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arXiv:1308.0567 · Physical Review A

Ground state of a two-component dipolar Fermi gas in a harmonic potential

Przemysław Bienias, Krzysztof Pawłowski, Tilman Pfau, Kazimierz Rza̧żewski

Published Oct 4, 2013• 7 citations
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Abstract

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 ${}^{161}$Dy.

DOI
10.1103/physreva.88.043604

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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.
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.
We study a homogeneous two-component dipolar Fermi gas with 1D spin-orbit coupling (SOC) at zero temperature and find that the system undergoes a transition from the paramagnetic phase to the ferromagnetic phase under suitable dipolar interaction constant λ d, SOC constant λ SOC and contact interaction constant λ s. This phase transition can be of either 1st order or 2nd order, depending on the parameters. Near the 2nd-order phase transition, the system is partially magnetized in the ferromagnetic phase. With SOC, the ferromagnetic phase can even exist in the absence of the contact interaction. The increase in dipolar interaction, SOC strength, and contact interaction are all helpful to stabilize the ferromagnetic state. The critical dipolar interaction strength at the phase transition can be reduced by the increase in SOC strength or contact interaction. Phase diagrams of these systems are obtained.
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.
Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.