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/9902140 · Physical Review A

Barrier effects on the collective excitations of split Bose-Einstein condensates

P. Capuzzi, E. Susana Hernández

Published May 1, 1999• 3 citations
arXivHTMLPDF

Abstract

We investigate the collective excitations of a single-species Bose gas at $T=0$ in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider one-dimensional potentials consisting of two harmonic wells separated by a distance ${2z}_{0}$, since they essentially contain all the barrier effects that one may visualize in the three-dimensional situation. We find, within a hydrodynamic approximation, that regardless of the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighboring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results obtained from exactly solving the time-dependent Gross-Pitaevskii equation. We also analyze the characteristics of the spatial pattern of excitations of three-dimensional boson systems according to the amount of splitting of the condensate.

DOI
10.1103/physreva.59.3902

Related papers

Bose-Einstein condensation in harmonic double wells

P. Capuzzi, E. Susana Hernández

We discuss Bose-Einstein condensation in harmonic traps where the confinement has undergone a splitting along one direction. We mostly consider three-dimensional potentials consisting of two cylindrical wells separated a distance $2a$ along the z axis. For ideal gases, the thermodynamics of the confined bosons has been investigated, performing exact numerical summations to describe the major details of the transition and comparing the results with the semiclassical density-of-states approximation. We find that for large particle number and increasing well separation, the condensation temperature evolves from the thermodynamic limit value ${T}_{c}^{(0)}(N)$ to ${T}_{c}^{(0)}(N/2).$ The effects of adding a repulsive interaction between atoms has been examined resorting to the Gross-Pitaevskii-Popov procedure, and it is found that the shift of the condensation temperature exhibits different signs according to the separation between wells. In particular, for sufficiently large splitting, the trend opposes the well-known results for harmonic traps, since the critical temperature appears to increase with growing repulsion strength.

arXiv:cond-mat/9810164•Physical Review A•Feb 1, 1999•11 citations

Collective modes of two-species Bose–Einstein condensates in a Josephson junction barrier

Harsimranjit Kaur, Kuldeep Suthar

Abstract The ultracold atoms are an ideal platform to implement atomtronics and Josephson junctions analogous to superconducting circuits. The collective modes of a Bose gas split by a potential barrier have been known. However, the role of barriers on the collective excitation spectra of ultracold atomic mixtures has not been examined. Here, we examine the low-lying collective modes of (an)harmonically trapped quasi-one-dimensional Bose–Einstein condensates (BECs) in a Josephson barrier by employing the variational approach and Bogoliubov theory. We first show that the anharmonicity of the external potential leads to an increase in the critical barrier strength of mode softening in a single-species condensate. The Josephson barrier drives the softening of in-phase and out-of-phase dipole modes of two-species BECs, and consequently leads to two additional zero-energy Goldstone modes in the miscible phase, in agreement with the variational approach. Furthermore, the sandwich immiscible state results in an additional Goldstone mode due to the barrier, in contrast to the spatially symmetry-broken side-by-side profile. Our results unveil the distinct collective response of the Josephson barrier in binary mixtures owing to interspecies atomic correlations.

arXiv:2412.19135•Journal of Physics B Atomic Molecular and Optical Physics•Sep 23, 2025•0 citations

Dynamic splitting of a Bose-Einstein condensate

C. Menotti, J. R. Anglin, J. I. Cirac +1 more

We study the dynamic process of splitting a condensate by raising a potential barrier in the center of a harmonic trap. We use a two-mode model to describe the phase coherence between the two halves of the condensate. Furthermore, we explicitly consider the spatial dependence of the mode funtions, which varies depending on the potential barrier. This allows us to get the tunneling coupling between the two wells and the on-site energy as a function of the barrier height. Moreover, we can get some insight into the collective modes that are excited by raising the barrier. We describe the internal and external degrees of freedom by variational ansatz. We distinguish the possible regimes as a function of the characteristic parameters of the problem and identify the adiabaticity conditions.

arXiv:cond-mat/0005302•Physical Review A•Jan 4, 2001•96 citations

Theoretical Studies of dilute Bose-Einstein condensates in a double-well potential

E. Sakellari

In this Thesis we apply the Gross-Pitaevskii equation (GPE) to describe properties of a dilute, near zero temperature Bose gas for various confining geometries. We start by reviewing some basic information about the density, the chemical potential and elementary excitations of a dilute atomic condensate confined in a single harmonic trap for a Bose condensate with repulsive and attractive interactions and we also discuss the stability in the case of attractive interactions. We extend our study to a one and three dimensional double-well trap. We investigate the eigenenergy levels and show that the nonlinearity leads to triangular structures which appear either in the ground or excited states for the case of a Bose condensate with attractive or repulsive interactions respectively. We apply the eigenenergy level picture to analyse Josephson effects induced when the barrier IS moved at a constant velocity across the trapping potential or by the application of a time-dependent potential gradient. The GPE simulations are compared to the predictions of a nonlinear two state model. Above a critical velocity there is a transition to a superposition of ground and excited states which leads to sudden changes in the population difference. The direction of Josephson flow depends critically on the initial state of the system and we discuss the feasibility of experimental control of the atomic flow using phase-imprinting. The stability of a low temperature Bose-Einstein condensate with attract interactions in one and three dimensional double-well potentiate is discussed. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. Finally we investigate the stability and tunnelling effects in a multi-well system.

•Jan 1, 2004•0 citations

Bose-Einstein condensate in a quartic potential:static and dynamic properties

Chaudhary, G.K., Amit Kumar Chattopadhyay, R. Ramakumar

In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.

•Nov 20, 2011•3 citations

BOSE–EINSTEIN CONDENSATE IN A QUARTIC POTENTIAL: STATIC AND DYNAMIC PROPERTIES

G. K. CHAUDHARY, AMIT K. CHATTOPADHYAY, R. RAMAKUMAR

In this paper, we present a theoretical study of a Bose–Einstein condensate of interacting bosons in a quartic trap in one-, two- and three-dimensions. Using Thomas–Fermi approximation, suitably complemented by numerical solutions of the Gross–Pitaevskii equation, we study the ground-state condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.

arXiv:0812.0246•International Journal of Modern Physics B•Jul 1, 2011•3 citations
We investigate the collective excitations of a single-species Bose gas at T=0T=0T=0 in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider one-dimensional potentials consisting of two harmonic wells separated by a distance 2z0{2z}_{0}2z0​, since they essentially contain all the barrier effects that one may visualize in the three-dimensional situation. We find, within a hydrodynamic approximation, that regardless of the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighboring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results obtained from exactly solving the time-dependent Gross-Pitaevskii equation. We also analyze the characteristics of the spatial pattern of excitations of three-dimensional boson systems according to the amount of splitting of the condensate.
We discuss Bose-Einstein condensation in harmonic traps where the confinement has undergone a splitting along one direction. We mostly consider three-dimensional potentials consisting of two cylindrical wells separated a distance 2a2a2a along the z axis. For ideal gases, the thermodynamics of the confined bosons has been investigated, performing exact numerical summations to describe the major details of the transition and comparing the results with the semiclassical density-of-states approximation. We find that for large particle number and increasing well separation, the condensation temperature evolves from the thermodynamic limit value Tc(0)(N){T}_{c}^{(0)}(N)Tc(0)​(N) to Tc(0)(N/2).{T}_{c}^{(0)}(N/2).Tc(0)​(N/2). The effects of adding a repulsive interaction between atoms has been examined resorting to the Gross-Pitaevskii-Popov procedure, and it is found that the shift of the condensation temperature exhibits different signs according to the separation between wells. In particular, for sufficiently large splitting, the trend opposes the well-known results for harmonic traps, since the critical temperature appears to increase with growing repulsion strength.
Abstract The ultracold atoms are an ideal platform to implement atomtronics and Josephson junctions analogous to superconducting circuits. The collective modes of a Bose gas split by a potential barrier have been known. However, the role of barriers on the collective excitation spectra of ultracold atomic mixtures has not been examined. Here, we examine the low-lying collective modes of (an)harmonically trapped quasi-one-dimensional Bose–Einstein condensates (BECs) in a Josephson barrier by employing the variational approach and Bogoliubov theory. We first show that the anharmonicity of the external potential leads to an increase in the critical barrier strength of mode softening in a single-species condensate. The Josephson barrier drives the softening of in-phase and out-of-phase dipole modes of two-species BECs, and consequently leads to two additional zero-energy Goldstone modes in the miscible phase, in agreement with the variational approach. Furthermore, the sandwich immiscible state results in an additional Goldstone mode due to the barrier, in contrast to the spatially symmetry-broken side-by-side profile. Our results unveil the distinct collective response of the Josephson barrier in binary mixtures owing to interspecies atomic correlations.
We study the dynamic process of splitting a condensate by raising a potential barrier in the center of a harmonic trap. We use a two-mode model to describe the phase coherence between the two halves of the condensate. Furthermore, we explicitly consider the spatial dependence of the mode funtions, which varies depending on the potential barrier. This allows us to get the tunneling coupling between the two wells and the on-site energy as a function of the barrier height. Moreover, we can get some insight into the collective modes that are excited by raising the barrier. We describe the internal and external degrees of freedom by variational ansatz. We distinguish the possible regimes as a function of the characteristic parameters of the problem and identify the adiabaticity conditions.
In this Thesis we apply the Gross-Pitaevskii equation (GPE) to describe properties of a dilute, near zero temperature Bose gas for various confining geometries. We start by reviewing some basic information about the density, the chemical potential and elementary excitations of a dilute atomic condensate confined in a single harmonic trap for a Bose condensate with repulsive and attractive interactions and we also discuss the stability in the case of attractive interactions. We extend our study to a one and three dimensional double-well trap. We investigate the eigenenergy levels and show that the nonlinearity leads to triangular structures which appear either in the ground or excited states for the case of a Bose condensate with attractive or repulsive interactions respectively. We apply the eigenenergy level picture to analyse Josephson effects induced when the barrier IS moved at a constant velocity across the trapping potential or by the application of a time-dependent potential gradient. The GPE simulations are compared to the predictions of a nonlinear two state model. Above a critical velocity there is a transition to a superposition of ground and excited states which leads to sudden changes in the population difference. The direction of Josephson flow depends critically on the initial state of the system and we discuss the feasibility of experimental control of the atomic flow using phase-imprinting. The stability of a low temperature Bose-Einstein condensate with attract interactions in one and three dimensional double-well potentiate is discussed. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. Finally we investigate the stability and tunnelling effects in a multi-well system.
In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.
In this paper, we present a theoretical study of a Bose–Einstein condensate of interacting bosons in a quartic trap in one-, two- and three-dimensions. Using Thomas–Fermi approximation, suitably complemented by numerical solutions of the Gross–Pitaevskii equation, we study the ground-state condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.