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

Journal of Experimental and Theoretical Physics

Flow of a Bose-Einstein condensate in a quasi-one-dimensional channel under the action of a piston

A. M. Kamchatnov, S. V. Korneev

Published Jan 1, 2010• 16 citations
Publisher

Abstract

The problem of the flow of a Bose—Einstein condensate in a channel under the action of a piston is considered. Problems of this kind are topical in connection with experiments on condensate flow control in quasi-one-dimensional (cigar-shaped) traps, in wh ich the repulsive potential produced by a laser beam focused across the trap acts as a piston. A dispersive shock wave characterized by rapid oscillations of the condensate density and flow velocity is shown to be formed in the condensate flow after some instant of time for an arbitrary law of piston motion. The Whitham averaging method is used to obtain a solution for the main parameters of the dispersive shock wave in the case of a uniformly accelerated piston motion. The evolution of the dispersive shock wave immediately after the breaking time, when the dispersionless solution is well approximated by a cubic parabola for the coordinate dependence of the density, is analyzed in the case of an arbitrary piston motion. Comparison shows good agreement of the numerical calculation with the approximate analytical theory. The developed theory complements the previously considered case of a piston moving with a constant velocity and is important for describing the condensate transport in atomic chips.

DOI
10.1134/s1063776110010206

Related papers

Wave Breaking in Dispersive Fluid Dynamics of the Bose–Einstein Condensate

A. M. Kamchatnov

Abstract The problem of wave breaking during its propagation in the Bose–Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form (–x)1/n. The evolution of the wave is described by the Gross–Pitaevskii equation so that a dispersive shock wave is formed as a result of breaking; this wave can be represented using the Gurevich–Pitaevskii approach as a modulated periodic solution to the Gross–Pitaevskii equation, and the evolution of the modulation parameters is described by the Whitham equations obtained by averaging the conservation laws over fast oscillations in the wave. The solution to the Whitham modulation equations is obtained in closed form for n = 2, 3, and the velocities of the dispersion shock wave edges for asymptotically long evolution times are determined for arbitrary integers n > 1. The problem considered here can be applied for describing the generation of dispersion shock waves observed in experiments with the Bose–Einstein condensate.

arXiv:1812.10683•Journal of Experimental and Theoretical Physics•Nov 1, 2018•10 citations

Expansion dynamics of a two-component quasi-one-dimensional Bose–Einstein condensate: Phase diagram, self-similar solutions, and dispersive shock waves

Sergey K. Ivanov, A. M. Kamchatnov

We investigate the expansion dynamics of a Bose–Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking into account the nonuniformity of the distributions of its components and construct the corresponding phase diagram in the plane of nonlinear interaction constants. The differential equations that describe the condensate evolution are derived by assuming that the condensate density and velocity depend on the spatial coordinate quadratically and linearly, respectively, which reproduces the initial equilibrium distribution of the condensate in the trap in the Thomas–Fermi approximation. We have obtained self-similar solutions of these differential equations for several important special cases and write out asymptotic formulas describing the condensate motion on long time scales, when the condensate density becomes so low that the interaction between atoms may be neglected. The problem on the dynamics of immiscible components with the formation of dispersive shock waves is considered. We compare the numerical solutions of the Gross–Pitaevskii equations with their approximate analytical solutions and numerically study the situations where the analytical method being used admits no exact solutions.

arXiv:1705.03708•Journal of Experimental and Theoretical Physics•Apr 1, 2017•4 citations

Transcritical flow of a Bose-Einstein condensate through a penetrable barrier

Antin M. Leszczyszyn, Gennady A. El, Yu. G. Gladush +1 more

The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the locally steady ``hydraulic'' solution of the one-dimensional Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters, the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train, and the drag force are determined in terms of the Bose-Einstein condensate oncoming flow velocity and the strength of the potential barrier. Good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.

arXiv:0901.3767•Physical Review A•Jun 3, 2009•47 citations

Shock Waves in a Bose-Einstein Condensate

Igor K. Kulikov, Michail A. Zak

A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.

•Jun 1, 2005•0 citations

Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics

Mark A. Hoefer, Mark J. Ablowitz, Ian R. Coddington +3 more

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.

arXiv:cond-mat/0603389•Physical Review A•Aug 29, 2006•318 citations

Dynamics of macroscopic tunneling in elongated Bose-Einstein condensates

G. Dekel, O. V. Farberovich, V. Fleurov +1 more

We investigate macroscopic tunneling from an elongated quasi-one-dimensional trap, forming a ``cigar-shaped'' Bose-Einstein condensate (BEC). Using a recently developed formalism we get the leading analytical approximation for the right-hand side of the potential wall, i.e., outside the trap, and a formalism based on Wigner functions, for the left side of the potential wall, i.e., inside the BEC. We then present accomplished results of numerical calculations, which show a ``blip'' in the particle density traveling with an asymptotic shock velocity, as resulted from previous works on a dotlike trap but with significant differences from the latter. Inside the BEC a pattern of a traveling dispersive shock wave is revealed. In the attractive case, we find trains of bright solitons frozen near the boundary.

arXiv:0911.1537•Physical Review A•Jun 28, 2010•14 citations
The problem of the flow of a Bose—Einstein condensate in a channel under the action of a piston is considered. Problems of this kind are topical in connection with experiments on condensate flow control in quasi-one-dimensional (cigar-shaped) traps, in wh ich the repulsive potential produced by a laser beam focused across the trap acts as a piston. A dispersive shock wave characterized by rapid oscillations of the condensate density and flow velocity is shown to be formed in the condensate flow after some instant of time for an arbitrary law of piston motion. The Whitham averaging method is used to obtain a solution for the main parameters of the dispersive shock wave in the case of a uniformly accelerated piston motion. The evolution of the dispersive shock wave immediately after the breaking time, when the dispersionless solution is well approximated by a cubic parabola for the coordinate dependence of the density, is analyzed in the case of an arbitrary piston motion. Comparison shows good agreement of the numerical calculation with the approximate analytical theory. The developed theory complements the previously considered case of a piston moving with a constant velocity and is important for describing the condensate transport in atomic chips.
Abstract The problem of wave breaking during its propagation in the Bose–Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form (–x)1/n. The evolution of the wave is described by the Gross–Pitaevskii equation so that a dispersive shock wave is formed as a result of breaking; this wave can be represented using the Gurevich–Pitaevskii approach as a modulated periodic solution to the Gross–Pitaevskii equation, and the evolution of the modulation parameters is described by the Whitham equations obtained by averaging the conservation laws over fast oscillations in the wave. The solution to the Whitham modulation equations is obtained in closed form for n = 2, 3, and the velocities of the dispersion shock wave edges for asymptotically long evolution times are determined for arbitrary integers n > 1. The problem considered here can be applied for describing the generation of dispersion shock waves observed in experiments with the Bose–Einstein condensate.
We investigate the expansion dynamics of a Bose–Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking into account the nonuniformity of the distributions of its components and construct the corresponding phase diagram in the plane of nonlinear interaction constants. The differential equations that describe the condensate evolution are derived by assuming that the condensate density and velocity depend on the spatial coordinate quadratically and linearly, respectively, which reproduces the initial equilibrium distribution of the condensate in the trap in the Thomas–Fermi approximation. We have obtained self-similar solutions of these differential equations for several important special cases and write out asymptotic formulas describing the condensate motion on long time scales, when the condensate density becomes so low that the interaction between atoms may be neglected. The problem on the dynamics of immiscible components with the formation of dispersive shock waves is considered. We compare the numerical solutions of the Gross–Pitaevskii equations with their approximate analytical solutions and numerically study the situations where the analytical method being used admits no exact solutions.
The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the locally steady ``hydraulic'' solution of the one-dimensional Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters, the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train, and the drag force are determined in terms of the Bose-Einstein condensate oncoming flow velocity and the strength of the potential barrier. Good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.
A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.
A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.
We investigate macroscopic tunneling from an elongated quasi-one-dimensional trap, forming a ``cigar-shaped'' Bose-Einstein condensate (BEC). Using a recently developed formalism we get the leading analytical approximation for the right-hand side of the potential wall, i.e., outside the trap, and a formalism based on Wigner functions, for the left side of the potential wall, i.e., inside the BEC. We then present accomplished results of numerical calculations, which show a ``blip'' in the particle density traveling with an asymptotic shock velocity, as resulted from previous works on a dotlike trap but with significant differences from the latter. Inside the BEC a pattern of a traveling dispersive shock wave is revealed. In the attractive case, we find trains of bright solitons frozen near the boundary.