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arXiv:0901.3148 · Physical Review Letters

Heavy-Light Fermion Mixtures at Unitarity

Alexandros Gezerlis, Stefano Gandolfi, Kevin E. Schmidt, Joseph Carlson

Published Aug 5, 2009• 66 citations
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Abstract

We investigate fermion pairing in the unitary regime for a mass ratio corresponding to a ;{6}Li-;{40}K mixture using quantum Monte Carlo methods. The ground-state energy and the average light- and heavy-particle excitation spectrum for the unpolarized superfluid state are nearly independent of the mass ratio. In the majority light system, the polarized superfluid is close to the energy of a phase separated mixture of nearly fully polarized normal and unpolarized superfluid. For a majority of heavy particles, we find an energy minimum for a normal state with a ratio of approximately 3ratio1 heavy to light particles. A slight increase in attraction to k_{F}a approximately 2.5 yields a ground state energy of nearly zero for this ratio. A cold unpolarized system in a harmonic trap at unitarity should phase separate into three regions, with a shell of unpolarized superfluid in the middle.

DOI
10.1103/physrevlett.103.060403

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•Jan 1, 2009•0 citations
We investigate fermion pairing in the unitary regime for a mass ratio corresponding to a ;{6}Li-;{40}K mixture using quantum Monte Carlo methods. The ground-state energy and the average light- and heavy-particle excitation spectrum for the unpolarized superfluid state are nearly independent of the mass ratio. In the majority light system, the polarized superfluid is close to the energy of a phase separated mixture of nearly fully polarized normal and unpolarized superfluid. For a majority of heavy particles, we find an energy minimum for a normal state with a ratio of approximately 3ratio1 heavy to light particles. A slight increase in attraction to k_{F}a approximately 2.5 yields a ground state energy of nearly zero for this ratio. A cold unpolarized system in a harmonic trap at unitarity should phase separate into three regions, with a shell of unpolarized superfluid in the middle.
We investigate a two-component mixture of resonantly interacting Fermi gases as a function of the ratio $\ensuremath{\kappa}$ of the heavy to the light mass of the two species. The diffusion Monte Carlo method is used to calculate the ground-state energy and the pair correlation function starting from two different guiding wave functions, which describe, respectively, the superfluid and the normal state of the gas. Results show that the mixture is stable and superfluid for mass ratios smaller than the critical value ${\ensuremath{\kappa}}_{c}=13\ifmmode\pm\else\textpm\fi{}1$. For larger values of $\ensuremath{\kappa}$ simulations utilizing the wave function of the normal state are unstable towards cluster formation. The relevant cluster states driving the instability appear to be formed by one light particle and two or more heavy particles within distances on the order of the range of the interatomic potential. The small overlap between the wave function of the trimer bound state and the guiding wave function used to describe the superfluid state produces the unphysical stability of the superfluid gas above ${\ensuremath{\kappa}}_{c}$.
We study the dilute fermion gas with pairing between two species and unequal concentrations in a harmonic trap using the mean-field theory and the local density approximation. We found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger than a certain critical value, which increases from the weak-coupling BCS region to the strong-coupling Bose-Einstein condensation (BEC) side. In the strong-coupling BEC regime, the radii of the superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. However, the lighter leftover fermions are easier to mix with the superfluid core than the heavier ones. A partially polarized superfluid can be found if the majority fermions are lighter, whereas phase separation is still found if they are heavier.
Using many-body results available from diagrammatic and ab initio Monte Carlo calculations we analyze the phase diagram $\ensuremath{\mu}=({\ensuremath{\mu}}_{\ensuremath{\uparrow}}+{\ensuremath{\mu}}_{\ensuremath{\downarrow}})/2$ versus $h=({\ensuremath{\mu}}_{\ensuremath{\uparrow}}\ensuremath{-}{\ensuremath{\mu}}_{\ensuremath{\downarrow}})/2$ of a unitary Fermi gas at zero temperature with population imbalance and unequal masses. We identify different regions where the gas is superfluid, partially polarized or fully polarized, and determine the corresponding coexistence conditions. The asymmetry in the phase diagram, caused by the mass imbalance, and its effect on the Chandrasekhar-Clogston limit for the critical polarization are explicitly discussed. The equation of state of the superfluid and normal phases is employed, within the local density approximation, to predict phase separated configurations in the presence of harmonic trapping potentials.
We present quantum Monte Carlo calculations of the properties of a two-component mass-imbalanced Fermi gas, corresponding to the $^{6}\mathrm{Li}\text{\ensuremath{-}}^{40}\mathrm{K}$ mixture. We compute the equation of state of the unpolarized system as a function of the scattering length with particular attention paid to the unitary limit, where the effect of the effective range of the interaction is explored. In order to investigate differences from the equal-mass case we also compute the pair-distribution function and the momentum distribution over a range of interaction strengths, which can provide information about the structure of the system. Finally, we compute the heavy-light quasiparticle spectrum for the full crossover regime. Our theoretical predictions, based on quantum Monte Carlo calculations, should inform future theoretical studies and can be tested by experiments with ultracold fermionic gases.
We study via mean-field theory the pairing between fermions of different masses, especially at the unitary limit. At equal populations, the thermodynamic properties are identical with the equal mass case provided an appropriate rescaling is made. At unequal populations, for sufficiently light majority species, the system does not phase separate. For sufficiently heavy majority species, the phase separated normal phase have a density larger than that of the superfluid. For atoms in harmonic traps, the density profiles for unequal mass fermions can be drastically different from their equal-mass counterparts.
In this thesis we first review the theory of the normal state of the unitary Fermi gas at T = 0 and the main properties of the normal-to-superfluid transition. Then we study the trapped gas under adiabatic rotation, i.e., avoiding the formation of vortices. We show that for polarized systems the rotation enhances the Chandrasekhar-Clogston limit due to pair breaking at the border between the superfluid and the normal phase, while it leaves the global critical polarization Pc of the trapped system unaffected. In the case of an unpolarized unitary superfluid the rotation causes a phase separation between a superfluid core and an unpolarized normal shell, in which the densities of the spin-up and spin-down atom numbers is equal. For both the polarized and the unpolarized systems we calculate experimental observables such as the density profiles and the angular momenta. From the study of Bose-Einstein condensates it is well known that an adiabatic rotation induces a quadrupole deformation of the trapped atomic cloud when the rotation exceeds a certain angular velocity. In Fermi gases the situation is different due to the phase separation discussed above, and the quadrupole instabilities are found to set on at smaller angular velocity than in the BEC case. This phenomenon together with a more general discussion concerning not only the energetic but also the dynamic instabilities of the phase separated system is presented. We use the present knowledge of the equation of state of Fermi mixtures with unequal masses to give quantitative predictions for the phase separation between the normal and superfluid components. The analysis is based on the study of the zero temperature μ-h phase diagram of the uniform two component gas. The phase diagram at unitarity is determined thanks to the knowledge of the equation of state available from diagrammatic techniques applied to highly polarized configurations and from Monte Carlo simulations. The phase diagram is then used, in the local density approximation, to calculate the density profiles of the two Fermi components in the presence of harmonic trapping. Eventually we investigate the polarization produced by the relative displacement of the potentials trapping two spin species of a unitary Fermi gas with population imbalance. We investigate the dipole polarizability of a polarized system both in the two-fluid and the three-fluid model at zero temperature and point out the major differences between the two treatments.