Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap
Abstract
In this study, we consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry-breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state, becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of the dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a bosonic Josephson junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.
- Authors:
-
- Univ. Hamburg, Hamburg (Germany)
- Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. Hamburg, Hamburg (Germany); The Hamburg Centre for Ultrafast Imaging, Hamburg (Germany)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1233190
- Alternate Identifier(s):
- OSTI ID: 1181069
- Report Number(s):
- LA-UR-14-28727
Journal ID: ISSN 1050-2947; PLRAAN; TRN: US1600427
- Grant/Contract Number:
- 885/26-1; NSF-DMS-1312856; FA9550-12-1-0332; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A - Atomic, Molecular, and Optical Physics
- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 4; Journal ID: ISSN 1050-2947
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING
Citation Formats
Karamatskos, E. T., Stockhofe, J., Kevrekidis, P. G., and Schmelcher, P. Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap. United States: N. p., 2015.
Web. doi:10.1103/PhysRevA.91.043637.
Karamatskos, E. T., Stockhofe, J., Kevrekidis, P. G., & Schmelcher, P. Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap. United States. https://doi.org/10.1103/PhysRevA.91.043637
Karamatskos, E. T., Stockhofe, J., Kevrekidis, P. G., and Schmelcher, P. Thu .
"Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap". United States. https://doi.org/10.1103/PhysRevA.91.043637. https://www.osti.gov/servlets/purl/1233190.
@article{osti_1233190,
title = {Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap},
author = {Karamatskos, E. T. and Stockhofe, J. and Kevrekidis, P. G. and Schmelcher, P.},
abstractNote = {In this study, we consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry-breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state, becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of the dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a bosonic Josephson junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.},
doi = {10.1103/PhysRevA.91.043637},
journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
number = 4,
volume = 91,
place = {United States},
year = {Thu Apr 30 00:00:00 EDT 2015},
month = {Thu Apr 30 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
Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
journal, June 2008
- Carretero-González, R.; Frantzeskakis, D. J.; Kevrekidis, P. G.
- Nonlinearity, Vol. 21, Issue 7
Dynamics of Bright Matter wave Solitons in a Bose–Einstein Condensate
journal, September 2005
- Kh. ABDULLAEV, Fatkhulla; Gammal, Arnaldo; Kamchatnov, Anatoly M.
- International Journal of Modern Physics B, Vol. 19, Issue 22
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
Discrete solitons in optics
journal, July 2008
- Lederer, Falk; Stegeman, George I.; Christodoulides, Demetri N.
- Physics Reports, Vol. 463, Issue 1-3
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
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
Dark–bright ring solitons in Bose–Einstein condensates
journal, September 2011
- Stockhofe, J.; Kevrekidis, P. G.; Frantzeskakis, D. J.
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 44, Issue 19
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
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
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
Generation of Dark-Bright Soliton Trains in Superfluid-Superfluid Counterflow
journal, February 2011
- Hamner, C.; Chang, J. J.; Engels, P.
- Physical Review Letters, Vol. 106, Issue 6
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
Instabilities of vortices in a binary mixture of trapped Bose-Einstein condensates: Role of collective excitations with positive and negative energies
journal, December 2000
- Skryabin, Dmitry V.
- Physical Review A, Vol. 63, Issue 1
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
Erratum: Stable Vortex–Bright-Soliton Structures in Two-Component Bose-Einstein Condensates [Phys. Rev. Lett. 105 , 160405 (2010)]
journal, May 2011
- Law, K. J. H.; Kevrekidis, P. G.; Tuckerman, Laurette S.
- Physical Review Letters, Vol. 106, Issue 19
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
Vortex–bright-soliton dipoles: Bifurcations, symmetry breaking, and soliton tunneling in a vortex-induced double well
journal, November 2012
- Pola, M.; Stockhofe, J.; Schmelcher, P.
- Physical Review A, Vol. 86, Issue 5
Dynamics of Bose-Einstein condensates in optical lattices
journal, February 2006
- Morsch, Oliver; Oberthaler, Markus
- Reviews of Modern Physics, Vol. 78, Issue 1
Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, oscillations, and macroscopic quantum self-trapping
journal, January 1999
- Raghavan, S.; Smerzi, A.; Fantoni, S.
- Physical Review A, Vol. 59, Issue 1
Transitions in coherent oscillations between two trapped Bose-Einstein condensates
journal, September 1999
- Raghavan, S.; Smerzi, A.; Kenkre, V. M.
- Physical Review A, Vol. 60, Issue 3
Macroscopic quantum fluctuations in the Josephson dynamics of two weakly linked Bose-Einstein condensates
journal, May 2000
- Smerzi, Augusto; Raghavan, Srikanth
- Physical Review A, Vol. 61, Issue 6
Direct Observation of Tunneling and Nonlinear Self-Trapping in a Single Bosonic Josephson Junction
journal, June 2005
- Albiez, Michael; Gati, Rudolf; Fölling, Jonas
- Physical Review Letters, Vol. 95, Issue 1
Coupled-mode theory for Bose-Einstein condensates
journal, February 2000
- Ostrovskaya, Elena A.; Kivshar, Yuri S.; Lisak, Mietek
- Physical Review A, Vol. 61, Issue 3
Bose-Einstein condensates in a one-dimensional double square well: Analytical solutions of the nonlinear Schrödinger equation
journal, December 2002
- Mahmud, K. W.; Kutz, J. N.; Reinhardt, W. P.
- Physical Review A, Vol. 66, Issue 6
Solitons in Bose–Einstein condensates trapped in a double-well potential
journal, February 2004
- Shchesnovich, Valery S.; Malomed, Boris A.; Kraenkel, Roberto A.
- Physica D: Nonlinear Phenomena, Vol. 188, Issue 3-4
Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond
journal, January 2006
- Ananikian, D.; Bergeman, T.
- Physical Review A, Vol. 73, Issue 1
Method for obtaining exact solutions of the nonlinear Schrödinger equation for a double-square-well potential
journal, February 2006
- Ziń, P.; Infeld, E.; Matuszewski, M.
- Physical Review A, Vol. 73, Issue 2
Bose–Einstein condensates in the presence of a magnetic trap and optical lattice: two-mode approximation
journal, August 2005
- Kapitula, Todd; Kevrekidis, P. G.
- Nonlinearity, Vol. 18, Issue 6
Symmetry breaking in symmetric and asymmetric double-well potentials
journal, November 2006
- Theocharis, G.; Kevrekidis, P. G.; Frantzeskakis, D. J.
- Physical Review E, Vol. 74, Issue 5
Ultracold Bosons in a Tilted Multilevel Double-Well Potential
journal, November 2007
- Dounas-Frazer, D. R.; Hermundstad, A. M.; Carr, L. D.
- Physical Review Letters, Vol. 99, Issue 20
Macroscopic self-trapping in Bose-Einstein condensates: Analysis of a dynamical quantum phase transition
journal, February 2010
- Juliá-Díaz, B.; Dagnino, D.; Lewenstein, M.
- Physical Review A, Vol. 81, Issue 2
Beyond-mean-field behavior of large Bose-Einstein condensates in double-well potentials
journal, September 2013
- Gertjerenken, Bettina; Weiss, Christoph
- Physical Review A, Vol. 88, Issue 3
Dynamic generation of spin-squeezed states in bosonic Josephson junctions
journal, August 2012
- Juliá-Díaz, B.; Zibold, T.; Oberthaler, M. K.
- Physical Review A, Vol. 86, Issue 2
Spontaneous symmetry breaking in a nonlinear double-well structure
journal, November 2008
- Mayteevarunyoo, Thawatchai; Malomed, Boris A.; Dong, Guangjiong
- Physical Review A, Vol. 78, Issue 5
Approximate model of soliton dynamics in all-optical couplers
journal, June 1990
- Paré, C.; Florjańczyk, M.
- Physical Review A, Vol. 41, Issue 11
Symmetry-Breaking Instability of Multimode Vector Solitons
journal, July 2002
- Cambournac, C.; Sylvestre, T.; Maillotte, H.
- Physical Review Letters, Vol. 89, Issue 8
Spontaneous symmetry breaking in photonic lattices: Theory and experiment
journal, June 2005
- Kevrekidis, P. G.; Chen, Zhigang; Malomed, B. A.
- Physics Letters A, Vol. 340, Issue 1-4
Classical Bifurcation at the Transition from Rabi to Josephson Dynamics
journal, November 2010
- Zibold, Tilman; Nicklas, Eike; Gross, Christian
- Physical Review Letters, Vol. 105, Issue 20
Dynamics of a Tunable Superfluid Junction
journal, January 2011
- LeBlanc, L. J.; Bardon, A. B.; McKeever, J.
- Physical Review Letters, Vol. 106, Issue 2
Floquet analysis of the modulated two-mode Bose-Hubbard model
journal, May 2012
- Watanabe, Gentaro; Mäkelä, Harri
- Physical Review A, Vol. 85, Issue 5
Kicked Bose–Hubbard systems and kicked tops—destruction and stimulation of tunneling
journal, January 2008
- Strzys, M. P.; Graefe, E. M.; Korsch, H. J.
- New Journal of Physics, Vol. 10, Issue 1
Coherent atomic oscillations and resonances between coupled Bose-Einstein condensates with time-dependent trapping potential
journal, July 2000
- Abdullaev, F. Kh.; Kraenkel, R. A.
- Physical Review A, Vol. 62, Issue 2
Nonlinear Phase Dynamics in a Driven Bosonic Josephson Junction
journal, June 2010
- Boukobza, Erez; Moore, Michael G.; Cohen, Doron
- Physical Review Letters, Vol. 104, Issue 24
Efficient creation of maximally entangled states by modulation of tunneling rates
journal, February 2010
- Watanabe, Gentaro
- Physical Review A, Vol. 81, Issue 2
Stability of multiple pulses in discrete systems
journal, February 2001
- Kapitula, T.; Kevrekidis, P. G.; Malomed, B. A.
- Physical Review E, Vol. 63, Issue 3
Collisions of matter-wave solitons
journal, November 2014
- Nguyen, Jason H. V.; Dyke, Paul; Luo, De
- Nature Physics, Vol. 10, Issue 12
Bose-Einstein condensates in the presence of a magnetic trap and optical lattice
journal, September 2005
- Kapitula, Todd; Kevrekidis, P. G.
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 15, Issue 3
Interaction of half-quantized vortices in two-component Bose-Einstein condensates
journal, June 2011
- Eto, Minoru; Kasamatsu, Kenichi; Nitta, Muneto
- Physical Review A, Vol. 83, Issue 6
Works referencing / citing this record:
Spontaneous generation of dark-bright and dark-antidark solitons upon quenching a particle-imbalanced bosonic mixture
journal, August 2019
- Kiehn, H.; Mistakidis, S. I.; Katsimiga, G. C.
- Physical Review A, Vol. 100, Issue 2