Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0406497 · Physical Review A

Solitary-wave description of condensate micromotion in a time-averaged orbiting potential trap

Katharine J. Challis, R. J. Ballagh, Crispin W. Gardiner

Published Nov 10, 2004• 5 citations
arXivHTMLPDF

Abstract

We present a detailed theoretical analysis of micromotion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time-dependent behavior of the trap systematically approximated to reduce the trapping potential to its dominant terms. We show that within some well specified approximations, the dynamic trap has solitary-wave solutions, and we identify a moving frame of reference which provides the most natural description of the system. In that frame eigenstates of the time-averaged orbiting potential trap can be found, all of which must be solitary-wave solutions with identical, circular center of mass motion in the laboratory frame. The validity regime for our treatment is carefully defined, and is shown to be satisfied by existing experimental systems.

DOI
10.1103/physreva.70.053605

Related papers

Bragg spectroscopy of an accelerating condensate with solitary-wave behavior

Katharine J. Challis, R. J. Ballagh

We present a theoretical treatment of Bragg spectroscopy of an accelerating condensate in a solitary-wave state. Our treatment is based on the Gross-Pitaevskii equation with an optical potential representing the Bragg pulse and an additional external time-dependent potential generating the solitary-wave behavior. By transforming to a frame translating with the condensate, we derive an approximate set of equations that can be readily solved to generate approximate Bragg spectra. Our analytic method is accurate within a well-defined parameter regime and provides physical insight into the structure of the spectra. We illustrate our formalism using the example of Bragg spectroscopy of a condensate in a time-averaged orbiting potential trap.

arXiv:cond-mat/0410168•Physical Review A•Mar 18, 2005•0 citations

Manipulation of a Bose-Einstein condensate by a time-averaged orbiting potential using phase jumps of the rotating field

Paul W. Cleary, Tom W. Hijmans, Jook T. M. Walraven

We report on the manipulation of the center-of-mass motion (``sloshing'') of a Bose-Einstein condensate in a time-averaged orbiting potential (TOP) trap. We start with a condensate at rest in the center of a static trapping potential. When suddenly replacing the static trap with a TOP trap centered about the same position, the condensate starts to slosh with an amplitude much larger than the TOP micromotion. We show, both theoretically and experimentally, that the direction of sloshing is related to the initial phase of the rotating magnetic field of the TOP. We show further that the sloshing can be quenched by applying a carefully timed and sized jump in the phase of the rotating field.

arXiv:1009.5565•Physical Review A•Dec 30, 2010•8 citations

Bright solitary-matter-wave collisions in a harmonic trap: Regimes of solitonlike behavior

Alan D. Martin, Charles S. Adams, S. A. Gardiner

Systems of solitary waves in the one-dimensional Gross-Pitaevskii equation, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. To analyze the soliton nature of these solitary waves, a particle analogy for the solitary waves is formulated. Exact soliton solutions exist in the absence of an external trapping potential, which behave in a particlelike manner, and we find the particle analogy we employ to be a good model also when a harmonic trapping potential is present up to a gradual shift in the trajectories when the harmonic trap period is short compared with the collision time of the solitons. We find that the collision time of the solitons is dependent on the relative phase of the solitons as they collide. In the case of two solitons, the particle model is integrable, and the dynamics are completely regular. In the case of a system of two solitary waves of equal norm, the solitons are shown to retain their phase difference for repeated collisions. This phase preservation can be used to find regimes where there is agreement between the wave and particle models. This also implies that soliton regimes may be found in three-dimensional geometries where solitary waves can be made to repeatedly collide out of phase, stabilizing the condensate against collapse. The extension to three particles supports both regular and chaotic regimes. The trajectory shift observed for two solitons carries over to the case of three solitons. This shift aside, the agreement between the particle model and the wave dynamics remains good, even in chaotic regimes.

arXiv:0709.2004•Physical Review A•Jan 25, 2008•47 citations

Bragg spectroscopy with an accelerating Bose-Einstein condensate

R. Geursen, N. R. Thomas, A. C. Wilson

We present the results of Bragg spectroscopy performed on an accelerating Bose-Einstein condensate. The Bose-Einstein condensate undergoes circular micromotion in a magnetic time-averaged orbiting potential trap and the effect of this motion on the Bragg spectrum is analyzed. A simple frequency modulation model is used to interpret the observed complex structure, and broadening effects are considered using numerical solutions to the Gross-Pitaevskii equation.

arXiv:cond-mat/0307224•Physical Review A•Oct 9, 2003•7 citations

Explicit solutions to an effective Gross–Pitaevskii equation: One-dimensional Bose–Einstein condensate in specific traps

Emmanuel Kengne, X. X. Liu, Boris A. Malomed +2 more

An effective Gross–Pitaevskii equation, which describes the dynamics of quasi-one-dimensional Bose–Einstein condensates in specific potential traps, is considered, and new families of exact solutions are reported, which include periodic and solitary waves. The solutions are applied to the description of BEC patterns trapped in optical-lattice potentials.

Journal of Mathematical Physics•Feb 1, 2008•17 citations

Investigation of oscillations of a soliton of a bose condensate of atoms in a trap in the limit of small oscillations of its walls

Nikolay A. Veretenov, Leonid A. Nesterov, Nikolay N. Rosanov

The motion of the center of a soliton in a trap with oscillating walls is studied analytically and numerically for the case in which the intrinsic frequency of small soliton oscillations in the equilibrium state considerably exceeds the frequency of wall oscillations. this problem can be solved either by applying the gross–pitaevskii equation, which most exactly describes the behavior of the soliton in the trap, or by using the approximate, “mechanical,” equation of motion of the newtonian type for the center of the soliton. an approximate analytical solution of the mechanical equation is obtained and is compared with the numerical solution of the newton equation, while the latter solution is compared with the numerical solution of the gross–pitaevskii equation. good agreement between the first two solutions is revealed. it is also shown that there is a range of parameters in which the numerical solutions of the newton and gross–pitaevskii equations are closest to each other. the frequency-sweeping effect of soliton center oscillations is revealed. an approximate analytical formula for the limiting frequency of these oscillations is obtained and the numerical analysis of this phenomenon is performed.

Optics and Spectroscopy•Jun 1, 2016•1 citation
We present a detailed theoretical analysis of micromotion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time-dependent behavior of the trap systematically approximated to reduce the trapping potential to its dominant terms. We show that within some well specified approximations, the dynamic trap has solitary-wave solutions, and we identify a moving frame of reference which provides the most natural description of the system. In that frame eigenstates of the time-averaged orbiting potential trap can be found, all of which must be solitary-wave solutions with identical, circular center of mass motion in the laboratory frame. The validity regime for our treatment is carefully defined, and is shown to be satisfied by existing experimental systems.
We present a theoretical treatment of Bragg spectroscopy of an accelerating condensate in a solitary-wave state. Our treatment is based on the Gross-Pitaevskii equation with an optical potential representing the Bragg pulse and an additional external time-dependent potential generating the solitary-wave behavior. By transforming to a frame translating with the condensate, we derive an approximate set of equations that can be readily solved to generate approximate Bragg spectra. Our analytic method is accurate within a well-defined parameter regime and provides physical insight into the structure of the spectra. We illustrate our formalism using the example of Bragg spectroscopy of a condensate in a time-averaged orbiting potential trap.
We report on the manipulation of the center-of-mass motion (``sloshing'') of a Bose-Einstein condensate in a time-averaged orbiting potential (TOP) trap. We start with a condensate at rest in the center of a static trapping potential. When suddenly replacing the static trap with a TOP trap centered about the same position, the condensate starts to slosh with an amplitude much larger than the TOP micromotion. We show, both theoretically and experimentally, that the direction of sloshing is related to the initial phase of the rotating magnetic field of the TOP. We show further that the sloshing can be quenched by applying a carefully timed and sized jump in the phase of the rotating field.
Systems of solitary waves in the one-dimensional Gross-Pitaevskii equation, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. To analyze the soliton nature of these solitary waves, a particle analogy for the solitary waves is formulated. Exact soliton solutions exist in the absence of an external trapping potential, which behave in a particlelike manner, and we find the particle analogy we employ to be a good model also when a harmonic trapping potential is present up to a gradual shift in the trajectories when the harmonic trap period is short compared with the collision time of the solitons. We find that the collision time of the solitons is dependent on the relative phase of the solitons as they collide. In the case of two solitons, the particle model is integrable, and the dynamics are completely regular. In the case of a system of two solitary waves of equal norm, the solitons are shown to retain their phase difference for repeated collisions. This phase preservation can be used to find regimes where there is agreement between the wave and particle models. This also implies that soliton regimes may be found in three-dimensional geometries where solitary waves can be made to repeatedly collide out of phase, stabilizing the condensate against collapse. The extension to three particles supports both regular and chaotic regimes. The trajectory shift observed for two solitons carries over to the case of three solitons. This shift aside, the agreement between the particle model and the wave dynamics remains good, even in chaotic regimes.
The motion of the center of a soliton in a trap with oscillating walls is studied analytically and numerically for the case in which the intrinsic frequency of small soliton oscillations in the equilibrium state considerably exceeds the frequency of wall oscillations. this problem can be solved either by applying the gross–pitaevskii equation, which most exactly describes the behavior of the soliton in the trap, or by using the approximate, “mechanical,” equation of motion of the newtonian type for the center of the soliton. an approximate analytical solution of the mechanical equation is obtained and is compared with the numerical solution of the newton equation, while the latter solution is compared with the numerical solution of the gross–pitaevskii equation. good agreement between the first two solutions is revealed. it is also shown that there is a range of parameters in which the numerical solutions of the newton and gross–pitaevskii equations are closest to each other. the frequency-sweeping effect of soliton center oscillations is revealed. an approximate analytical formula for the limiting frequency of these oscillations is obtained and the numerical analysis of this phenomenon is performed.