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

Physical review. B, Condensed matter

Instability and stratification of a two-component Bose-Einstein condensate in a trapped ultracold gas

Eugene P. Bashkin, Alexei Vagov

Published Sep 1, 1997• 92 citations
Publisher

Abstract

The thermodynamic stability of a trapped Bose gas with a two-component condensate, e.g., a gas of atoms in two distinct hyperfine states or a binary gaseous mixture, is considered on the basis of modified Gross-Pitaevskii equations. Under certain conditions the system becomes unstable with respect to stratification, i.e., to spatial separation between the two condensates. One condensate assumes a donutlike spatial distribution, while the other retains a centered distribution. Possible applications of the theory to recent experimental data on two overlapping condensates in ${}^{87}$Rb are discussed.

DOI
10.1103/physrevb.56.6207

Related papers

Modulation Instability in Two Component Bose-Einstein Condensate with Dissipation

A. P. Ivashin, Elena Marinenko

In this paper, we consider the dynamic evolution of a binary mixture of a Bose-Einstein condensate taking into account the presence of dissipation inside the components. Using the introduction of the dissipative function, the modified Gross-Pitaevskii equations are obtained. These equations, in contrast to the usual Gross-Pitaevskii equations for two-component condensate, allow us to take into account the dissipation in the system. The influence of dissipative processes on the development of modulation instability in a spatially homogeneous two-component Bose-Einstein condensate is investigated. In contrast to the one-component Bose-Einstein condensate, in which modulation instability arises only when there are forces of attraction between atoms, in a two-component Bose-Einstein condensate nonlinear dynamics, leading to modulation instability is more complex. It essentially depends on the signs and values of the constant interaction of the components, which leads to a greater variety of possible scenarios for the development of modulation instability. The paper considers two cases. The first case is when repulsive forces act inside the components, and the second is when repulsive forces act in the first component, and in the second one - attractive forces. At the same time, the situation when there is a repulsion in the first component, and attraction between the particles in the second component differs significantly from the case of only positive interaction inside the components. The relations between the interaction constants that determine the development of the modulation instability turn out to be different. Given the relations between the interaction constants, taking into account dissipation processes, the occurrence of modulation instability in two-component Bose-Einstein condensates was studied, the maximum growth rate of oscillations was found, and the limits of the existence of modulation instability in the space of wave numbers were found. It is shown that the small effect of dissipation on the modulation instability in the Bose – Einstein condensate is explained not only by the smallness of the friction forces. For wave vectors corresponding to a mode with a maximum increment, the contribution of dissipation in the linear approximation with respect to the dissipative parameter is strictly zero. Thus, the condition for the development of the most rapidly growing mode of oscillations, which determines the beginning of the modulation instability, remains the same as in the nondissipative case.

East European Journal of Physics•Jan 1, 2019•1 citation

Modulational Instability of Trapped Two-Component Bose–Einstein Condensates*

Jian-Wen Zhou, X. X. Li, Rui Gao +4 more

Abstract The modulational instability of two-component Bose–Einstein condensates (BECs) under an external parabolic potential is discussed. Based on the trapped two-component Gross–Pitaevskill equations, a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis. It is shown that a modulational unstable time scale exists for trapped two-component BECs. The modulational properties—which are determined by the wave number, external trapping parameter, intra- and inter-species atomic interactions—are modified significantly. The analytical results are confirmed by direct numerical simulation. Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.

Chinese Physics Letters•Sep 1, 2019•3 citations

Vortex excitations in binary mixture of trapped Bose-Einstein condensates

Dmitry V. Skryabin

Summary form only given. I present results of the detailed asymptotic and numerical results on stability of unit and higher order vortices in coupled Gross-Pitaevskii equations, which model the experimental work. Low lying eigenfrequencies, including ones generating instability of the unit vortex placed in one component of a binary mixture of BEC, have been calculated applying perturbative theory in the limit of the weak interparticle interaction. Results of the perturbative theory have been verified and significantly extended using numerical analysis of the linearised equations for excitations and direct numerical simulation of the coupled Gross-Pitaevskii equations. Two main instability mechanisms have been identified and their dependencies on the relative number of the particles in the condensates and on the strength of the inter-species interaction have been studied. The first mechanism is the drift instability induced by the vortex free component of the condensate and resulting in the motion of the vortex out of the condensate center to its periphery. The second mechanism is the splitting of the higher order vortices into unit ones. Absolute and/or relative increase of the number of particles in the vortex free condensate component has been found to have stabilizing effect on both drift and splitting instabilities. Different scenarios of the splitting instabilities have been found.

Conference on Lasers and Electro-Optics•Aug 29, 2005•0 citations

Stability and dynamics of a two-component Bose-Einstein condensate in ring ladders

Eulàlia Nicolau Jiménez

We investigate the dynamics of a two-component Bose-Einstein condensate trapped in two coupled rings in ladder configuration. First, we derive from the two-component Gross-Pitaevskii equation a few state model for the angular momentum modes. Then, we analyse the stability of the stationary states by solving the Bogoliubov-de Gennes equations. Also, we study the dynamics of the system for an arbitrary population imbalance between the rings, characterizing the transition from Josephson oscillations to quantum self-trapping. We also derive the self-trapping condition for the bosonic mixture, finding simultaneous self-trapping of the two components.

•Jul 19, 2018•0 citations

Stable and unstable regimes in Bose-Fermi mixtures with attraction between components

A. M. Belemuk, Valentin Nikolaevich Ryzhov, S. T. Chui

The collapse of a trapped boson-fermion mixture with attraction between bosons and fermions is investigated in the framework of the effective Hamiltonian for the Bose system. The properties of an $^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}$ mixture are analyzed quantitatively at $T=0$. We find numerically solutions of the modified Gross-Pitaevskii equation which continuously go from the stable to the unstable branch. We discuss how the conditions for the onset of collapse are related to the macroscopic properties of the system. A comparison with the case of a Bose condensate of the atomic $^{7}\mathrm{Li}$ system is given.

arXiv:cond-mat/0612572•Physical Review A•Jul 9, 2007•16 citations

Modulation instability and solitary-wave formation in two-component Bose-Einstein condensates

Kenichi Kasamatsu, Makoto Tsubota

We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled Gross-Pitaevskii equations. The unstable modulation grows from initially miscible condensates into various types of vector solitary waves, depending on the combinations of the sign of the coupling constants (intracomponent and intercomponent). We discuss the detailed features of the modulation instability, dynamics of solitary wave formation, and an analogy with the collapsing dynamics in a single-component condensate with attractive interactions.

arXiv:cond-mat/0603838•Physical Review A•Jul 18, 2006•112 citations
The thermodynamic stability of a trapped Bose gas with a two-component condensate, e.g., a gas of atoms in two distinct hyperfine states or a binary gaseous mixture, is considered on the basis of modified Gross-Pitaevskii equations. Under certain conditions the system becomes unstable with respect to stratification, i.e., to spatial separation between the two condensates. One condensate assumes a donutlike spatial distribution, while the other retains a centered distribution. Possible applications of the theory to recent experimental data on two overlapping condensates in 87{}^{87}87Rb are discussed.
In this paper, we consider the dynamic evolution of a binary mixture of a Bose-Einstein condensate taking into account the presence of dissipation inside the components. Using the introduction of the dissipative function, the modified Gross-Pitaevskii equations are obtained. These equations, in contrast to the usual Gross-Pitaevskii equations for two-component condensate, allow us to take into account the dissipation in the system. The influence of dissipative processes on the development of modulation instability in a spatially homogeneous two-component Bose-Einstein condensate is investigated. In contrast to the one-component Bose-Einstein condensate, in which modulation instability arises only when there are forces of attraction between atoms, in a two-component Bose-Einstein condensate nonlinear dynamics, leading to modulation instability is more complex. It essentially depends on the signs and values of the constant interaction of the components, which leads to a greater variety of possible scenarios for the development of modulation instability. The paper considers two cases. The first case is when repulsive forces act inside the components, and the second is when repulsive forces act in the first component, and in the second one - attractive forces. At the same time, the situation when there is a repulsion in the first component, and attraction between the particles in the second component differs significantly from the case of only positive interaction inside the components. The relations between the interaction constants that determine the development of the modulation instability turn out to be different. Given the relations between the interaction constants, taking into account dissipation processes, the occurrence of modulation instability in two-component Bose-Einstein condensates was studied, the maximum growth rate of oscillations was found, and the limits of the existence of modulation instability in the space of wave numbers were found. It is shown that the small effect of dissipation on the modulation instability in the Bose – Einstein condensate is explained not only by the smallness of the friction forces. For wave vectors corresponding to a mode with a maximum increment, the contribution of dissipation in the linear approximation with respect to the dissipative parameter is strictly zero. Thus, the condition for the development of the most rapidly growing mode of oscillations, which determines the beginning of the modulation instability, remains the same as in the nondissipative case.
Abstract The modulational instability of two-component Bose–Einstein condensates (BECs) under an external parabolic potential is discussed. Based on the trapped two-component Gross–Pitaevskill equations, a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis. It is shown that a modulational unstable time scale exists for trapped two-component BECs. The modulational properties—which are determined by the wave number, external trapping parameter, intra- and inter-species atomic interactions—are modified significantly. The analytical results are confirmed by direct numerical simulation. Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.
Summary form only given. I present results of the detailed asymptotic and numerical results on stability of unit and higher order vortices in coupled Gross-Pitaevskii equations, which model the experimental work. Low lying eigenfrequencies, including ones generating instability of the unit vortex placed in one component of a binary mixture of BEC, have been calculated applying perturbative theory in the limit of the weak interparticle interaction. Results of the perturbative theory have been verified and significantly extended using numerical analysis of the linearised equations for excitations and direct numerical simulation of the coupled Gross-Pitaevskii equations. Two main instability mechanisms have been identified and their dependencies on the relative number of the particles in the condensates and on the strength of the inter-species interaction have been studied. The first mechanism is the drift instability induced by the vortex free component of the condensate and resulting in the motion of the vortex out of the condensate center to its periphery. The second mechanism is the splitting of the higher order vortices into unit ones. Absolute and/or relative increase of the number of particles in the vortex free condensate component has been found to have stabilizing effect on both drift and splitting instabilities. Different scenarios of the splitting instabilities have been found.
We investigate the dynamics of a two-component Bose-Einstein condensate trapped in two coupled rings in ladder configuration. First, we derive from the two-component Gross-Pitaevskii equation a few state model for the angular momentum modes. Then, we analyse the stability of the stationary states by solving the Bogoliubov-de Gennes equations. Also, we study the dynamics of the system for an arbitrary population imbalance between the rings, characterizing the transition from Josephson oscillations to quantum self-trapping. We also derive the self-trapping condition for the bosonic mixture, finding simultaneous self-trapping of the two components.
The collapse of a trapped boson-fermion mixture with attraction between bosons and fermions is investigated in the framework of the effective Hamiltonian for the Bose system. The properties of an 87Rb^{87}\mathrm{Rb}87Rb and 40K^{40}\mathrm{K}40K mixture are analyzed quantitatively at T=0T=0T=0. We find numerically solutions of the modified Gross-Pitaevskii equation which continuously go from the stable to the unstable branch. We discuss how the conditions for the onset of collapse are related to the macroscopic properties of the system. A comparison with the case of a Bose condensate of the atomic 7Li^{7}\mathrm{Li}7Li system is given.
We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled Gross-Pitaevskii equations. The unstable modulation grows from initially miscible condensates into various types of vector solitary waves, depending on the combinations of the sign of the coupling constants (intracomponent and intercomponent). We discuss the detailed features of the modulation instability, dynamics of solitary wave formation, and an analogy with the collapsing dynamics in a single-component condensate with attractive interactions.