Dipolar Fermi gases in anisotropic traps

Abstract

The quest for quantum degenerate Fermi gases interacting through the anisotropic and long-range dipole-dipole interaction is an exciting and fast developing branch within the cold-atoms research program. Recent experimental progress in trapping, cooling, and controlling polar molecules with large electric dipole moments has, therefore, motivated much theoretical effort. In a recent letter, we have briefly discussed the application of a variational time-dependent Hartree-Fock approach to study theoretically both the static and the dynamic properties of such a system in a cylindersymmetric harmonic trap. We focused on the hydrodynamic regime, where collisions assure the equilibrium locally. Here, we present a detailed theory, extended to encompass the general case of a harmonic trap geometry without any symmetry. After deriving the equations of motion for the gas, we explore their static solutions to investigate key properties like the aspect ratios in both real and momentum space as well as the stability diagram. We find that, despite the lack of symmetry of the trap, the momentum distribution remains cylinder symmetric. The equations of motion are then used to study the low-lying hydrodynamic excitations, where, apart from the quadrupole and monopole modes, also the radial quadrupole mode is investigated. Furthermore, we study the timeof-flight dynamics as it represents an important diagnostic tool for quantum gases. We find that the real-space aspect ratios are inverted during the expansion, while the one in momentum space becomes asymptotically unity. In addition, anisotropic features of the dipole-dipole interaction are discussed in detail. These results could be particularly useful for future investigations of strongly dipolar heteronuclear polar molecules deep in the quantum degenerate regime.

Magnetostriction and exchange effects in trapped dipolar Bose and Fermi gases

“…We plot the direct interaction derivative term, λ −2 J (λ −2 − 1), appearing in Eq. (16) [also in Eq. (19)], in Fig.…”

“…Releasing the system from the trap requires a model of the expansion dynamics (e.g. see [17,25,28]) and does not simply reveal the momentum behavior. Bragg spectroscopy could be used to probe the momentum distribution in situ [36,37].…”

“…phase space densities greater than unity are not prohibited for Fermions), and thus is only applicable at temperatures well above the relevant degeneracy temperatures. 2 In the appendix, we minimize the free energy 3 derived from (17) to determine the variational parameters and hence the distortion parameters. To first order we find…”

“…For normal Fermi gases Hartree calculations (excluding exchange) were used to study position space magnetostriction in [14]. The first theories including exchange interactions for the trapped Fermi gas were based on simple variational approximations [15][16][17][18] (also see [19]), and revealed distortion of the momentum distribution. In this paper we use full Hartree-Fock (HF) calculations to provide a unified quantitative treatment of trapped Bose and Fermi gases.…”

Dipolar Bose-Einstein condensates in weak anisotropic disorder

“…Realization of atomic dipolar BECs [45][46][47] with longrange anisotropic interaction has generated large interest in the theory of dipolar quantum gases [48][49][50][51][52][53][54][55][56]. Increase in the strength of dipolar interaction is possible by substituting atoms with magnetic dipoles by heteronuclear molecules, which have a strong electric dipolar moment in rovibrational ground state [57], or by inducing radiative coupling by placing dipoles into a resonator [58].…”