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arXiv:cond-mat/0606706 · Physical Review B

Superfluidity and excitations at unitarity

Dean Lee

Published Apr 3, 2007• 18 citations
arXivHTMLPDF

Abstract

We present lattice results for spin-$1∕2$ fermions at unitarity, where the effective range of the interaction is zero and the scattering length is infinite. We measure the spatial coherence of difermion pairs for a system of 6, 10, 14, 18, 22, 26 particles with equal numbers of up and down spins in a periodic cube. Using Euclidean time projection, we analyze ground-state properties and transient behavior due to low-energy excitations. At asymptotically large values of $t$ we see long-range order consistent with spontaneously broken U(1) fermion-number symmetry and a superfluid ground state. At intermediate times we see exponential decay in the $t$-dependent signal due to an unknown low-energy excitation. We probe this low-energy excitation further by calculating two-particle correlation functions. We find that the excitation has the properties of a chain of particles extending across the periodic lattice.

DOI
10.1103/physrevb.75.134502

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The unitary Fermi gas is a many-body system of two-component fermions with zero-range interactions tuned to infinite scattering length. Despite much activity and interest in unitary Fermi gas and its universal properties, there have been great difficulties in performing accurate calculations of the superfluid condensate fraction and pairing wave function. In this paper, we present auxiliary-field lattice Monte Carlo simulations using a lattice interaction which accelerates the approach to the continuum limit, thereby allowing for robust calculations of these difficult observables. As a benchmark test, we compute the ground-state energy of 33 spin-up and 33 spin-down particles. As a fraction of the free Fermi gas energy EFG{E}_{\text{FG}}EFG​, we find E0/EFG=0.369(2),0.372(2),{E}_{0}/{E}_{\text{FG}}=0.369(2),0.372(2),E0​/EFG​=0.369(2),0.372(2), using two different definitions of the finite-system energy ratio, in agreement with the latest theoretical and experimental results. We then determine the condensate fraction by measuring off-diagonal long-range order in the two-body density matrix. We find that the fraction of condensed pairs is $\ensuremath{\alpha}=0.43(2)$. We also extract the pairing wave function and find the pair correlation length to be ${\ensuremath{\zeta}}_{p}{k}_{F}=1.8(3)\ensuremath{\hbar}$, where kF{k}_{F}kF​ is the Fermi momentum. Provided that the simulations can be performed without severe sign oscillations, the methods we present here can be applied to superfluid neutron matter as well as more exotic PPP-wave and DDD-wave superfluids.
We investigate the e↵ect of a spherical cuto↵ in the single particle momentum on the lattice calculations of unitary fermions, and use this to explore the ground state configuration. The unitarity limit, corresponding to an infinite s-wave scattering length and zero interaction range, is achieved by tuning the lattice coupling of four-fermi interactions to reproduce the scattering phase shift of σ = π/2 in the continuum. We particularly compute the ground state energies of three unitary fermions at zero and non-zero net momenta. We show that in the continuum limit the spherical cuto↵ does not a↵ect the results, while it violates the unitarity for a boosted pair of fermions. Our findings suggest that the pair of fermions in the ground state of three unitary fermions has zero momentum, while the total net momentum of the system is carried by the unpaired fermion.
We investigate the e↵ect of a spherical cuto↵ in the single particle momentum on the lattice calculations of unitary fermions, and use this to explore the ground state configuration. The unitarity limit, corresponding to an infinite s -wave scattering length and zero interaction range, is achieved by tuning the lattice coupling of four-fermi interactions to reproduce the scattering phase shift of σ = π/2 in the continuum. We particularly compute the ground state energies of three unitary fermions at zero and non-zero net momenta. We show that in the continuum limit the spherical cuto↵ does not a↵ect the results, while it violates the unitarity for a boosted pair of fermions. Our findings suggest that the pair of fermions in the ground state of three unitary fermions has zero momentum, while the total net momentum of the system is carried by the unpaired fermion.
We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low-energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground-state (T=0)(T=0)(T=0) superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground-state energy, and low-energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the sss-wave case where the BCS to BEC evolution is just a crossover. Third, we present a Gaussian fluctuation theory near the critical temperature (T=Tc)(T={T}_{\mathrm{c}})(T=Tc​), and we analyze the number of bound, scattering, and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near Tc{T}_{\mathrm{c}}Tc​, and compare the Ginzburg-Landau coherence length with the zero-temperature average Cooper pair size.