Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.063604· OSTI ID:21439512

Theocharis, G; Kevrekidis, P G ^[1]; Weller, A; Ronzheimer, J P; Gross, C; Oberthaler, M K ^[2]; Frantzeskakis, D J ^[3]

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1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States)
2. Kirchhoff Institut fuer Physik, INF 227, Universitaet Heidelberg, D-69120 Heidelberg (Germany)
3. Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens GR-15784 (Greece)

We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.

• OSTI ID: 21439512
• Journal Information: Physical Review. A, Vol. 81, Issue 6; Other Information: DOI: 10.1103/PhysRevA.81.063604; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOSE-EINSTEIN CONDENSATION
COLLISIONS
COMPARATIVE EVALUATIONS
EIGENFREQUENCY
EIGENSTATES
EQUATIONS OF MOTION
EXCITATION
HARMONIC OSCILLATORS
MEAN-FIELD THEORY
NONLINEAR PROBLEMS
POTENTIALS
RESONANCE
SOLITONS
STABILITY
TRAPS
VELOCITY
DIFFERENTIAL EQUATIONS
ENERGY-LEVEL TRANSITIONS
EQUATIONS
EVALUATION
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES