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Register a new userThomas-Fermi von Weizsacker theory for a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas
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We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas-Fermi von Weizsacker approximation. We pay particular attention to the construction of the two-dimensional kinetic energy functional, where corrections beyond the local density approximation must be motivated with care. We also present an intuitive derivation of the interaction energy functional associated with the dipolar interactions, and provide physical insight into why it can be represented as a local functional. Finally, a simple, and highly efficient self-consistent numerical procedure is developed to determine the equilibrium density of the system for a range of dipole interaction strengths.
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The collective excitations of a zero-temperature, spin-polarized, harmonically trapped, two-dimensional dipolar Fermi gas are examined within the Thomas-Fermi von Weizsacker hydrodynamic theory. We focus on repulsive interactions, and investigate the dependence of the excitation frequencies on the strength of the dipolar interaction and particle number. We find that the mode spectrum can be classified according to bulk modes, whose frequencies are shifted upward as the interaction strength is increased, and an infinite ladder of surface modes, whose frequencies are {em independent} of the interactions in the large particle limit. We argue quite generally that it is the {em local} character of the two-dimensional energy density which is responsible for the insensitivity of surface excitations to the dipolar interaction strength, and not the precise form of the equation of state. This property will not be found for the collective excitations of harmonically trapped, dipolar Fermi gases in one and three dimensions, where the energy density is manifestly nonlocal.
We study zero sound in a weakly interacting 2D gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes in experiments with 2D fermionic dipoles, although the zero sound peak in the structure function is very close to the particle-hole continuum.
We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.
We derive the criteria for the Thomas-Fermi regime of a dipolar Bose-Einstein condensate in cigar, pancake and spherical geometries. This also naturally gives the criteria for the mean-field one- and two-dimensional regimes. Our predictions, including the Thomas-Fermi density profiles, are shown to be in excellent agreement with numerical solutions. Importantly, the anisotropy of the interactions has a profound effect on the Thomas-Fermi/low-dimensional criteria.
Density-functional theory is utilized to investigate the zero-temperature transition from a Fermi liquid to an inhomogeneous stripe, or Wigner crystal phase, predicted to occur in a one-component, spin-polarized, two-dimensional dipolar Fermi gas. Correlations are treated semi-exactly within the local-density approximation using an empirical fit to Quantum Monte Carlo data. We find that the inclusion of the nonlocal contribution to the Hartree-Fock energy is crucial for the onset of an instability to an inhomogeneous density distribution. Our density-functional theory supports a transition to both a one-dimensional stripe phase, and a triangular Wigner crystal. However, we find that there is an instability first to the stripe phase, followed by a transition to the Wigner crystal at higher coupling.
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