© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1407.7915 · Physical Review A

Metastability, excitations, fluctuations, and multiple-swallowtail structures of a superfluid in a Bose-Einstein condensate in the presence of a uniformly moving defect

Masaya Kunimi, Yusuke S. Kato

Published May 11, 2015• 17 citations

Abstract

We solve the Gross-Pitaevskii (GP) and Bogoliubov equations to investigate the metastability of superfluidity in a Bose-Einstein condensate in the presence of a uniformly moving defect potential in a two-dimensional torus. We calculate the total energy and momentum as functions of the driving velocity of the moving defect and find metastable states with negative effective mass near the critical velocity. We also find that the first excited energy (energy gap) in the finite-sized torus closes at the critical velocity, that it obeys one-fourth power-law scaling, and that the dynamical fluctuation of the density (amplitude of the order parameter) is strongly enhanced near the critical velocity. We confirm the validity of our results near the critical velocity by calculating the quantum depletion. We find an unconventional swallowtail structure (multiple-swallowtail structure) through calculations of the unstable stationary solutions of the GP equation.

DOI: 10.1103/physreva.91.053608

Related papers

Superfluid dynamics of a Bose–Einstein condensate in a periodic potential

C Menotti, A Smerzi, A Trombettoni

We investigate the superfluid properties of a Bose–Einstein condensate (BEC) trapped in a one-dimensional periodic potential. We study, both analytically (in the tight binding limit) and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubov dispersion relation, and we introduce two different, density dependent, effective masses and group velocities. The Bogoliubov spectrum predicts the existence of sound waves, and the arising of energetic and dynamical instabilities at critical values of the BEC quasi-momentum which dramatically affect its coherence properties. We investigate the dependence of the dipole and Bloch oscillation frequencies in terms of an effective mass averaged over the density of the condensate. We illustrate our results with several animations obtained solving numerically the time-dependent Gross–Pitaevskii equation.

arXiv:cond-mat/0310780•New Journal of Physics•Sep 15, 2003•89 citations

Thermodynamics of solitonic matter waves in a toroidal trap

Luca Salasnich, Alberto Parola, L. Reatto

We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov--de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime, three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state, and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.

arXiv:cond-mat/0609167•Physical Review A•Sep 19, 2006•15 citations

Collapse of the metastable state in an attractive Bose-Einstein condensate

Jae Gil Kim, Yoon-Hyuck Sean Choi, Eok Kyun Lee

The characteristic features of the collapse of the ground state in trapped one-component attractive Bose-Einstein condensates are studied by applying the catastrophe theory. From numerically obtained stable and unstable solutions of the Gross-Pitaevskii equation, we derive the catastrophe function defining the stability of the stationary points on the Gross-Pitaevskii energy functional. The bifurcation diagram and the universal scaling laws stemming from the catastrophe function show quantitative agreement with the numerical results.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 12, 2002•4 citations

Bose-Einstein condensate confined in a one-dimensional ring stirred with a rotating delta link

Axel Pérez-Obiol, Taksu Cheon

We consider a Bose-Einstein condensate with repulsive interactions confined in a one-dimensional ring where a Dirac δ is rotating at constant speed. The spectrum of stationary solutions in the δ comoving frame is analyzed in terms of the nonlinear coupling, δ velocity, and δ strength, which may take positive and negative values. It is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting of bright solitons, gray and dark solitonic trains, and vortex states. Analytical expressions in terms of Jacobi elliptic functions are provided for the wave functions and chemical potentials. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray and dark solitons, and vortex states of arbitrary quantized angular momenta, are obtained from the ground state by setting and unsetting a rotating δ. These cycles are reproduced by simulations of the time-dependent Gross-Pitaevskii equation with a rotating Gaussian link.

arXiv:1907.04574•Physical review. E•Feb 18, 2020•11 citations

Dynamical Density Fluctuations of Superfluids near the Critical Velocity

Yusuke S. Kato, Shohei Watabe

We propose a stability criterion of superfluids in condensed Bose-Einstein systems, which incorporates the spectral function or the autocorrelation function of the local density. Within the Gross-Pitaevskii-Bogoliubov theory, we demonstrate the validity of our criterion for the soliton-emission instability, with use of explicit forms of zero modes of the Bogoliubov equation and a dynamical scaling near the saddle-node bifurcation. We also show that the criterion is applicable to the Landau phonon instability and the Landau roton instability within the single-mode approximation.

arXiv:1006.2999•Physical Review Letters•Jul 16, 2010•12 citations

Superfluidity and Critical Velocities in Nonequilibrium Bose-Einstein Condensates

Michiel Wouters, Iacopo Carusotto

We theoretically study the superfluidity properties of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity under incoherent pumping. The dynamics of the condensate is described at mean-field level in terms of a generalized Gross-Pitaevskii equation. The drag force on a small moving object and the onset of fringes in the density profile are shown to have a sharp threshold as a function of the velocity; a generalized Landau criterion is developed to explain this behavior in terms of the dispersion of elementary excitations. Metastability of supercurrents in multiply-connected geometries is shown to persist up to higher flow speeds.

Physical Review Letters•Jul 8, 2010•156 citations

We solve the Gross-Pitaevskii (GP) and Bogoliubov equations to investigate the metastability of superfluidity in a Bose-Einstein condensate in the presence of a uniformly moving defect potential in a two-dimensional torus. We calculate the total energy and momentum as functions of the driving velocity of the moving defect and find metastable states with negative effective mass near the critical velocity. We also find that the first excited energy (energy gap) in the finite-sized torus closes at the critical velocity, that it obeys one-fourth power-law scaling, and that the dynamical fluctuation of the density (amplitude of the order parameter) is strongly enhanced near the critical velocity. We confirm the validity of our results near the critical velocity by calculating the quantum depletion. We find an unconventional swallowtail structure (multiple-swallowtail structure) through calculations of the unstable stationary solutions of the GP equation.

We investigate the superfluid properties of a Bose–Einstein condensate (BEC) trapped in a one-dimensional periodic potential. We study, both analytically (in the tight binding limit) and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubov dispersion relation, and we introduce two different, density dependent, effective masses and group velocities. The Bogoliubov spectrum predicts the existence of sound waves, and the arising of energetic and dynamical instabilities at critical values of the BEC quasi-momentum which dramatically affect its coherence properties. We investigate the dependence of the dipole and Bloch oscillation frequencies in terms of an effective mass averaged over the density of the condensate. We illustrate our results with several animations obtained solving numerically the time-dependent Gross–Pitaevskii equation.

We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov--de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime, three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state, and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.

The characteristic features of the collapse of the ground state in trapped one-component attractive Bose-Einstein condensates are studied by applying the catastrophe theory. From numerically obtained stable and unstable solutions of the Gross-Pitaevskii equation, we derive the catastrophe function defining the stability of the stationary points on the Gross-Pitaevskii energy functional. The bifurcation diagram and the universal scaling laws stemming from the catastrophe function show quantitative agreement with the numerical results.

We consider a Bose-Einstein condensate with repulsive interactions confined in a one-dimensional ring where a Dirac δ is rotating at constant speed. The spectrum of stationary solutions in the δ comoving frame is analyzed in terms of the nonlinear coupling, δ velocity, and δ strength, which may take positive and negative values. It is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting of bright solitons, gray and dark solitonic trains, and vortex states. Analytical expressions in terms of Jacobi elliptic functions are provided for the wave functions and chemical potentials. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray and dark solitons, and vortex states of arbitrary quantized angular momenta, are obtained from the ground state by setting and unsetting a rotating δ. These cycles are reproduced by simulations of the time-dependent Gross-Pitaevskii equation with a rotating Gaussian link.

We propose a stability criterion of superfluids in condensed Bose-Einstein systems, which incorporates the spectral function or the autocorrelation function of the local density. Within the Gross-Pitaevskii-Bogoliubov theory, we demonstrate the validity of our criterion for the soliton-emission instability, with use of explicit forms of zero modes of the Bogoliubov equation and a dynamical scaling near the saddle-node bifurcation. We also show that the criterion is applicable to the Landau phonon instability and the Landau roton instability within the single-mode approximation.

We theoretically study the superfluidity properties of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity under incoherent pumping. The dynamics of the condensate is described at mean-field level in terms of a generalized Gross-Pitaevskii equation. The drag force on a small moving object and the onset of fringes in the density profile are shown to have a sharp threshold as a function of the velocity; a generalized Landau criterion is developed to explain this behavior in terms of the dispersion of elementary excitations. Metastability of supercurrents in multiply-connected geometries is shown to persist up to higher flow speeds.