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arXiv:cond-mat/0203542 · Physical Review A

Ground state and elementary excitations of single and binary Bose-Einstein condensates of trapped dipolar gases

Krzysztof Góral, Luis Santos

Published Aug 28, 2002• 233 citations
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Abstract

We analyze the ground-state properties and the excitation spectrum of Bose-Einstein condensates of trapped dipolar particles. First, we consider the case of a single-component polarized dipolar gas. For this case we discuss the influence of the trapping geometry on the stability of the condensate as well as the effects of the dipole-dipole interaction on the excitation spectrum. We discuss also the ground state and excitations of a gas composed of two antiparallel dipolar components.

DOI
10.1103/physreva.66.023613

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Stability of trapped degenerate dipolar Bose and Fermi gases

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Abstract. Trapped degenerate dipolar Bose and Fermi gases of cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose-Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using variational approximation and numerical solution of a mean-field model. In the disk shape, with the polarization vector perpendicular to the plane of the disk, the atoms experience an overall dipolar repulsion and this fact should contribute to the stability. However, a complete numerical solution of the dynamics leads to the collapse of a strongly disk-shaped dipolar BEC due to the long-range anisotropic dipolar interaction. In the case of fermions, the stability of a trapped single-component degenerate dipolar Fermi gas is studied including the Hartree-Fock exchange and Brueckner-Goldstone correlation energies in the local-density approximation valid for a large number of atoms. Estimates for the maximum allowed number of polar Bose and Fermi molecules in BEC and degenerate Fermi gas are given. PACS numbers: 03.75.Hh,03.75.Ss,03.75.Kk,05.30.Fk ar

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We analyze the ground-state properties and the excitation spectrum of Bose-Einstein condensates of trapped dipolar particles. First, we consider the case of a single-component polarized dipolar gas. For this case we discuss the influence of the trapping geometry on the stability of the condensate as well as the effects of the dipole-dipole interaction on the excitation spectrum. We discuss also the ground state and excitations of a gas composed of two antiparallel dipolar components.
This thesis contains a study of ultracold paramagnetic atoms or polar molecules characterized by a long-range anisotropic dipolar interaction. We particularly focus on two aspects of ultracold dipolar gases. In the first problem the ground state properties of dipolar Bose-Einstein condensates (BEC) are investigated. This problem has gained importance due to recent experimental advances in achieving a condensate of Chromium atoms and ongoing research to produce quantum degenerate polar molecules. In the second problem, we consider possible applications of ultracold polar molecules to rotation sensing and interferometry. First, we concentrate on the interplay between the trapping geometry and dipole-dipole interaction for a polarized dipolar bosonic condensate. As the dipole-dipole interaction is attractive along the polarized direction, the lowest energy state of the BEC is always a collapsed state. However by applying a trapping potential along the polarization direction it is possible to achieve a metastable dipolar BEC. By numerically solving the Gross-Pitaevskii equation, we show that below a critical interaction strength, a metastable state exists depending on the trapping geometry. We also show that a novel feature of dipolar BEC is the appearance of different structural metastable ground states for certain combinations of trapping geometry and particle number. Next, by mixing in single component fermions we show that dipolar BEC can be stabilized against collapse in pancake shaped or cylindrical traps. We also show that the excitation spectrum of the BEC may have a minimum for non-zero momentum, termed a “roton minimum”. This minimum leads to a transition to stable or metastable density-wave states depending on the density of the bosons and boson-fermion interaction strength. In the second problem, we study a proposal for a large-angle coherent beam splitter for polar molecules. By taking into account the effect of a quasi-static external electric field on the rotational levels of the polarized molecules we show that it is possible to coherently split a stationary cloud of molecules into two counter-propagating components. We then investigate the effect of longitudinal acceleration on the transverse motion of the particles, assuming that the longitudinal motion of the molecules can be approximated classically by a wave packet with some mean velocity while the transverse motion is governed by quantum mechanics. We propose a particular time-dependent shape of acceleration to minimize the excitations in the transverse motion. Our theory is also applicable to the general case of particles moving along a circular guide with time-dependent longitudinal velocity. In addition, we include the effects of velocity fluctuations due to noise in the accelerating field.
We consider the ground state and the collective excitations of dipolar Bose-Einstein condensates in a bubble trap, i.e., a shell-shaped spherically symmetric confining potential. By means of an appropriate Gaussian ansatz, we determine the ground-state properties in the case where the particles interact by means of both the isotropic and short-range contact and the anisotropic and long-range dipole-dipole potential in the thin-shell limit. Moreover, with the ground state at hand, we employ the sum-rule approach to study the monopole, the two-, the three-dimensional quadrupole as well as the dipole modes. We find situations in which neither the virial nor Kohn's theorem can be applied. On top of that, we demonstrate the existence of anisotropic particle density profiles, which are absent in the case with repulsive contact interaction only. These significant deviations from what one would typically expect are then traced back to both the anisotropic nature of the dipolar interaction and the novel topology introduced by the bubble trap.
We theoretically investigate various beyond mean-field effects on Bose gases at zero temperature featuring the anisotropic and long-range dipole-dipole interaction in addition to the isotropic and short-range contact interaction. Within the realm of the Bogoliubov--de Gennes theory, we consider static properties and low-lying excitations of both homogeneous and harmonically trapped dipolar bosonic gases. For the homogeneous system, the condensate depletion, the ground-state energy, the equation of state, and the speed of sound are discussed in detail. Making use of the local density approximation, we extend these results in order to study the properties of a dipolar Bose gas in a harmonic trap and in the regime of large particle numbers. After deriving the equations of motion for the general case of a triaxial trap, we analyze the influence of quantum fluctuations on important properties of the gas, such as the equilibrium configuration and the low-lying excitations in the case of a cylinder-symmetric trap. In addition to the monopole and quadrupole oscillation modes, we also discuss the radial quadrupole mode. We find that the latter acquires a quantum correction exclusively due to the dipole-dipole interaction. As a result, we identify the radial quadrupole as a reasonably accessible source for the signature of dipolar many-body effects and stress the enhancing character that dipolar interactions have for quantum fluctuations in the other oscillation modes.
Trapped degenerate dipolar Bose and Fermi gases of the cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose–Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using a variational approximation and a numerical solution of a mean-field model. In the disc shape, with the polarization vector perpendicular to the plane of the disc, the atoms experience an overall dipolar repulsion and this fact should contribute to the stability. However, a complete numerical solution of the dynamics leads to the collapse of a strongly disc-shaped dipolar BEC due to the long-range anisotropic dipolar interaction. In the case of fermions, the stability of a trapped single-component degenerate dipolar Fermi gas is studied including the Hartree–Fock exchange and Brueckner–Goldstone correlation energies in the local-density approximation valid for a large number of atoms. Estimates for the maximum allowed number of polar Bose and Fermi molecules in the BEC and degenerate Fermi gas are given.
Abstract. Trapped degenerate dipolar Bose and Fermi gases of cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose-Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using variational approximation and numerical solution of a mean-field model. In the disk shape, with the polarization vector perpendicular to the plane of the disk, the atoms experience an overall dipolar repulsion and this fact should contribute to the stability. However, a complete numerical solution of the dynamics leads to the collapse of a strongly disk-shaped dipolar BEC due to the long-range anisotropic dipolar interaction. In the case of fermions, the stability of a trapped single-component degenerate dipolar Fermi gas is studied including the Hartree-Fock exchange and Brueckner-Goldstone correlation energies in the local-density approximation valid for a large number of atoms. Estimates for the maximum allowed number of polar Bose and Fermi molecules in BEC and degenerate Fermi gas are given. PACS numbers: 03.75.Hh,03.75.Ss,03.75.Kk,05.30.Fk ar