Using the time-dependent Hartree–Fock theory (TDHF), we study the ground states of dipolar fermion gases in a spherical trap. It is found that deformed configurations which have prolate shape both in real and momentum space are energetically favored and that when the dipolar interaction is not very strong, the deformation of the gases shows a prominent shell structure at closed oscillator-shell configurations. The quadrupole and breathing modes are also studied in TDHF and it is found that these modes are little affected by the dipolar interaction when the gases have the closed-shell configurations. The effects of the two-body correlations on the ground-state properties and also on the damping of the quadrupole mode are also investigated using a time-dependent density-matrix formalism. It is found that the effects of the two-body correlations are not significant for the closed-shell configurations.
Using the time-dependent Hartree–Fock theory (TDHF), we study the ground states of dipolar fermion gases in a spherical trap. It is found that deformed configurations which have prolate shape both in real and momentum space are energetically favored and that when the dipolar interaction is not very strong, the deformation of the gases shows a prominent shell structure at closed oscillator-shell configurations. The quadrupole and breathing modes are also studied in TDHF and it is found that these modes are little affected by the dipolar interaction when the gases have the closed-shell configurations. The effects of the two-body correlations on the ground-state properties and also on the damping of the quadrupole mode are also investigated using a time-dependent density-matrix formalism. It is found that the effects of the two-body correlations are not significant for the closed-shell configurations.
Finite fermion systems are known to exhibit shell structure in the weakly interacting regime, as is well known from atoms, nuclei, metallic clusters, or even quantum dots in two dimensions. All these systems have in common that the particle interactions between electrons or nucleons are spatially isotropic. Dipolar quantum systems as they have been realized with ultracold gases, however, are governed by an intrinsic anisotropy of the two-body interaction that depends on the orientation of the dipoles relative to each other. Here we investigate how this interaction anisotropy modifies the shell structure in a weakly interacting two-dimensional anisotropic harmonic trap. Going beyond Hartree-Fock analysis by applying the so-called importance-truncated configuration-interaction (CI) method as well as quadratic CI with single and double substitutions, we show how the magnetostriction in the system may be counteracted upon by a deformation of the confinement.
Many-body dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS). Recently it was experimentally observed that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and long-range dipole-dipole interaction. Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the Fermi surface follows their rotation, thereby keeping the major axis of the momentum-space ellipsoid parallel to the dipoles. Here we generalise a previous Hartree-Fock mean-field theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap. With this we study for the first time the effects of the dipoles' arbitrary orientation on the ground-state properties of the system. Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable real-space aspect ratio after a free expansion. We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations. The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation. Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles but softens showing a change in the aspect ratio depending on the dipoles' orientation relative to the trap geometry, as well as on the trap anisotropy itself. Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.
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-atom 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 cylinder-symmetric harmonic trap. We focused on the hydrodynamic regime, where collisions ensure 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, the radial quadrupole mode is also investigated. Furthermore, we study the time-of-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 that 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.
The ground states and collective excitations of trapped Fermion gases consisting of atoms with magnetic dipole moment are studied using a time-dependent density-matrix approach. The advantages of the density-matrix approach are that one-body and two-body observables are directly calculated using one-body and two-body density matrices and that it has a clear relation to the Hartree-Fock (HF) and time-dependent HF theory. The HF calculations show the magnetization of the gases when the dipole-dipole interaction is strong. It is shown that the tensor properties of the dipole-dipole interaction are revealed in the excitation modes associated with spin degrees of freedom.
In this paper, we investigate the dynamical properties of a one-component Fermi gas with dipole–dipole interaction between particles. Using a variational function based on the Thomas–Fermi density distribution in phase space representation, the total energy is described as a function of deformation parameters in both real and momentum spaces. Various thermodynamic quantities of a uniform dipolar Fermi gas are derived, and then instability of this system is discussed. For a trapped dipolar Fermi gas, the collective oscillation frequencies are derived with the energy-weighted sum rule method. The frequencies for the monopole, quadrupole, radial and axial modes are calculated, and softening against collapse is shown as the dipolar strength approaches the critical value. Finally, we investigate the expansion dynamics of the Fermi gas and show how the dipolar interaction manifests itself in the shape of an expanded cloud.
Many-body dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS).Recently it was experimentally observed in a sample of erbium atoms that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and long-range dipole-dipole interaction Aikawa et al (2014 Science 345 1484).Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the FS follows their rotation, thereby keeping the major axis of the momentum-space ellipsoid parallel to the dipoles.Here we generalise a previous Hartree-Fock mean-field theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap.With this we study for the first time the effects of the dipoles' arbitrary orientation on the ground-state properties of the system.Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable real-space aspect ratio after a free expansion.We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations.The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation.Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles, but softens showing a change in the aspect ratio depending on the dipoles' orientation relative to the trap geometry, as well as on the trap anisotropy itself.Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.