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arXiv:0805.2130 · Physical Review A

Trapped polarized Fermi gas at unitarity

D. Blume

Published Jul 24, 2008• 14 citations
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Abstract

We consider population-imbalanced two-component Fermi gases under external harmonic confinement interacting through short-range two-body potentials with diverging $s$-wave scattering length. Using the fixed-node diffusion Monte Carlo method, the energies of the ``normal state'' are determined as functions of the population imbalance and the number of particles. The energies of the trapped system follow, to a good approximation, a universal curve even for fairly small systems. A simple parametrization of the universal curve is presented and related to the equation of state of the bulk system.

DOI
10.1103/physreva.78.013635

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We consider population-imbalanced two-component Fermi gases under external harmonic confinement interacting through short-range two-body potentials with diverging sss-wave scattering length. Using the fixed-node diffusion Monte Carlo method, the energies of the ``normal state'' are determined as functions of the population imbalance and the number of particles. The energies of the trapped system follow, to a good approximation, a universal curve even for fairly small systems. A simple parametrization of the universal curve is presented and related to the equation of state of the bulk system.
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Using two different numerical methods, we study the behavior of two-component Fermi gases interacting through short-range sss-wave interactions in a harmonic trap. A correlated Gaussian basis-set expansion technique is used to determine the energies and structural properties, i.e., the radial one-body densities and pair distribution functions, for small systems with either even or odd NNN, as functions of the sss-wave scattering length and the mass ratio $\ensuremath{\kappa}$ of the two species. Particular emphasis is put on a discussion of the angular momentum of the system in the BEC-BCS crossover regime. At unitarity, the excitation spectrum of the four-particle system with total angular momentum L=0L=0L=0 is calculated as a function of the mass ratio $\ensuremath{\kappa}$. The results are analyzed from a hyperspherical perspective, which offers unique insight into the problem. Additionally, fixed-node diffusion Monte Carlo calculations are performed for equal-mass Fermi gases with up to N=30N=30N=30 atoms. We focus on the odd-even oscillations of the ground-state energy of the equal-mass unitary system having up to N=30N=30N=30 particles, which are related to the excitation gap of the system. Furthermore, we present a detailed analysis of the structural properties of these systems.
The properties of two-component Fermi gases with zero-range interactions are universal. We use an explicitly correlated Gaussian basis set expansion approach to investigate small equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement. At unitarity, we determine the ground-state energy for systems with up to 10 particles interacting through finite-range two-body potentials for both even and odd numbers of particles. We extrapolate the energies to the zero-range limit using a novel scheme that removes the linear and, in some cases, also the quadratic dependence of the ground-state energies on the two-body range. Our extrapolated zero-range energies are compared with results from the literature. We also calculate the two-body Tan contact and structural properties.
Equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement with large sss-wave scattering length are considered. Using the stochastic variational approach, we determine the lowest 286 and 164 relative eigenenergies of the (2,2)(2,2)(2,2) and (3,1)(3,1)(3,1) systems at unitarity as a function of the range r0{r}_{0}r0​ of the underlying two-body potential and extrapolate to the ${r}_{0}\ensuremath{\rightarrow}0$ limit. Our calculations include all states with vanishing and finite angular momentum LLL (and natural and unnatural parity $\ensuremath{\Pi}$) with relative energy up to 10.5 $\ensuremath{\hbar}\ensuremath{\Omega}$, where $\ensuremath{\Omega}$ denotes the angular trapping frequency of the external confinement. Our extrapolated zero-range energies are estimated to have uncertainties of 0.1% or smaller. The (2,2)(2,2)(2,2) and (3,1)(3,1)(3,1) energies are used to determine the fourth-order virial coefficient of the trapped unitary two-component Fermi gas in the low-temperature regime. Our results are compared with recent predictions for the fourth-order virial coefficient of the homogeneous system. We also calculate small portions of the energy spectra of the (3,2)(3,2)(3,2) and (4,1)(4,1)(4,1) systems at unitarity.
We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging sss-wave scattering length as{a}_{s}as​, that is, with 1/as=01/{a}_{s}=01/as​=0. The high-temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio $\ensuremath{\kappa}$ increases and diverges when Efimov physics sets in at $\ensuremath{\kappa}=13.61$. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for $\ensuremath{\kappa}=1$, but finite for $\ensuremath{\kappa}\ensuremath{\ne}1$ (with a majority of heavy particles). Compared to the equilibrium polarization of the noninteracting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations.
The ground-state properties of two-component repulsive Fermi gases in two dimensions are investigated by means of fixed-node diffusion Monte Carlo simulations. The energy per particle is determined as a function of the intercomponent interaction strength and of the population imbalance. The regime of universality in terms of the sss-wave scattering length is identified by comparing results for hard-disk and for soft-disk potentials. In the large imbalance regime, the equation of state turns out to be well described by a Landau-Pomeranchuk functional for two-dimensional polarons. To fully characterize this expansion, we determine the polarons' effective mass and their coupling parameter, complementing previous studies on their chemical potential. Furthermore, we extract the magnetic susceptibility from low-imbalance data, finding only small deviations from the mean-field prediction. While the mean-field theory predicts a direct transition from a paramagnetic to a fully ferromagnetic phase, our diffusion Monte Carlo results suggest that the partially ferromagnetic phase is stable in a narrow interval of the interaction parameter. This finding calls for further analyses on the effects due to the fixed-node constraint.