004), 263-282.
doi: 10.1016/j.physd.2004.03.018. |
[25] |
P. G. Kevrekidis, D. J. Frantzeskakis and R. Carretero-González R (eds.), "Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment," Springer, Berlin, 2007. |
[26] |
Yu. S. Kivshar and W. Królikowski, Lagrangian approach for dark solitons, Opt. Commun., 114 (1995), 353-362.
doi: 10.1016/0030-4018(94)00644-A. |
[27] |
Yu. S. Kivshar and X. Yang, Perturbation-induced dynamics of dark solitons, Phys. Rev. E, 49 (1994), 1657-1670.
doi: 10.1103/PhysRevE.49.1657. |
[28] |
C. K. Law, P. T. Leung and M.-C. Chu, Quantum fluctuations of coupled dark solitons in a trapped Bose-Einstein condensate, J. Phys. B: At. Mol. Opt. Phys., 35 (2002), 3583-3590.
doi: 10.1088/0953-4075/35/16/316. |
[29] |
M. D. Lee and C. W. Gardiner, Quantum kinetic theory. VI. The growth of a Bose-Einstein condensate, Phys. Rev. A, 62 (2000), 033606.
doi: 10.1103/PhysRevA.62.033606. |
[30] |
E. J. M. Madarassy and C. F. Barenghi, Vortex dynamics in trapped Bose-Einstein condensate, J. Low Temp. Phys., 152 (2008), 122-135.
doi: 10.1007/s10909-008-9811-9. |
[31] |
A. A. Penckwitt, R. J. Ballagh and C. W. Gardiner, Nucleation, growth and stabilization of Bose-Einstein condensate vortex lattices, Phys. Rev. Lett., 89 (2002), 260402.
doi: 10.1103/PhysRevLett.89.260402. |
[32] |
L. P. Pitaevskii, , Zh. Eksp. Teor. Fiz., 35 (1958), 408; [Sov. Phys. JETP, 35 (1959), 282]. |
[33] |
L. P. Pitaevskii and S. Stringari, "Bose-Einstein Condensation," Oxford University Press, Oxford, 2003. |
[34] |
N. P. Proukakis, N. G. Parker, C. F. Barenghi and C. S. Adams, Parametric driving of dark solitons in atomic Bose-Einstein condensates, Phys. Rev. Lett., 93 (2004), 130408.
doi: 10.1103/PhysRevLett.93.130408. |
[35] |
R. Sásik, L. M. A. Bettencourt and S. Habib, Thermal vortex dynamics in a two-dimensional condensate, Phys. Rev. B, 62 (2000), 1238-1243.
doi: 10.1103/PhysRevB.62.1238. |
[36] |
D. V. Skryabin, Energy of internal modes of nonlinear waves and complex frequencies due to symmetry breaking, Phys. Rev. E, 64 (2001), 055601.
doi: 10.1103/PhysRevE.64.055601. |
[37] |
S. Stellmer, C. Becker, P. Soltan-Panahi, E.-M. Richter, S. Dörscher, M. Baumert, J. Kronjäger, K. Bongs and K. Sengstock, Collisions of dark solitons in elongated Bose-Einstein condensates, Phys. Rev. Lett., 101 (2008), 120406.
doi: 10.1103/PhysRevLett.101.120406. |
[38] |
G. Theocharis, P. G. Kevrekidis, M. K. Oberthaler and D. J. Frantzeskakis, Dark matter-wave solitons in the dimensionality crossover, Phys. Rev. A, 76 (2007), 045601.
doi: 10.1103/PhysRevA.76.045601. |
[39] |
G. Theocharis, A. Weller, J. P. Ronzheimer, C. Gross, M. K. Oberthaler, P. G. Kevrekidis and D. J. Frantzeskakis, Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates, Phys. Rev. A, 81 (2009), 063604.
doi: 10.1103/PhysRevA.81.063604. |
[40] |
M. Tsubota, K. Kasamatsu and M. Ueda, Vortex lattice formation in a rotating Bose-Einstein condensate, Phys. Rev. A, 65 (2002), 023603; ibid Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate, 67 (2003), 033610. |
[41] |
A. Weller, J. P. Ronzheimer, C. Gross, J. Esteve, M. K. Oberthaler, D. J. Frantzeskakis, G. Theocharis and P. G. Kevrekidis, Experimental observation of oscillating and interacting matter-wave dark solitons, Phys. Rev. Lett., 101 (2008), 130401.
doi: 10.1103/PhysRevLett.101.130401. |
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