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arXiv:cond-mat/0611421 · Physical Review B

Pairing in asymmetrical Fermi systems with intra- and interspecies correlations

Renyuan Liao, Khandker Quader

Published Dec 7, 2007• 5 citations
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Abstract

We explore ground states of asymmetrical Fermi systems where both inter- $({g}_{o})$ and intra- $({g}_{1})$ species pairing interactions are present. Using the equation of motion method, we obtain coupled mean-field equations for superfluid gap functions and population densities. We construct a phase diagram across BCS-BEC regimes. At low polarizations $P$, we find stable superfluid phases on BCS and BCS sides of unitarity for ${g}_{1}>{g}_{1}^{c}$, a critical value, for a given ${g}_{o}$. For larger $P$, we find phase separations in both regimes. A superfluid phase exists for all polarizations deep in the BEC regime. Our results should apply to a broad range of Fermi systems.

DOI
10.1103/physrevb.76.212502

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We consider inter- and intra-species pairing interactions in an asymmetrical Fermi system. Using equation of motion method, we obtain coupled mean-field equations for superfluid gap functions and population densities. We construct a phase diagram across BCS-BEC regimes. Due to intra-species correlations, the BCS singlet superfluid state can sustain finite polarizations, P. For larger P, we find phase separations in BCS and BEC regimes. A superfluid phase exists for all P deep in BEC regime. Our results may apply to pairing in ultracold fermions, nuclear and quark matter physics.
We study the dilute fermion gas with pairing between two species and unequal concentrations in a harmonic trap using the mean-field theory and the local density approximation. We found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger than a certain critical value, which increases from the weak-coupling BCS region to the strong-coupling Bose-Einstein condensation (BEC) side. In the strong-coupling BEC regime, the radii of the superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. However, the lighter leftover fermions are easier to mix with the superfluid core than the heavier ones. A partially polarized superfluid can be found if the majority fermions are lighter, whereas phase separation is still found if they are heavier.
We study the phase diagram of the dilute two-component Fermi gas at zero temperature as a function of the polarization and coupling strength. We map out the detailed phase separations between superfluid and normal states near the Feshbach resonance. We show that there are three different coexistence of superfluid and normal phases corresponding to phase separated states between: (I) the partially polarized superfluid and the fully polarized normal phases, (II) the unpolarized superfluid and the fully polarized normal phases and (III) the unpolarized superfluid and the partially polarized normal phases from strong-coupling BEC side to weak-coupling BCS side. For pairing between two species, we found this phase separation regime gets wider and moves toward the BEC side for the majority species are heavier but shifts to BCS side and becomes narrow if they are lighter.
We study ppp-wave pairing in a two-component Fermi system with unequal population across weak-coupling BCS to strong-coupling BEC regimes. We find a rich ms=0{m}_{s}=0ms​=0 spin triplet ppp-wave superfluid (SF) ground state (GS) structure as a function of population imbalance. Under a phase stability condition, the ``global'' energy minimum is given by a multitude of ``mixed'' SF states formed of linear combinations of $m=\ifmmode\pm\else\textpm\fi{}1,0$ substates of the $\ensuremath{\ell}=1$ orbital angular momentum state. Except for the ``pure'' SF states ($\ensuremath{\ell}=1,m=\ifmmode\pm\else\textpm\fi{}1$), other states exhibit oscillation in energy with the relative phase between the constituent gap amplitudes. We also find states with ``local'' energy minimum that can be stable at higher polarizations, suggesting a quantum phase transition between the ``global'' and ``local'' minima phases driven by polarization. We relate the local and global minimum states to Morse and non-Morse critical points. We calculate the variations of the ground state energy with a relative phase angle, coupling, and polarization, and discuss possible consequences for experiments.
Similar to what has recently been achieved with Bose-Bose mixtures [G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)], mixed-dimensional Fermi-Fermi mixtures can be created by applying a species-selective one-dimensional optical lattice to a two-species Fermi gas ($\ensuremath{\sigma}\ensuremath{\equiv}{\ensuremath{\uparrow},\ensuremath{\downarrow}}$), in such a way that both species are confined to quasi--two-dimensional geometries determined by their hoppings along the lattice direction. We investigated the ground-state phase diagram of superfluidity for such mixtures in the BCS-BEC evolution, and found normal, gapped superfluid, gapless superfluid, and phase separated regions. In particular, we found a stable gapless superfluid phase where the unpaired $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ fermions coexist with the paired (or superfluid) ones in different momentum space regions. This phase is in some ways similar to the Sarma state found in mixtures with densities, but in our case, the gapless superfluid phase is unpolarized and most importantly it is stable against phase separation.
We investigate a two-component Fermi gas with unequal spin populations along the BCS-BEC crossover. By using the extended BCS equations and the concept of off-diagonal-long-range-order we derive a formula for the condensate number of Cooper pairs as a function of energy gap, average chemical potential, imbalance chemical potential and temperature. Then we study the zero-temperature condensate fraction of Cooper pairs by varying interaction strength and polarization, finding a depletion of the condensate fraction by increasing the population imbalance. We also consider explicitly the presence of an external harmonic confinement and we study, within the local-density approximation, the phase separation between superfluid and normal phase regions of the polarized fermionic cloud. In particular, we calculate both condensate density profiles and total density profiles from the inner superfluid core to the normal region passing for the interface, where a finite jump in the density is a clear manifestation of this phase-separated regime. Finally, we compare our theoretical results with the available experimental data on the condensate fraction of polarized 6Li atoms [Science 311, 492 (2006)]. These experimental data are in reasonable agreement with our predictions in a suitable range of polarizations, but only in the BCS side of the crossover up to unitarity.