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/0005054 · Physical Review A

Trapped condensates of atoms with dipole interactions

S. Yi, Li You

Published Apr 18, 2001• 272 citations
arXivHTMLPDF

Abstract

We discuss in detail properties of trapped atomic condensates with anisotropic dipole interactions. A practical procedure for constructing anisotropic low-energy pseudopotentials is proposed and justified by the agreement with results of numerical multichannel calculations. The time dependent variational method is adapted to reveal several interesting features observed in numerical solutions of condensate wave function. Collective low-energy shape oscillations and their stability inside electric fields are investigated. Our results shed new light into macroscopic coherence properties of interacting quantum degenerate atomic gases.

DOI
10.1103/physreva.63.053607

Related papers

Trapped atomic condensates with anisotropic interactions

S. Yi, Li You

We study ground-state properties of trapped atomic condensates with electric-field-induced dipole-dipole interactions. A rigorous method for constructing the pseudopotential in the spirit of ladder approximation is developed for general nonspherical (polarized) particles interacting anisotropically. We discuss interesting features not previously considered for currently available alkali-metal condensates. In addition, to provide a quantitative assessment for controlling atomic interactions with electric fields, our investigation may also shed a different light into the macroscopic coherence properties of the Bose-Einstein condensation (BEC) of dilute interacting atoms.

arXiv:cond-mat/0002079•Physical Review A•Mar 13, 2000•325 citations

Bose-Einstein condensation of trapped atoms with dipole interactions

Kwangsik T. Nho, David Paul Landau

The path-integral Monte Carlo method is used to simulate dilute trapped Bose gases and to investigate the equilibrium properties at finite temperatures. The quantum particles have a long-range dipole-dipole interaction and a short-range $s$-wave interaction. Using an anisotropic pseudopotential for the long-range dipolar interaction and a hard-sphere potential for the short-range $s$-wave interaction, we calculate the energetics and structural properties as a function of temperature and the number of particles. Also, in order to determine the effects of dipole-dipole forces and the influence of the trapping field on the dipolar condensate, we use two cylindrically symmetric harmonic confinements (a cigar-shaped trap and a disk-shaped trap). We find that the net effect of dipole-dipole interactions is governed by the trapping geometry. For a cigar-shaped trap, the net contribution of dipolar interactions is attractive and the shrinking of the density profiles is observed. For a disk-shaped trap, the net effect of long-range dipolar forces is repulsive and the density profiles expand.

arXiv:cond-mat/0509498•Physical Review A•Aug 23, 2005•25 citations

Variational approaches to dipolar Bose-Einstein condensates

Rüdiger Fortanier

In this work several aspects of dipolar Bose-Einstein condensates are investigated. These condensates have attracted much interest since their experimental realization and offer the chance to explore the novel, fascinating, and sometimes unexpected physics originating from the dipole-dipole interaction. For the theoretical description the time-dependent variational principle with an ansatz of coupled Gaussian wave packets is applied to the analysis of this form of matter. In order to describe physical systems, where the shape of the condensate wave function cannot be approximated adequately by origin-centered Gaussian functions, translational and rotational degrees of freedom of the particular wave packets are included. This provides not only a full-fledged alternative method to full-numerical grid calculations that are demanding in computation time, used for the determination of ground states and investigation of the real-time dynamics, but also allows for the calculation of excited states and the examination of stability properties and offers the possibility for a deeper physical understanding of dipolar condensates. The variational method is applied to three different physical systems. In the first one anisotropic quasi-two-dimensional solitons are investigated. Ground states and small excitations are presented and the full flexibility of the approach is utilized in the simulation of the collision of two solitons. Thereby simulations of collisions are performed, where initially the solitons are in the repelling side-by-side configuration and move towards each other with a specific momentum. It is shown that the results are in excellent agreement with full-numerical grid calculations. Collisions with various initial parameters such as the initial momentum and impact factor are performed, allowing to classify the qualitative interactions of two solitons and illuminating the effects of the solitons' two-dimensional nature on the collision process. In the second system dipolar Bose-Einstein condensates in a triple-well potential are investigated. This constitutes a well-suited model system for periodic optical potentials with important contributions of the non-local and anisotropic dipole-dipole interaction, which show a variety of effects such as self-organization and formation of patterns. Here, a macroscopic sample of dipolar bosons in the mean-field limit is addressed. The analysis goes beyond the calculation of ground states and clarifies the role of excited and metastable states in such systems. In particular, the formation of phases is found to originate from the interplay of several states with distinct stability properties. As some of the phases are formed by metastable states, special attention is paid to the characteristics of phase transitions in real time and the dynamical stabilization of the condensate. The dynamical simulations that support these results, constitute a way for an experimental observation of these findings. The third physical application is an open quantum system. Here, an external potential models gain and loss of particles and features parity with simultaneous time-reversal symmetry. For these dipolar condensates real eigenvalues of the nonlinear Hamiltonian are found, preserving the PT-symmetry of the external potential, as well as states that break this symmetry. A detailed stability analysis of these, in general complex states, is performed. The comparison with a similar system featuring a non-dipolar condensate demonstrates the role of the dipolar interaction for novel effects. Furthermore, the real-time dynamics is investigated, which reveals, among other effects, long-living oscillations of the two wells' population.

•Jan 1, 2014•3 citations

Properties of quasi-two-dimensional condensates in highly anisotropic traps

Gerald Hechenblaikner, J. M. Krueger, Christopher J. Foot

We theoretically investigate some of the observable properties of quasi-two-dimensional condensates. Using a variational model based on a Gaussian-parabolic trial wave function we calculate chemical potential, condensate size in time-of-flight, release energy, and collective excitation spectrum for varying trap geometries and atom numbers and find good agreement with recent published experimental results.

arXiv:cond-mat/0410148•Physical Review A•Jan 20, 2005•20 citations

Probing dipolar effects with condensate shape oscillation

S. Yi, Li You

We discuss the low-energy shape oscillations of a magnetically trapped atomic condensate including the spin dipole interaction. When the nominal isotropic s-wave interaction strength becomes tunable through a Feshbach resonance (e.g., as for ${}^{85}\mathrm{Rb}$ atoms), anisotropic dipolar effects are shown to be detectable under current experimental conditions [E. A. Donley et al., Nature (London) 412, 295 (2001)].

arXiv:cond-mat/0111256•Physical Review A•Jul 18, 2002•47 citations

Calibrating Dipolar Interaction in an Atomic Condensate

S. Yi, Li You

We reexamine the topic of a dipolar condensate with the recently derived more rigorous pseudopotential for dipole-dipole interaction [Phys. Rev. A 67, 033607 (2003)]]. Based on the highly successful variational technique, we find that all dipolar effects estimated before (using the bare dipole-dipole interaction) become significantly larger, i.e., are amplified by the new velocity-dependent pseudopotential, especially in the limit of large or small trap aspect ratios. This result points to a promising prospect for detecting dipolar effects inside an atomic condensate.

arXiv:cond-mat/0405041•Physical Review Letters•May 14, 2004•41 citations
We discuss in detail properties of trapped atomic condensates with anisotropic dipole interactions. A practical procedure for constructing anisotropic low-energy pseudopotentials is proposed and justified by the agreement with results of numerical multichannel calculations. The time dependent variational method is adapted to reveal several interesting features observed in numerical solutions of condensate wave function. Collective low-energy shape oscillations and their stability inside electric fields are investigated. Our results shed new light into macroscopic coherence properties of interacting quantum degenerate atomic gases.
We study ground-state properties of trapped atomic condensates with electric-field-induced dipole-dipole interactions. A rigorous method for constructing the pseudopotential in the spirit of ladder approximation is developed for general nonspherical (polarized) particles interacting anisotropically. We discuss interesting features not previously considered for currently available alkali-metal condensates. In addition, to provide a quantitative assessment for controlling atomic interactions with electric fields, our investigation may also shed a different light into the macroscopic coherence properties of the Bose-Einstein condensation (BEC) of dilute interacting atoms.
The path-integral Monte Carlo method is used to simulate dilute trapped Bose gases and to investigate the equilibrium properties at finite temperatures. The quantum particles have a long-range dipole-dipole interaction and a short-range sss-wave interaction. Using an anisotropic pseudopotential for the long-range dipolar interaction and a hard-sphere potential for the short-range sss-wave interaction, we calculate the energetics and structural properties as a function of temperature and the number of particles. Also, in order to determine the effects of dipole-dipole forces and the influence of the trapping field on the dipolar condensate, we use two cylindrically symmetric harmonic confinements (a cigar-shaped trap and a disk-shaped trap). We find that the net effect of dipole-dipole interactions is governed by the trapping geometry. For a cigar-shaped trap, the net contribution of dipolar interactions is attractive and the shrinking of the density profiles is observed. For a disk-shaped trap, the net effect of long-range dipolar forces is repulsive and the density profiles expand.
In this work several aspects of dipolar Bose-Einstein condensates are investigated. These condensates have attracted much interest since their experimental realization and offer the chance to explore the novel, fascinating, and sometimes unexpected physics originating from the dipole-dipole interaction. For the theoretical description the time-dependent variational principle with an ansatz of coupled Gaussian wave packets is applied to the analysis of this form of matter. In order to describe physical systems, where the shape of the condensate wave function cannot be approximated adequately by origin-centered Gaussian functions, translational and rotational degrees of freedom of the particular wave packets are included. This provides not only a full-fledged alternative method to full-numerical grid calculations that are demanding in computation time, used for the determination of ground states and investigation of the real-time dynamics, but also allows for the calculation of excited states and the examination of stability properties and offers the possibility for a deeper physical understanding of dipolar condensates. The variational method is applied to three different physical systems. In the first one anisotropic quasi-two-dimensional solitons are investigated. Ground states and small excitations are presented and the full flexibility of the approach is utilized in the simulation of the collision of two solitons. Thereby simulations of collisions are performed, where initially the solitons are in the repelling side-by-side configuration and move towards each other with a specific momentum. It is shown that the results are in excellent agreement with full-numerical grid calculations. Collisions with various initial parameters such as the initial momentum and impact factor are performed, allowing to classify the qualitative interactions of two solitons and illuminating the effects of the solitons' two-dimensional nature on the collision process. In the second system dipolar Bose-Einstein condensates in a triple-well potential are investigated. This constitutes a well-suited model system for periodic optical potentials with important contributions of the non-local and anisotropic dipole-dipole interaction, which show a variety of effects such as self-organization and formation of patterns. Here, a macroscopic sample of dipolar bosons in the mean-field limit is addressed. The analysis goes beyond the calculation of ground states and clarifies the role of excited and metastable states in such systems. In particular, the formation of phases is found to originate from the interplay of several states with distinct stability properties. As some of the phases are formed by metastable states, special attention is paid to the characteristics of phase transitions in real time and the dynamical stabilization of the condensate. The dynamical simulations that support these results, constitute a way for an experimental observation of these findings. The third physical application is an open quantum system. Here, an external potential models gain and loss of particles and features parity with simultaneous time-reversal symmetry. For these dipolar condensates real eigenvalues of the nonlinear Hamiltonian are found, preserving the PT-symmetry of the external potential, as well as states that break this symmetry. A detailed stability analysis of these, in general complex states, is performed. The comparison with a similar system featuring a non-dipolar condensate demonstrates the role of the dipolar interaction for novel effects. Furthermore, the real-time dynamics is investigated, which reveals, among other effects, long-living oscillations of the two wells' population.
We discuss the low-energy shape oscillations of a magnetically trapped atomic condensate including the spin dipole interaction. When the nominal isotropic s-wave interaction strength becomes tunable through a Feshbach resonance (e.g., as for 85Rb{}^{85}\mathrm{Rb}85Rb atoms), anisotropic dipolar effects are shown to be detectable under current experimental conditions [E. A. Donley et al., Nature (London) 412, 295 (2001)].
We reexamine the topic of a dipolar condensate with the recently derived more rigorous pseudopotential for dipole-dipole interaction [Phys. Rev. A 67, 033607 (2003)]]. Based on the highly successful variational technique, we find that all dipolar effects estimated before (using the bare dipole-dipole interaction) become significantly larger, i.e., are amplified by the new velocity-dependent pseudopotential, especially in the limit of large or small trap aspect ratios. This result points to a promising prospect for detecting dipolar effects inside an atomic condensate.