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Physical Review A

Phase separation in trapped dipolar Fermi gases

Takahiko Miyakawa, Shin Nakamura, Hiroyuki Yabu

Published Mar 17, 2020• 4 citations
Publisher

Abstract

We study the ground state of a two-component dipolar Fermi gas in a spherically symmetric harmonic trap at zero temperature. We obtain the ground state of the system with equal but opposite values of the magnetic moment on the basis of the Thomas--Fermi--von Weizs\"acker approximation. It is found that two types of phase-separated states which break the spherical symmetry emerge across the phase transition between a spin-symmetric phase and a phase-separation phase. One is an axially symmetric phase-separated state and the other is a one-dimensional alternating-spin layered state. We also study a Fermi-Fermi mixture of polarized Dy and Er atoms and show that a structural transition of phase separation can be observed in current experiments by varying the relative number of particles.

DOI
10.1103/physreva.101.033613

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We study the ground state of a two-component dipolar Fermi gas in a spherically symmetric harmonic trap at zero temperature. We obtain the ground state of the system with equal but opposite values of the magnetic moment on the basis of the Thomas--Fermi--von Weizs"acker approximation. It is found that two types of phase-separated states which break the spherical symmetry emerge across the phase transition between a spin-symmetric phase and a phase-separation phase. One is an axially symmetric phase-separated state and the other is a one-dimensional alternating-spin layered state. We also study a Fermi-Fermi mixture of polarized Dy and Er atoms and show that a structural transition of phase separation can be observed in current experiments by varying the relative number of particles.
Interacting two-component Fermi gases are at the heart of our understanding of macroscopic quantum phenomena such as superconductivity. The changing nature of the interaction is expected to head to novel quantum phases. Here we study the ground state of a two-component fermionic gas in a harmonic potential with dipolar and contact interactions. Using a variational Wigner function we present the phase diagram of the system with equal but opposite values of the magnetic moment. We identify the second-order phase transition from paramagnetic to ferronematic phases. Moreover, we show the impact of the experimentally relevant magnetic field on the stability and magnetization of the system. We also investigate a two-component Fermi gas with large but almost equal values of the magnetic moment to study how the interplay between contact and dipolar interactions affects the stability properties of the mixture. To be specific we discuss experimentally relevant parameters for ultracold 161{}^{161}161Dy.
Abstract Investigation of ground state structures and phase separation under confinement is of great interest in spinor Bose–Einstein condensates. In this paper we show that, in general, within the Thomas–Fermi approximation, the phase separation scenario of stationary states can be obtained including all the mixed states on an equal footing for a spin-1 condensate under any confinement. According to the process used here, the density of each and every stationary states can be determined exactly in terms of the system parameters. This allows to write the expression for energy density of all states in a form which are not an explicit function of densities of those states. An energy density comparison therefore, among all the allowed stationary states can be done which will reveal domain structures depending on the system parameters. We study here, in details, a particular case of spherically symmetric harmonic confinement as an example and show a wide range of potential phase separation scenario for anti-ferromagnetic and ferromagnetic interactions.
Abstract A short review is given of recent progress in understanding the demixing transition in a mesoscopic gaseous cloud of bosonic and fermionic alkali atoms under the effect of their mutual repulsions at zero temperature. The mixture is confined inside a magnetic trap exerting external harmonic potentials on the atoms and the bosonic component is taken in a Bose-Einstein condensed state while the fermions are in a spin-polarized state. Main emphasis is placed on the role of the confinement: in a mesoscopic system (i) the phase transition becomes smooth as a function of the driving parameter, which is the boson-fermion s-wave scattering length; and (ii) various configurations of the phase-separated gaseous cloud are allowed, including some very exotic ones in an anisotropic trap. The transition inside a spherical trap leads to an egg-type structure, with the bosonic condensate being surrounded by a shell of fermions, and is best identified from a sharp upturn of the frequency of low-lying monopolar and dipolar oscillations of fermionic character. This dynamical signature of the transition appears when the overlap between the two components has already started to decrease, but is still quite appreciable. A system of specific experimental interest is the mixture of 6Li and 7Li isotopes, whose parameters could be driven towards the phase transition.
We briefly review current research on strongly interacting ultracold atomic polarized Fermi gases.In three dimensions the ground state of such systems is under strong debate.To gain some insights we investigate a system of one-dimensional strongly interacting polarized Fermi gases.In free space this is an integrable system,and therefore an exact phase diagram can be obtained.We show that an inhomogeneous superfluid state is most widespread in the phase diagram.We consider also the trapped case with an external harmonic trap,where two novel phase separation phases are found using the local density approximation.
We predict the phase separations of two-dimensional Fermi gases with repulsive contact-type interactions between two spin components. Using density-potential functional theory with systematic semiclassical approximations, we address the long-standing problem of itinerant ferromagnetism in realistic settings. We reveal a universal transition from the paramagnetic state at small repulsive interactions toward ferromagnetic density profiles at large interaction strengths, with intricate particle-number dependent phases in between. Building on quantum Monte Carlo results for uniform systems, we benchmark our simulations against Hartree–Fock calculations for a small number of trapped fermions. We thereby demonstrate that our employed corrections to the bare contact interaction energy and especially to the Thomas–Fermi kinetic energy functional are necessary for reliably predicting properties of trapped mesoscopic Fermi gases. The density patterns of the ground state survive at low finite temperatures and confirm the Stoner-type polarization behavior across a universal interaction parameter, albeit with substantial quantitative differences that originate in the trapping potential and the quantum-corrected kinetic energy. We also uncover a plethora of metastable configurations that are energetically comparable to the ground-state density profiles and are thus likely to be observed in experiments. We argue that our density-functional approach can be easily applied to interacting multi-component Fermi gases in general.