Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds
Abstract
We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a “crystalline” configuration to that of a disordered state that can be characterized as a soliton “gas.” As our illustrative examples, we use both one-component, as well as two-component, one-dimensional atomic gases very close to zero temperature, where in the presence of repulsive interatomic interactions and of a parabolic trap, a cloud of dark (dark-bright) solitons can form in the one- (two-) component system. We corroborate our findings through three distinct types of approaches, namely a Gross-Pitaevskii type of partial differential equation, particle-based ordinary differential equations describing the soliton dynamical system, and Monte Carlo simulations for the particle system. In addition, we define an “empirical” order parameter to characterize the order of the soliton lattices and study how this changes as a function of the strength of the “thermally” (i.e., kinetically) induced perturbations. As may be anticipated by the one-dimensional nature of our system, the transition from order to disorder is gradual without, apparently, a genuine phase transition ensuing in the intermediate regime.
- Authors:
-
- Univ. of Massachusetts, Amherst, MA (United States)
- Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1233262
- Report Number(s):
- LA-UR-14-29477
Journal ID: ISSN 1539-3755; PLEEE8; TRN: US1600429
- Grant/Contract Number:
- DMR-1208046; FA950-12-1-0332; IRSES-605096; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 3; Journal ID: ISSN 1539-3755
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING
Citation Formats
Wang, Wenlong, and Kevrekidis, P. G. Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds. United States: N. p., 2015.
Web. doi:10.1103/PhysRevE.91.032905.
Wang, Wenlong, & Kevrekidis, P. G. Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds. United States. https://doi.org/10.1103/PhysRevE.91.032905
Wang, Wenlong, and Kevrekidis, P. G. Mon .
"Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds". United States. https://doi.org/10.1103/PhysRevE.91.032905. https://www.osti.gov/servlets/purl/1233262.
@article{osti_1233262,
title = {Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds},
author = {Wang, Wenlong and Kevrekidis, P. G.},
abstractNote = {We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a “crystalline” configuration to that of a disordered state that can be characterized as a soliton “gas.” As our illustrative examples, we use both one-component, as well as two-component, one-dimensional atomic gases very close to zero temperature, where in the presence of repulsive interatomic interactions and of a parabolic trap, a cloud of dark (dark-bright) solitons can form in the one- (two-) component system. We corroborate our findings through three distinct types of approaches, namely a Gross-Pitaevskii type of partial differential equation, particle-based ordinary differential equations describing the soliton dynamical system, and Monte Carlo simulations for the particle system. In addition, we define an “empirical” order parameter to characterize the order of the soliton lattices and study how this changes as a function of the strength of the “thermally” (i.e., kinetically) induced perturbations. As may be anticipated by the one-dimensional nature of our system, the transition from order to disorder is gradual without, apparently, a genuine phase transition ensuing in the intermediate regime.},
doi = {10.1103/PhysRevE.91.032905},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 3,
volume = 91,
place = {United States},
year = {Mon Mar 09 00:00:00 EDT 2015},
month = {Mon Mar 09 00:00:00 EDT 2015}
}
Web of Science
Works referenced in this record:
Emergent Nonlinear Phenomena in Bose-Einstein Condensates
book, January 2008
- Kevrekidis, Panayotis G.; Frantzeskakis, Dimitri J.; Carretero-González, Ricardo
- Atomic, Optical, and Plasma Physics
Formation and propagation of matter-wave soliton trains
journal, May 2002
- Strecker, Kevin E.; Partridge, Guthrie B.; Truscott, Andrew G.
- Nature, Vol. 417, Issue 6885
Formation of a Matter-Wave Bright Soliton
journal, May 2002
- Khaykovich, L.
- Science, Vol. 296, Issue 5571
Formation of Bright Matter-Wave Solitons during the Collapse of Attractive Bose-Einstein Condensates
journal, May 2006
- Cornish, Simon L.; Thompson, Sarah T.; Wieman, Carl E.
- Physical Review Letters, Vol. 96, Issue 17
Bright Bose-Einstein Gap Solitons of Atoms with Repulsive Interaction
journal, June 2004
- Eiermann, B.; Anker, Th.; Albiez, M.
- Physical Review Letters, Vol. 92, Issue 23
Dark solitons in atomic Bose–Einstein condensates: from theory to experiments
journal, May 2010
- Frantzeskakis, D. J.
- Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue 21
Vortices in a trapped dilute Bose-Einstein condensate
journal, March 2001
- Fetter, Alexander L.; Svidzinsky, Anatoly A.
- Journal of Physics: Condensed Matter, Vol. 13, Issue 12
Rotating trapped Bose-Einstein condensates
journal, May 2009
- Fetter, Alexander L.
- Reviews of Modern Physics, Vol. 81, Issue 2
Vortex rings and solitary waves in trapped Bose–Einstein condensates
journal, August 2007
- Komineas, S.
- The European Physical Journal Special Topics, Vol. 147, Issue 1
Dark Solitons in Bose-Einstein Condensates
journal, December 1999
- Burger, S.; Bongs, K.; Dettmer, S.
- Physical Review Letters, Vol. 83, Issue 25
Generating Solitons by Phase Engineering of a Bose-Einstein Condensate
journal, January 2000
- Denschlag, J.
- Science, Vol. 287, Issue 5450
Observation of Quantum Shock Waves Created with Ultra- Compressed Slow Light Pulses in a Bose-Einstein Condensate
journal, July 2001
- Dutton, Z.
- Science, Vol. 293, Issue 5530
Stationary and Nonstationary Fluid Flow of a Bose-Einstein Condensate Through a Penetrable Barrier
journal, October 2007
- Engels, P.; Atherton, C.
- Physical Review Letters, Vol. 99, Issue 16
Inelastic collisions of solitary waves in anisotropic Bose–Einstein condensates: sling-shot events and expanding collision bubbles
journal, November 2013
- Becker, C.; Sengstock, K.; Schmelcher, P.
- New Journal of Physics, Vol. 15, Issue 11
Collisions of Dark Solitons in Elongated Bose-Einstein Condensates
journal, September 2008
- Stellmer, S.; Becker, C.; Soltan-Panahi, P.
- Physical Review Letters, Vol. 101, Issue 12
Experimental Observation of Oscillating and Interacting Matter Wave Dark Solitons
journal, September 2008
- Weller, A.; Ronzheimer, J. P.; Gross, C.
- Physical Review Letters, Vol. 101, Issue 13
Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates
journal, June 2010
- Theocharis, G.; Weller, A.; Ronzheimer, J. P.
- Physical Review A, Vol. 81, Issue 6
Evidence for an oscillating soliton/vortex ring by density engineering of a Bose–Einstein condensate
journal, January 2009
- Shomroni, I.; Lahoud, E.; Levy, S.
- Nature Physics, Vol. 5, Issue 3
Incoherently coupled dark–bright photorefractive solitons
journal, January 1996
- Chen, Zhigang; Coskun, Tamer H.; Kivshar, Yuri S.
- Optics Letters, Vol. 21, Issue 22
Interaction between vector solitons and solitonic gluons
journal, January 1999
- Ostrovskaya, Elena A.; Kivshar, Yuri S.; Chen, Zhigang
- Optics Letters, Vol. 24, Issue 5
Coupled photorefractive spatial-soliton pairs
journal, January 1997
- Chen, Zhigang; Segev, Mordechai; Coskun, Tamer H.
- Journal of the Optical Society of America B, Vol. 14, Issue 11
Oscillations and interactions of dark and dark–bright solitons in Bose–Einstein condensates
journal, May 2008
- Becker, Christoph; Stellmer, Simon; Soltan-Panahi, Parvis
- Nature Physics, Vol. 4, Issue 6
Dynamics of dark–bright solitons in cigar-shaped Bose–Einstein condensates
journal, January 2011
- Middelkamp, S.; Chang, J. J.; Hamner, C.
- Physics Letters A, Vol. 375, Issue 3
Multiple dark-bright solitons in atomic Bose-Einstein condensates
journal, November 2011
- Yan, D.; Chang, J. J.; Hamner, C.
- Physical Review A, Vol. 84, Issue 5
Dark-dark solitons and modulational instability in miscible two-component Bose-Einstein condensates
journal, October 2011
- Hoefer, M. A.; Chang, J. J.; Hamner, C.
- Physical Review A, Vol. 84, Issue 4
Beating dark–dark solitons in Bose–Einstein condensates
journal, May 2012
- Yan, D.; Chang, J. J.; Hamner, C.
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 45, Issue 11
Topological Wigner Crystal of Half-Solitons in a Spinor Bose-Einstein Condensate
journal, January 2013
- Terças, H.; Solnyshkov, D. D.; Malpuech, G.
- Physical Review Letters, Vol. 110, Issue 3
Kinetic Equation for a Dense Soliton Gas
journal, November 2005
- El, G. A.; Kamchatnov, A. M.
- Physical Review Letters, Vol. 95, Issue 20
Soliton turbulence as a thermodynamic limit of stochastic soliton lattices
journal, May 2001
- El, Gennady A.; Krylov, Alexander L.; Molchanov, Stanislav A.
- Physica D: Nonlinear Phenomena, Vol. 152-153
Turbulence in Integrable Systems
journal, April 2009
- Zakharov, Vladimir E.
- Studies in Applied Mathematics, Vol. 122, Issue 3
Non-thermal fixed points and solitons in a one-dimensional Bose gas
journal, July 2012
- Schmidt, Maximilian; Erne, Sebastian; Nowak, Boris
- New Journal of Physics, Vol. 14, Issue 7
Excited states in the large density limit: a variational approach
journal, June 2010
- Coles, M. P.; Pelinovsky, D. E.; Kevrekidis, P. G.
- Nonlinearity, Vol. 23, Issue 8
Dark-bright solitons and their lattices in atomic Bose-Einstein condensates
journal, February 2015
- Yan, D.; Tsitoura, F.; Kevrekidis, P. G.
- Physical Review A, Vol. 91, Issue 2
Population annealing with weighted averages: A Monte Carlo method for rough free-energy landscapes
journal, August 2010
- Machta, J.
- Physical Review E, Vol. 82, Issue 2
Evidence against a mean-field description of short-range spin glasses revealed through thermal boundary conditions
journal, November 2014
- Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut G.
- Physical Review B, Vol. 90, Issue 18
Monte Carlo Methods for Rough Free Energy Landscapes: Population Annealing and Parallel Tempering
journal, June 2011
- Machta, J.; Ellis, R. S.
- Journal of Statistical Physics, Vol. 144, Issue 3
Dark-Bright Solitons in Inhomogeneous Bose-Einstein Condensates
journal, June 2001
- Busch, Th.; Anglin, J. R.
- Physical Review Letters, Vol. 87, Issue 1
Bright-dark soliton complexes in spinor Bose-Einstein condensates
journal, March 2008
- Nistazakis, H. E.; Frantzeskakis, D. J.; Kevrekidis, P. G.
- Physical Review A, Vol. 77, Issue 3
Bright-dark solitons and their collisions in mixed -coupled nonlinear Schrödinger equations
journal, January 2008
- Vijayajayanthi, M.; Kanna, T.; Lakshmanan, M.
- Physical Review A, Vol. 77, Issue 1
Interaction of dark–bright solitons in two-component Bose–Einstein condensates
journal, June 2009
- Rajendran, S.; Muruganandam, P.; Lakshmanan, M.
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 42, Issue 14
Stable multidimensional soliton stripes in two-component Bose–Einstein condensates
journal, June 2011
- Brazhnyi, Valeriy A.; Pérez-García, Víctor M.
- Chaos, Solitons & Fractals, Vol. 44, Issue 6
Coherent atomic soliton molecules for matter-wave switching
journal, May 2011
- Yin, Chenyun; Berloff, Natalia G.; Pérez-García, Víctor M.
- Physical Review A, Vol. 83, Issue 5
Stable Vortex–Bright-Soliton Structures in Two-Component Bose-Einstein Condensates
journal, October 2010
- Law, K. J. H.; Kevrekidis, P. G.; Tuckerman, Laurette S.
- Physical Review Letters, Vol. 105, Issue 16
Dark–bright discrete solitons: A numerical study of existence, stability and dynamics
journal, April 2011
- Álvarez, A.; Cuevas, J.; Romero, F. R.
- Physica D: Nonlinear Phenomena, Vol. 240, Issue 8
Statics and dynamics of atomic dark-bright solitons in the presence of impurities
journal, November 2011
- Achilleos, V.; Kevrekidis, P. G.; Rothos, V. M.
- Physical Review A, Vol. 84, Issue 5
Dark-bright solitons in Bose–Einstein condensates at finite temperatures
journal, May 2012
- Achilleos, V.; Yan, D.; Kevrekidis, P. G.
- New Journal of Physics, Vol. 14, Issue 5
Matter-wave solitons in the counterflow of two immiscible superfluids
journal, June 2013
- Tsitoura, F.; Achilleos, V.; Malomed, B. A.
- Physical Review A, Vol. 87, Issue 6
Dynamics and statistical mechanics of a one-dimensional model Hamiltonian for structural phase transitions
journal, May 1975
- Krumhansl, J. A.; Schrieffer, J. R.
- Physical Review B, Vol. 11, Issue 9
A unified approach to the interpretation of displacive and order–disorder systems. I. Thermodynamical aspect
journal, April 1975
- Aubry, S.
- The Journal of Chemical Physics, Vol. 62, Issue 8
Toda lattice: Statistical mechanics and solitons
journal, March 1979
- Büttner, H.; Mertens, F. G.
- Solid State Communications, Vol. 29, Issue 9
The soliton-gas analogy for the Toda lattice
journal, August 1981
- Mertens, F. G.; Büttner, H.
- Physics Letters A, Vol. 84, Issue 6
Variational approximations of trapped vortices in the large-density limit
journal, March 2011
- Pelinovsky, D. E.; Kevrekidis, P. G.
- Nonlinearity, Vol. 24, Issue 4
Vortex Precession in Bose-Einstein Condensates: Observations with Filled and Empty Cores
journal, October 2000
- Anderson, B. P.; Haljan, P. C.; Wieman, C. E.
- Physical Review Letters, Vol. 85, Issue 14
Watching Dark Solitons Decay into Vortex Rings in a Bose-Einstein Condensate
journal, April 2001
- Anderson, B. P.; Haljan, P. C.; Regal, C. A.
- Physical Review Letters, Vol. 86, Issue 14
Scattering and leapfrogging of vortex rings in a superfluid
journal, September 2014
- Caplan, R. M.; Talley, J. D.; Carretero-González, R.
- Physics of Fluids, Vol. 26, Issue 9
Works referencing / citing this record:
Dark–bright soliton dynamics beyond the mean-field approximation
journal, July 2017
- Katsimiga, G. C.; Koutentakis, G. M.; Mistakidis, S. I.
- New Journal of Physics, Vol. 19, Issue 7