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arXiv:1006.5002 · Physical Review Letters

Breakdown of Universality for Unequal-Mass Fermi Gases with Infinite Scattering Length

D. Blume, K. M. Daily

Published Oct 19, 2010• 48 citations
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Abstract

We treat small trapped unequal-mass two-component Fermi gases at unitarity within a nonperturbative microscopic framework and investigate the system properties as functions of the mass ratio κ, and the numbers N1 and N2 of heavy and light fermions. While equal-mass Fermi gases with infinitely large interspecies s-wave scattering length a(s) are universal, we find that unequal-mass Fermi gases are, for sufficiently large κ and in the regime where Efimov physics is absent, not universal. In particular, the (N₁,N₂) = (2, 1) and (3, 1) systems exhibit three-body and four-body resonances at κ=12.314(2) and 10.4(2), respectively, as well as surprisingly large finite-range effects. These findings have profound implications for ongoing experimental efforts and quantum simulation proposals that utilize unequal-mass atomic Fermi gases.

DOI
10.1103/physrevlett.105.170403

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We treat small trapped unequal-mass two-component Fermi gases at unitarity within a nonperturbative microscopic framework and investigate the system properties as functions of the mass ratio κ, and the numbers N1 and N2 of heavy and light fermions. While equal-mass Fermi gases with infinitely large interspecies s-wave scattering length a(s) are universal, we find that unequal-mass Fermi gases are, for sufficiently large κ and in the regime where Efimov physics is absent, not universal. In particular, the (N₁,N₂) = (2, 1) and (3, 1) systems exhibit three-body and four-body resonances at κ=12.314(2) and 10.4(2), respectively, as well as surprisingly large finite-range effects. These findings have profound implications for ongoing experimental efforts and quantum simulation proposals that utilize unequal-mass atomic Fermi gases.
Two-component Fermi and Bose gases with infinitely large interspecies sss-wave scattering length as{a}_{s}as​ exhibit a variety of intriguing properties. Among these are the scale invariance of two-component Fermi gases with equal masses, and the favorable scaling of Efimov features for two-component Bose gases and Bose-Fermi mixtures with unequal masses. This paper builds on our earlier work [Phys. Rev. Lett. 105, 170403 (2010)] and presents a detailed discussion of our studies of small unequal-mass two-component systems with infinite as{a}_{s}as​ in the regime where three-body Efimov physics is absent. We report on nonuniversal few-body resonances. Just like with two-body systems on resonance, few-body systems have a zero-energy bound state in free space and a diverging generalized scattering length. Our calculations are performed within a nonperturbative microscopic framework and investigate the energetics and structural properties of small unequal-mass two-component systems as functions of the mass ratio $\ensuremath{\kappa}$, and the numbers N1{N}_{1}N1​ and N2{N}_{2}N2​ of heavy and light atoms. For purely attractive Gaussian two-body interactions, we find that the (N1,N2)=(2,1)({N}_{1},{N}_{2})=(2,1)(N1​,N2​)=(2,1) and (3,1)(3,1)(3,1) systems exhibit three-body and four-body resonances at mass ratios $\ensuremath{\kappa}=12.314(2)$ and 10.4(2)10.4(2)10.4(2), respectively. The three- and four-particle systems on resonance are found to be large. It seems feasible that the features discussed in this paper can be probed experimentally with present-day technology.
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.
Two-component equal-mass Fermi gases, in which unlike atoms interact through a short-range two-body potential and like atoms do not interact, are stable even when the interspecies sss-wave scattering length becomes infinitely large. Solving the many-body Schr\"odinger equation within a hyperspherical framework and by Monte Carlo techniques, this paper investigates how the properties of trapped two-component gases change if a third or fourth component are added. If all interspecies scattering lengths are equal and negative, our calculations suggest that both three- and four-component Fermi gases become unstable for a certain critical set of parameters. The relevant length scale associated with the collapse is set by the interspecies scattering length and we argue that the collapse is similar to the collapse of an attractive trapped Bose gas, a many-body phenomenon. Furthermore, we consider a three-component Fermi gas in which two interspecies scattering lengths are negative while the other interspecies scattering length is zero. In this case, the stability of the Fermi system is predicted to depend appreciably on the range of the underlying two-body potential. We find parameter combinations for which the system appears to become unstable for a finite negative scattering length and parameter combinations for which the system appears to be made up of weakly bound trimers that consist of one fermion of each species.
We consider a superfluid state in a two-component gas of fermionic atoms with equal densities and unequal masses in the BCS limit. We develop a perturbation theory along the lines proposed by Gorkov and Melik-Barkhudarov and find that for a large difference in the masses of heavy (M)(M)(M) and light (m)(m)(m) atoms one has to take into account both the second-order and third-order contributions. The result for the critical temperature and order parameter is then quite different from the prediction of the simple BCS approach. Moreover, the small parameter of the theory turns out to be $({p}_{F}\ensuremath{\mid}a\ensuremath{\mid}∕\ensuremath{\hbar})\sqrt{M∕m}⪡1$, where pF{p}_{F}pF​ is the Fermi momentum and aaa the scattering length. Thus, for a large mass ratio M∕mM∕mM∕m the conventional perturbation theory requires significantly smaller Fermi momenta (densities) or scattering lengths than in the case of $M\ensuremath{\sim}m$, where the small parameter is ${p}_{F}\ensuremath{\mid}a\ensuremath{\mid}∕\ensuremath{\hbar}⪡1$. We show that three-body scattering resonances appearing at a large mass ratio due to the presence of three-body bound Efimov states do not influence the result, which in this sense becomes universal.
We report on previously unobserved intersystem degeneracies in two-component equal-mass Fermi gases with interspecies zero-range interactions under isotropic harmonic confinement. Over the past 10 years, two-component Fermi gases consisting of n1 spin-up and n2 spin-down atoms with interspecies zero-range interactions have become a paradigm for modeling condensed matter systems, nuclear matter, and neutron matter. We show that the eigenenergies of the (n1 + 1, n2 - 1) system are degenerate with the eigenenergies of the (n1, n2) system for any s-wave scattering length a(s), including infinitely large, positive, and negative a(s). The existence of the intersystem degeneracies is demonstrated explicitly for few-body systems with n1 + n2 = 4, 5, and 6. The degeneracies and associated symmetries are explained within a group theoretical framework.
We consider a Fermi gas with two components of different masses, with the s-wave two-body interaction tuned to unitarity. In the range of mass ratio 8.62<M/m<13.6, it is possible for a short-range interaction between heavy fermions to produce a resonance in a three-body channel. The resulting system is scale invariant and has universal properties, and is very strongly interacting. When M/m is slightly above the lower limit 8.62, the ground state energy of a 2ratio1 mixture of heavy and light fermions is less than 2% of the energy of a noninteracting gas with the same number densities. We derive exact relationships between the pressures of the unitary Fermi gases with and without three-body resonance when the mass ratio is close to the critical values of 8.62 and 13.6.