Heavy-Light Fermion Mixtures at Unitarity

We investigate fermion pairing in the unitary regime for a mass ratio corresponding to a 6Li-40K 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 ~ 3:1 heavy to light particles. A slight increase in attraction to kF*a ~ 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.

💡 Research Summary

The authors present a comprehensive quantum Monte‑Carlo (QMC) study of a two‑component Fermi mixture with unequal masses at the unitary limit, focusing on the experimentally relevant 6Li–40K system (mass ratio r ≈ 6.5). By employing diffusion Monte‑Carlo with trial wave functions for both superfluid and normal phases, they compute ground‑state energies, quasiparticle dispersion relations, and the equation of state as a function of polarization P = (N_h − N_l)/(N_h + N_l).

First, they verify the BCS prediction that the average chemical potential μ̄ and pairing gap Δ, when expressed in units of the reduced Fermi energy E_F^r (defined by the reduced mass m_r = m_l m_h/(m_l + m_h)), are essentially independent of the mass ratio. Their QMC results give ξ = E_SF/E_FG ≈ 0.390(5) and η = Δ/E_F ≈ 0.38(4) for r = 6.5, only about 5 % lower than the equal‑mass values (ξ ≈ 0.41, η ≈ 0.50). This modest reduction reflects the larger total pair mass, which suppresses the diffusion of pair centers of mass.

Second, they calculate the quasiparticle excitation spectra for the heavy and light species. The heavy‑particle branch lies lower in energy, while the light‑particle branch is shifted upward and its minimum moves toward zero momentum. The average of the two branches reproduces the equal‑mass dispersion, confirming that the overall superfluid properties are governed by the reduced mass. The lower minimum energy of the heavy branch implies a reduced critical temperature for superfluidity as the mass ratio increases.

Third, the authors explore the polarized regime by computing the energy versus polarization for both the normal and the gapless superfluid (polarized superfluid) states. The normal‑state energy is fitted with a polynomial constrained to reproduce the free‑particle limits at P = ±1 and the impurity binding energies B_h ≈ 0.36 E_F^l (heavy impurity in a light sea) and B_l ≈ 2.3 E_F^h (light impurity in a heavy sea). An energy minimum appears near P ≈ 0.5, corresponding to a particle‑number ratio of roughly 3 heavy to 1 light fermion. At this composition the energy rapidly approaches zero when the interaction strength is increased to k_F a ≈ 2.5, indicating a tendency toward collapse (or Efimov‑type three‑body instability) at a much lower mass ratio than in equal‑mass systems. For the opposite case (light‑majority, P < 0) the polarized superfluid lies very close in energy to a phase‑separated mixture of an almost fully polarized normal component and an unpolarized superfluid, suggesting near‑degeneracy of these two possibilities.

Finally, using the local‑density approximation (LDA) they map these bulk results onto a harmonically trapped gas where the heavy species experiences a potential twice as steep as the light species (as in recent Li–K experiments). The calculated radial polarization profiles reveal distinct shell structures. For large negative total polarization (light‑majority) the trap hosts a central unpolarized superfluid surrounded by a fully polarized normal shell of light atoms. Near zero total polarization the system exhibits three concentric regions: a central normal phase with P ≈ 0.5, an intermediate shell of unpolarized superfluid, and an outer layer of almost pure light atoms (or possibly a polarized superfluid). For large positive total polarization the entire cloud remains normal with a smoothly varying polarization.

In summary, the study shows that (i) the universal parameters ξ and η of the unitary superfluid are essentially set by the reduced mass and are only weakly affected by mass imbalance; (ii) the polarized equation of state is dramatically altered by the mass ratio, leading to an energy minimum at a 3:1 heavy‑to‑light composition and a rapid approach to zero energy with modest increase of interaction strength; (iii) trapped mixtures are predicted to display rich shell structures markedly different from the equal‑mass case, providing clear experimental signatures of mass‑imbalance effects. These findings offer valuable benchmarks for future cold‑atom experiments with heteronuclear Fermi mixtures and for theoretical treatments of strongly interacting, mass‑imbalanced fermionic systems.