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arXiv:0906.2580 · International Journal of Modern Physics A

EXOTIC SUPERFLUIDITY IN COLD ATOMS

Elena Gubankova

Published Jan 30, 2010• 0 citations
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Abstract

We derived the low energy effective action for the collective modes in asymmetric fermionic systems with attractive interaction. We obtained the phase diagram in terms of the chemical potentials. It features a stable gapless superfluidity with one Fermi surface on the BEC side of the resonance. Also we predict a sharp increase in outer core of a vortex, i.e. vortex size, upon entering into the gapless phase. This may serve as a signature of a gapless phase.

DOI
10.1142/s0217751x10048925

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We derived the low energy effective action for the collective modes in asymmetric fermionic systems with attractive interaction. We obtained the phase diagram in terms of the chemical potentials. It features a stable gapless superfluidity with one Fermi surface on the BEC side of the resonance. Also we predict a sharp increase in outer core of a vortex, i.e. vortex size, upon entering into the gapless phase. This may serve as a signature of a gapless phase.
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Gapless superconductivity can arise when pairing occurs between fermion species with different Fermi surface sizes, provided there is a sufficiently large mismatch between Fermi surfaces and/or at sufficiently large coupling constant. In gapless states, secondary Fermi surfaces appear where quasiparticle excitation energy vanishes. This work focuses on homogeneous and isotropic superfluids in the s-wave channel, with either zero (conventional superconductor), one, or two spherical Fermi surfaces. The stability conditions for these candidate phases are analyzed. It is found that gapless states with one Fermi surface are stable in the BEC region, while gapless states with two Fermi surfaces are unstable in all parameter space. The results can be applied to ultracold fermionic atom systems.
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We construct a Galilean invariant low-energy effective field theory of boson-fermion mixtures and study bound fermion states on a vortex of boson superfluid. We derive a simple criterion to determine for which values of the fermion angular momentum lll there exist an infinite number of bound energy levels. We apply our formalism to two boson-fermion mixed systems: the dilute solution of 3He^{3}\mathrm{He}3He in 4He^{4}\mathrm{He}4He superfluid and the cold polarized Fermi gas on the BEC side of the ``splitting point.'' For the $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixture, we determine parameters of the effective theory from experimental data as functions of pressure. We predict that infinitely many bound 3He^{3}\mathrm{He}3He states on a superfluid vortex with $l=\ensuremath{-}2,\ensuremath{-}1,0$ are realized in a whole range of pressure 0−−20atm0--20\phantom{\rule{0.3em}{0ex}}\mathrm{atm}0−−20atm, where experimental data are available. As for the cold polarized Fermi gas, while only SSS-wave (l=0)(l=0)(l=0) and PPP-wave $(l=\ifmmode\pm\else\textpm\fi{}1)$ bound fermion states are possible in the BEC limit, those with higher negative angular momentum become available as one moves away from the BEC limit.
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In this paper, we study phase transitions in asymmetrical fermion superfluids. In this scenario, the candidates to form pair are particles with mismatched masses and chemical potentials. We derive an expression for the critical temperature in terms of the gap and masses (or chemical potentials) when the constraint of equal Fermi surfaces maμa=mbμbm_a\mu_a = m_b\mu_bma​μa​=mb​μb​ is imposed.