Dipolar Fermi Gas Research Articles

Ultracold fermi gases with resonant dipole-dipole interaction.

The superfluid phases in resonant dipolar Fermi gases are investigated by the standard mean-field theory. In contrast to the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer superfluid in Fermi gases with isotropic interactions, resonant dipolar interaction leads to two completely different BEC phases of the tight-binding Fermi molecules on both sides of the resonance, which are characterized by two order parameters with distinct internal symmetries. We point out that, near the resonances, the two competitive phases can coexist, and an emergent relative phase between the two order parameters spontaneously breaks time-reversal symmetry, which could be observed in momentum resolved rf spectroscopy.

Density-wave phases of dipolar fermions in a bilayer

We investigate the phase diagram of dipolar fermions with aligned dipole moments in a two-dimensional (2D) bilayer. Using a version of the Singwi-Tosi-Land-Sjolander scheme recently adapted to dipolar fermions in a single layer [M. M. Parish and F. M. Marchetti, Phys. Rev. Lett. 108, 145304 (2012)], we determine the density-wave instabilities of the bilayer system within linear response theory. We find that the bilayer geometry can stabilize the collapse of the 2D dipolar Fermi gas with intralayer attraction to form a new density wave phase that has an orientation perpendicular to the density wave expected for strong intralayer repulsion. We thus obtain a quantum phase transition between stripe phases that is driven by the interplay between strong correlations and the architecture of the low dimensional system.

Properties of the Trapped Dipolar Ultracold Gases at Finite Temperatures

We study the equilibrium and dynamical properties of dipolar Fermi gases at finite temperatures within the semiclassical treatment. The equilibrium property is discussed by introducing a variational ansatz for the phase-space distribution function. As for the dynamics, we apply the moment method to the kinetic equation to study quadrupole oscillation. We find that the quadrupole mode of polar molecules at high-temperture regime is in the hydrodynamic regime because of their large dipole moment.

Study of a degenerate dipolar Fermi gas of 161Dy atoms

We study the properties of a single-component (spin polarized) degenerate dipolar Fermi gas of 161Dy atoms using a hydrodynamic description. Under axially-symmetric trapping we suggest reduced one- (1D) and two-dimensional (2D) descriptions for the cigar and disc shapes, respectively. In addition to a complete numerical solution of the hydrodynamic model we also consider a variational approximation. For a trapped system under appropriate conditions, the variational approximation as well as the reduced 1D and 2D models are found to yield results for the shape, size and chemical potential of the system in agreement with the full numerical solution of the three-dimensional (3D) model. For the uniform system we consider anisotropic sound propagation in 3D. An analytical result for anisotropic sound propagation in a uniform dipolar degenerate Fermi gas is found to be in agreement with the results of numerical simulation in 3D.

Topologicalpx+ipysuperfluid phase of a dipolar Fermi gas in a two-dimensional optical lattice

In a dipolar Fermi gas, the anisotropic interaction between electric dipoles can be turned into an effectively attractive interaction in the presence of a rotating electric field. We show that the topological $p_{x}+ip_{y}$ superfluid phase can be realized in a single-component dipolar Fermi gas trapped in a 2D square optical lattice with this attractive interaction at low temperatures. The $p_{x}+ip_{y}$ superfluid state has potential applications for topological quantum computing. We obtain the phase diagram of this system at zero temperature. In the weak-coupling limit, the p-wave superfluid phase is stable for all filling factors. As the interaction strength increases, it is stable close to filling factors $n=0$ or $n=1$, and phase separation takes place in between. When the interaction strength is above a threshold, the system is phase separated for any $0<n<1$. The transition temperature of the $p_{x}+ip_{y}$ superfluid state is estimated and the implication for experiments is discussed.

Magnetostriction and exchange effects in trapped dipolar Bose and Fermi gases

We examine the magnetostrictive position and momentum space distortions that occur in harmonically confined dipolar Bose and Fermi gases. Direct interactions give rise to position space magnetostriction and exchange interactions give rise to momentum space magnetostriction. While the position space magnetostriction is similar in Bose and Fermi systems, the momentum space magnetostriction is markedly different: the Bose gas momentum distribution distorts in the opposite sense to that of the Fermi gas. By relating exchange effects to short range correlations between the particles we discuss the energetic origin of this difference. Our main calculations are based on Hartree-Fock theory, but we also provide analytic approximations for the magnetostriction effects at zero and finite temperature. Our predictions should be verifiable in current experiments with ultra-cold polar molecules.

Quantum Degenerate Dipolar Fermi Gas

We report the first quantum degenerate dipolar Fermi gas, the realization of which opens a new frontier for exploring strongly correlated physics and, in particular, quantum liquid crystalline phases. A quantum degenerate Fermi gas of the most magnetic atom 161Dy is produced by laser cooling to 10 μK before sympathetically cooling with ultracold, bosonic 162Dy. The temperature of the spin-polarized 161Dy is a factor T/T(F)=0.2 below the Fermi temperature T(F)=300 nK. The cotrapped 162Dy concomitantly cools to approximately T(c) for Bose-Einstein condensation, thus realizing a novel, nearly quantum degenerate dipolar Bose-Fermi gas mixture. Additionally, we achieve the forced evaporative cooling of spin-polarized 161Dy without 162Dy to T/T(F)=0.7. That such a low temperature ratio is achieved may be a first signature of universal dipolar scattering.

Spin-orbit coupled Fermi liquid theory of ultracold magnetic dipolar fermions

We investigate Fermi liquid states of the ultracold magnetic dipolar Fermi gases in the simplest two-component case including both thermodynamic instabilities and collective excitations. The magnetic dipolar interaction is invariant under the simultaneous spin-orbit rotation but not under either the spin or the orbit one. Therefore, the corresponding Fermi liquid theory is intrinsically spin-orbit coupled. This is a fundamental feature of magnetic dipolar Fermi gases different from electric dipolar ones. The Landau interaction matrix is calculated and is diagonalized in terms of the spin-orbit coupled partial-wave channels of the total angular momentum $J$. The leading thermodynamic instabilities lie in the channels of ferromagnetism hybridized with the ferronematic order with $J={1}^{+}$ and the spin-current mode with $J={1}^{\ensuremath{-}}$, where $+$ and $\ensuremath{-}$ represent even and odd parities, respectively. An exotic propagating collective mode is identified as spin-orbit coupled Fermi surface oscillations in which spin distribution on the Fermi surface exhibits a topologically nontrivial hedgehog configuration.

Density Instabilities in a Two-Dimensional Dipolar Fermi Gas

We study the density instabilities of a two-dimensional gas of dipolar fermions with aligned dipole moments. The random phase approximation (RPA) for the density-density response function is never accurate for the dipolar gas, and so we incorporate correlations beyond RPA via an improved version of the Singwi-Tosi-Land-Sjölander scheme. In addition to density-wave instabilities, our formalism captures the collapse instability that is expected from Hartree-Fock calculations but is absent from RPA. Crucially, we find that when the dipoles are perpendicular to the layer, the system spontaneously breaks rotational symmetry and forms a stripe phase, in defiance of conventional wisdom.

Quadrupole oscillation in a dipolar Fermi gas: Hydrodynamic versus collisionless regime

The surface quadrupole mode of an harmonically trapped dipolar Fermi gas is studied in both the hydrodynamic and collisionless regimes. The anisotropy and long-range effects of the dipolar force as well as the role of the trapping geometry are explicitly investigated. In the hydrodynamic regime the frequency is always slightly smaller than the $\sqrt{2}{\ensuremath{\omega}}_{\ensuremath{\perp}}$ value holding for gases interacting with contact interactions. In the collisionless regime the frequency can be either pretty smaller or larger than the noninteracting value $2{\ensuremath{\omega}}_{\ensuremath{\perp}}$, depending on the cloud aspect ratio. Our results suggest that the frequency of the surface quadrupole oscillation can provide a useful test for studying, at very low temperatures, the transition between the normal and the superfluid phase and, in the normal phase at higher temperatures, the crossover between the collisional and collisionless regimes. The consequences of the anisotropy of the dipolar force on the virial theorem are also discussed.

Spontaneous generation of spin-orbit coupling in magnetic dipolar Fermi gases

The stability of an unpolarized two-component dipolar Fermi gas is studied within mean-field theory. Besides the known instability towards spontaneous magnetization with Fermi sphere deformation, another instability toward spontaneous formation of a spin-orbit coupled phase with a Rashba-like spin texture is found. A phase diagram is presented and consequences are briefly discussed.

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

We examine collective modes, stability, and BCS pairing in a quasi-two-dimensional gas of dipolar fermions aligned by an external field. By using the (conserving) Hartree-Fock approximation, which treats direct and exchange interactions on an equal footing, we obtain the spectrum of single-particle excitations and long wavelength collective modes (zero sound) in the normal phase. It appears that exchange interactions result in strong damping of zero sound when the tilting angle between the dipoles and the normal to the plane of confinement is below some critical value. In particular, zero sound cannot propagate if the dipoles are perpendicular to the plane of confinement. At intermediate coupling we find unstable modes that can lead either to collapse of the system or the formation of a density wave. The BCS transition to a superfluid phase, on the other hand, occurs at arbitrarily weak strengths of the dipole-dipole interaction, provided the tilting angle exceeds a critical value. We determine the critical temperature of the transition taking into account many-body effects as well as virtual transitions to higher excited states in the confining potential, and discuss prospects of experimental observations.

Correlation effect on the roton minimum of the rotating dipolar Fermi gas

The collective-excitation spectrum from a filled Landau level in a rotating dipolar Fermi gas is investigated through the equation of motion method. The predicted excitation spectrum exhibits a roton structure which is affected by the strength of dipolar interactions and trapping potential. The correlation effect on the roton minimum is observed by varying the dipolar interaction strength. An increase of the dipolar interaction strength leads to a deeper roton minimum. The roton minimum can even become zero, where the system exhibits instability, as the dipolar strength approaches a critical value. As the dynamical stability of the system is studied through the roton structure, we find that this zero-value roton minimum is a precursor of the occurrence of a bubble crystal.

Correlation energy of a homogeneous dipolar Fermi gas

We study the normal state of a 3$d$ homogeneous dipolar Fermi gas beyond the Hartree-Fock approximation. The correlation energy is found of the same order as the Fock energy, unusually strong for a Fermi-liquid system. As a result, the critical density of mechanical collapse is smaller than that estimated in the Hartree-Fock approximation. With the correlation energy included, an energy functional is proposed for the trapped system, and its property is explored.

Antiferromagnetism and superfluidity of a dipolar Fermi gas in a two-dimensional optical lattice

In a dipolar Fermi gas, the dipole-dipole interaction between fermions can be turned into a dipolar Ising interaction between pseduospins in the presence of an AC electric field. When trapped in a 2D optical lattice, such a dipolar Fermi gas has a very rich phase diagram at zero temperature, due to the competition between antiferromagnetism and superfluidity. At half filling, the antiferromagnetic state is the favored ground state. The superfluid state appears as the ground state at a smaller filling factor. In between there is a phase-separated region. The order parameter of the superfluid state can display different symmetries depending on the filling factor and interaction strength, including d-wave ($d$), extend s-wave ($xs$), or their linear combination ($xs+i\times d$). The implication for the current experiment is discussed.

Quantum Hall effects in fast-rotating Fermi gases with anisotropic dipolar interaction

We investigate fast rotating quasi-two-dimensional dipolar Fermi gases in the quantum Hall regime. By tuning the direction of the dipole moments with respect to the $z$ axis, the dipole-dipole interaction becomes anisotropic in the $x$-$y$ plane. For a soft confining potential we find that, as we tilt the angle of the dipole moments, the system evolves from a $\ensuremath{\nu}=1/3$ Laughlin state with dipoles being polarized along the $z$ axis to a series of ground states characterized by distinct mean total angular momentum, and finally to an anisotropic integer quantum Hall state. During the transition from the fractional regime to the integer regime, we find that the density profile of the system exhibits crystal-like structures. We map out the ground states as a function of the tilt angle and the confining potential, revealing the competition of the isotropic confining potential and both the isotropic and anisotropic components of the dipole-dipole interaction.

Dynamical properties of a trapped dipolar Fermi gas at finite temperature

We investigate the dynamical properties of a trapped finite-temperature normal Fermi gas with dipole-dipole interaction. For the free expansion dynamics, we show that the expanded gas always becomes stretched along the direction of the dipole moment. In addition, we present the temperature and interaction dependences of the asymptotical aspect ratio. We further study the collapse dynamics of the system by suddenly increasing the dipolar interaction strength. We show that, in contrast to the anisotropic collapse of a dipolar Bose-Einstein condensate, a dipolar Fermi gas always collapses isotropically when the system becomes globally unstable. We also explore the interaction and temperature dependences for the frequencies of the low-lying collective excitations.

Statistical Difference in the Normal Phase of the Dipolar Ultracold Gases at Finite Temperatures

We study the equilibrium properties of dipolar Bose and Fermi gases at finite temperatures. We have recently developed a variational ansatz for the phase-space distribution function of a dipolar Fermi gas at finite temperatures. We extend the variational formalism to a Bose gas and discuss the effect of dipolar interactions with different statistics on thermal equilibrium, with particular emphasis on deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio, and dipole moment. In addition, we discuss how deformation in both real and momentum spaces can be observed in the high-temperature regime, which is relevant for the current experiments at JILA [Ni et al. : Science 322 (2008) 231] and at the University of Tokyo [Aikawa et al. : New J. Phys. 11 (2009) 055035].

Thermodynamics and coherence of a trapped dipolar Fermi gas

We develop a meanfield treatment of a polarized trapped Fermi gas with dipole-dipole interactions. Our approach is based on self-consistent semiclassical Hartree-Fock theory that accounts for direct and exchange interactions. We discuss our procedure for numerically implementing the calculation. We study the thermodynamic and the first and second order correlation properties of the system. We find that the system entropy depends on the trap geometry, allowing the system to be cooled as the trap aspect ratio is increased, and that exchange interactions cause the correlation functions to be anisotropic in the low temperature regime. We also find that many uniform gas thermodynamic predictions, for which direct interaction effects vanish, are qualitatively unreliable for trapped systems, most notably for oblate traps. We develop a simplified Hartree formalism that is applicable to anisotropic harmonic traps.

Free Expansion of a Weakly-Interacting Dipolar Fermi Gas

We theoretically investigate a polarized dipolar Fermi gas in free expansion. The inter-particle dipolar interaction deforms phase-space distribution in trap and also in the expansion. We exactly predict the minimal quadrupole deformation in the expansion for the high-temperature Maxwell–Boltzmann and zero-temperature Thomas–Fermi gases in the Hartree–Fock and Landau–Vlasov approaches. In conclusion, we provide a proper approach to develop the time-of-flight method for the weakly-interacting dipolar Fermi gas and also reveal a scaling law associated with the Liouville's theorem in the long-time behaviors of the both gases.