We consider a system of quantum degenerate spin polarized fermions in a harmonic trap at zero temperature, interacting via dipole-dipole forces. We introduce a variational Wigner function to describe the deformation and compression of the Fermi gas in phase space and use it to examine the stability of the system. We emphasize the important roles played by the Fock exchange term of the dipolar interaction which results in a non-spherical Fermi surface.PACS numbers: 03.75. Ss, 05.30.Fk, 75.80.+q Two-body collisions in usual ultracold atomic systems can be described by short-range interactions. The successful realization of chromium Bose-Einstein condensate (BEC) [1] and recent progress in creating heteronuclear polar molecules [2] have stimulated great interest in quantum degenerate dipolar gases. The anisotropic and long-range nature of the dipolar interaction makes the dipolar systems different from non-dipolar ones in many qualitative ways [3]. Although most of the theoretical studies of dipolar gases have been focused on dipolar BECs, where the stability and excitations of the system are investigated (see Ref.[3] and references therein, and also Ref. [4]) and new quantum phases are predicted [5,6], some interesting works about dipolar Fermi gas do exist. These studies concern the ground state properties [7,8,9], dipolar-induced superfluidity [10], and strongly correlated states in rotating dipolar Fermi gases [11]. None of these studies, however, takes the Fock exchange term of dipolar interaction into proper account [12].In this Letter, we study a system of dipolar spin polarized Fermi gas. We will show that the Fock exchange term that is neglected in previous studies plays a crucial role. In particular, it leads to the deformation of Fermi surface which controls the properties of fermionic systems, and it affects the stability property of the system. As Fermi surface can be readily imaged using time-offlight technique [13], this property thus offers a straightforward way of detecting dipolar effects in Fermi gases.In our work, we consider a trapped dipolar gas of single component fermions of mass m and magnetic or electric dipole moment d at zero temperature. The dipoles are assumed to be polarized along the z-axis. The system is described by the Hamiltonianwhere V dd (r) = (d 2 /r 3 )(1−3z 2 /r 2 ) is the two-body dipolar interaction and U (r) the trap potential. To characterize the system, we use a semiclassical approach in which the one-body density matrix is given by, k e ik(r−rwhere f (r, k) is the Wigner distribution function. The density distributions in real and momentum space are then given respectively byOur goal is to examine n(r) andñ(k), as well as the stability of the system by minimizing the energy functional using a variational method. Within the ThomasFermi-Dirac approximation [7], the total energy of the system is given by E = E kin + E tr + E d + E ex , whereThe dipolar interaction induces two contributions: the Hartree direct energy E d and the Fock exchange energy E ex . The latter ar...
We investigate 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 by a function of deformation parameters in both real and momentum space. 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 and quadrupole modes are calculated, and softening against collapse is shown as the dipolar strength approaches the critical value. Finally, we investigate the effects of the dipolar interaction on the expansion dynamics of the Fermi gas and show how the dipolar effects manifest in an expanded cloud.
We consider a uniform dipolar Fermi gas in two-dimensions (2D) where the dipole moments of fermions are aligned by an orientable external field. We obtain the ground state of the gas in HartreeFock approximation and investigate RPA stability against density fluctuations of finite momentum. It is shown that the density wave instability takes place in a broad region where the system is stable against collapse. We also find that the critical temperature can be a significant fraction of Fermi temperature for a realistic system of polar molecules.
α-particle (quartet) condensation in homogeneous spin-isospin symmetric nuclear matter is investigated. The usual Thouless criterion for the critical temperature is extended to the quartet case. The in-medium four-body problem is strongly simplified by the use of a momentum-projected mean-field ansatz for the quartet. The self-consistent single-particle wave functions are shown and discussed for various values of the density at the critical temperature. Excellent agreement of the critical temperature with a numerical solution of the Faddeev-Yakubovsky equation is obtained.
The theory for condensation of higher fermionic clusters is developed. Fully selfconsistent nonlinear equations for the quartet order parameter in strongly coupled fermionic systems are established and solved. The breakdown of the quasiparticle picture is pointed out. Derivation of numerically tractable approximation is described. The momentum projected factorisation ansatz of Ref. [21] for the order parameter is employed again. As a definite example the condensation of α particles in nuclear matter is worked out.
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