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arXiv:cond-mat/0604580 · Physical Review A

Superfluidity in a three-flavor Fermi gas with SU(3) symmetry

Lianyi He, Meng Jin, Pengfei Zhuang

Published Sep 8, 2006• 54 citations
arXivHTMLPDF

Abstract

We investigate the superfluidity and the associated Nambu-Goldstone modes in a three-flavor atomic Fermi gas with $\mathrm{SU}(3)$ global symmetry. The $s$-wave pairing occurs in flavor antitriplet channel due to the Pauli principle, and the superfluid state contains both gapped and gapless fermionic excitations. Corresponding to the spontaneous breaking of the $\mathrm{SU}(3)$ symmetry to a $\mathrm{SU}(2)$ symmetry with five broken generators, there are only three Nambu-Goldstone modes, one is with linear dispersion law and two are with quadratic dispersion law. The other two expected Nambu-Goldstone modes become massive with a mass gap of the order of the fermion energy gap in a wide coupling range. The abnormal number of Nambu-Goldstone modes, the quadratic dispersion law, and the mass gap have significant effect on the low-temperature thermodynamics of the matter.

DOI
10.1103/physreva.74.033604

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We investigate the superfluidity and the associated Nambu-Goldstone modes in a three-flavor atomic Fermi gas with SU(3)\mathrm{SU}(3)SU(3) global symmetry. The sss-wave pairing occurs in flavor antitriplet channel due to the Pauli principle, and the superfluid state contains both gapped and gapless fermionic excitations. Corresponding to the spontaneous breaking of the SU(3)\mathrm{SU}(3)SU(3) symmetry to a SU(2)\mathrm{SU}(2)SU(2) symmetry with five broken generators, there are only three Nambu-Goldstone modes, one is with linear dispersion law and two are with quadratic dispersion law. The other two expected Nambu-Goldstone modes become massive with a mass gap of the order of the fermion energy gap in a wide coupling range. The abnormal number of Nambu-Goldstone modes, the quadratic dispersion law, and the mass gap have significant effect on the low-temperature thermodynamics of the matter.
Interacting Bose-Fermi mixtures possess a fermionic (super)symmetry when bosons and fermions in the mixture have equal masses, and when the interaction strengths are appropriately tuned. This symmetry is spontaneously broken in the ground state of the mixture, leading to a novel Goldstone mode with fermionic statistics and quadratic dispersion. Here we examine the effect of explicit symmetry-breaking perturbations on the Goldstone mode. When the symmetry is not exact and the system is allowed to deviate from the symmetric point, we find that the Goldstone mode acquires an energy gap. We show that the excitations manifest themselves as a nonanalyticity of the thermodynamic pressure.
Bragg spectroscopy shows the evolution of gapless Goldstone modes and single-particle-like excitations in an atomic Fermi superfluid as it crosses from a Bardeen–Cooper–Schrieffer superfluid to the Bose–Einstein condensate regime. Spontaneous symmetry breaking is a central paradigm of elementary particle physics1, magnetism2, superfluidity3 and superconductivity4. According to Goldstone’s theorem, phase transitions that break continuous symmetries lead to the existence of gapless excitations in the long-wavelength limit5. These Goldstone modes can become the dominant low-energy excitation, showing that symmetry breaking has a profound impact on the physical properties of matter. Here, we present a comprehensive study of the elementary excitations in a homogeneous strongly interacting Fermi gas through the crossover from a Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC) of molecules using two-photon Bragg spectroscopy. The spectra exhibit a discrete Goldstone mode, associated with the broken-symmetry superfluid phase, as well as pair-breaking single-particle excitations. Our techniques yield a direct determination of the superfluid pairing gap and speed of sound in close agreement with strong-coupling theories.
The low-energy modes of a superfluid atomic Fermi gas at zero temperature are investigated. The Bose-Einstein-condensate (BEC) side of the superfluid phase is studied in detail. The atoms are assumed to be in only one internal state, so that for a sufficiently diluted gas the pairing of fermions can be considered effective in the l=1 channel only. In agreement with previous works on p-wave superfluidity in Fermi systems, it is found that the px+ipyp_x+ip_ypx​+ipy​ phase represents the lowest energy state in both the Bardeen-Cooper-Schrieffer (BCS) and BEC sides. Our calculations show that at low energy three branches of collective modes can emerge, with different species of dispersion relations: a phonon-like mode, a single-particle-like mode and a gapped mode. A comparison with the Bogoliubov excitations of the corresponding spinor Bose condensate is made. They reproduce the dispersion relations of the excitation modes of the p-wave superfluid Fermi gas to a high accuracy.
We study theoretically interspecies Cooper pairing in a fermionic system with SU(2) $\ifmmode\times\else\texttimes\fi{}$ SU(6) symmetry. We show that, with suitable unitary transformations, the order parameter for the ground state can be reduced to only two nonvanishing complex components. The ground state has a large degeneracy. We find that while some Goldstone modes have linear dispersion, others are quadratic at low frequencies. We compare our results with the case of SU(NNN).
We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges QQQ and ${Q}^{\ifmmode\dagger\else\textdagger\fi{}}$. Each supercharge is built solely from spinless fermion operators and depends on a parameter ggg. The system is strongly interacting for small ggg, and in the extreme limit g=0g=0g=0, the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-ggg limit, the system is noninteracting and SUSY is broken spontaneously. We study the model for modest values of ggg and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.
Motivated by the prospect of Bardeen-Cooper-Schrieffer (BCS) pairing in cold fermionic gases we analyze the superfluid phase of three fermionic flavors in the attractive Hubbard model. We show that there are several low-lying collective pairing modes and investigate their damping due to the partially gapless nature of the single-particle spectrum. Furthermore, we analyze how these modes show up in the density response of the system. Apart from the Anderson-Bogoliubov phase mode of the pairing between two flavors, the dynamical structure factor contains signatures of the gapless third flavor. This picture is found to be robust against perturbations that break the global SU(3) symmetry of the Hamiltonian.