Dark solitons as quasiparticles in trapped condensates

Journal Article · Mon May 15 04:00:00 EDT 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.73.0· OSTI ID:20787282

Brazhnyi, V A ^[1]; Konotop, V V ^[2]; Pitaevskii, L P ^[3]

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1. Centro de Fisica Teorica e Computacional, Universidade de Lisboa, Complexo Interdisciplinar, Avenida Professor Gama Pinto 2, Lisboa 1649-003 (Portugal)
2. Centro de Fisica Teorica e Computacional, Universidade de Lisboa, Complexo Interdisciplinar, Avenida Professor Gama Pinto 2, Lisbon 1649-003 (Portugal)
3. Dipartimento di Fisica, Universita di Trento and Istituto Nazionale per la Fisica della Materia, CNR-BEC, 38050 Trento (Italy) and Kapitza Institute for Physical Problems, 119334 Moscow (Russian Federation)

We present a theory of dark soliton dynamics in trapped quasi-one-dimensional Bose-Einstein condensates, which is based on the local-density approximation. The approach is applicable for arbitrary polynomial nonlinearities of the mean-field equation governing the system as well as to arbitrary polynomial traps. In particular, we derive a general formula for the frequency of the soliton oscillations in confining potentials. A special attention is dedicated to the study of the soliton dynamics in adiabatically varying traps. It is shown that the dependence of the amplitude of oscillations vs the trap frequency (strength) is given by the scaling law X{sub 0}{proportional_to}{omega}{sup -{gamma}} where the exponent {gamma} depends on the type of the two-body interactions, on the exponent of the polynomial confining potential, on the density of the condensate, and on the initial soliton velocity. Analytical results obtained within the framework of the local-density approximation are compared with the direct numerical simulations of the dynamics, showing a remarkable match. Various limiting cases are addressed. In particular for the slow solitons we computed a general formula for the effective mass and for the frequency of oscillations.

• OSTI ID: 20787282
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 73; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
AMPLITUDES
APPROXIMATIONS
BOSE-EINSTEIN CONDENSATION
COMPUTERIZED SIMULATION
DENSITY
DENSITY FUNCTIONAL METHOD
EFFECTIVE MASS
MEAN-FIELD THEORY
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
OSCILLATIONS
POLYNOMIALS
POTENTIALS
SCALING LAWS
SOLITONS
TRAPPING
TRAPS
TWO-BODY PROBLEM