Phase-space deformation of a trapped dipolar Fermi gas

Abstract

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...

Collective modes, stability, and superfluid transition of a quasi-two-dimensional dipolar Fermi gas

“…[25] to obtain the spectrum of singleparticle excitations at zero and finite temperature. At zero temperature, the results were found to agree very well with the outcome of a variational approach that was initially used to study Fermi surface deformations in the 3D case [26] and adapted to the 2D case by the authors of Ref. [12].…”

Stability and free expansion of a dipolar Fermi gas

“…5, we presented the direct and exchange dipolar interaction ratio E dd /E ex based on the variational calculation developed in Ref. [11]. It can be seen that the exchange interaction has most dramatic effect when the trapping potential is near spherical, and it becomes less important in highly prolate and oblate traps.…”

“…During the preparation of the manuscript, we become aware of a preprint by Miyakawa et al [11]. They revisited the equilibrium state properties of a dipolar Fermi gas using a variational ansatz capable of describing the deformation in momentum space.…”

“…Therefore, without tuning η, a highly oblate trap with λ = 100 can only sustain about N ≃ 4.7 × 10 4 fermions. Taking into account the deformation of momentum distribution may further lower the critical number of molecules [11]. More efficiently, we may tune |η| to a small value to stabilize the system.…”

Roton instabilities and correlated Wigner crystals of rotating dipolar fermions in the fractional quantum Hall regime

“…The vortex lattice of the rotating dipolar BEC exhibits novel bubble, stripe, and square structures [8]. For the dipolar Fermi gases, the s-wave scattering is prohibited due to the Pauli Exclusion Principle and the Fermi surface is distorted by dipolar effects [9]. Bond pairs of fermions with resonant interaction are formed and the system of a Fermi gas behaves as a bosonic gas of molecules [10,11].…”