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arXiv:0711.4594 · Physical Review B

p -wave pairing in a two-component Fermi system with unequal population: Weak-coupling BCS to strong-coupling BEC regimes

Renyuan Liao, Florentin Popescu, Khandker Quader

Published Oct 10, 2013• 6 citations
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Abstract

We study $p$-wave pairing in a two-component Fermi system with unequal population across weak-coupling BCS to strong-coupling BEC regimes. We find a rich ${m}_{s}=0$ spin triplet $p$-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.

DOI
10.1103/physrevb.88.134507

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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±\else\textpm\fi1,0m=\ifmmode\pm\else\textpm\fi{}1,0m=\ifmmode±\else\textpm\fi1,0 substates of the \ensuremathℓ=1\ensuremath{\ell}=1\ensuremathℓ=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.
We explore p-wave pairing in a single-channel two-component Fermi system with unequal population near Feshbach resonance. Our analytical and numerical study reveal a rich superfluid (SF) ground state structure as a function of imbalance. In addition to the state Δ±1 ∝ Y1±1, a multitude of “mixed” SF states formed of linear combinations of Y1m's give global energy minimum under a phase stability condition; these states exhibit variation in energy with the relative phase between the constituent gap amplitudes. States with local energy minimum are also obtained. We provide a geometric representation of the states. A T = 0 polarization vs. p-wave coupling phase diagram is constructed across the BEC-BCS regimes. With increased polarization, the global minimum SF state may undergo a quantum phase transition to the local minimum SF state.
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Superfluidity in atomic Fermi gases with population imbalance has recently become an exciting research focus. There is considerable disagreement in the literature about the appropriate stability conditions for states in the phase diagram throughout the BCS to Bose-Einstein condensation crossover. Here we discuss these stability conditions for homogeneous polarized superfluid phases, and compare with recent alternative proposals. The requirement of a positive second-order partial derivative of the thermodynamic potential with respect to the fermionic excitation gap $\ensuremath{\Delta}$ (at fixed chemical potentials) is demonstrated to be equivalent to the positive definiteness of the particle number susceptibility matrix. In addition, we show the positivity of the effective pair mass constitutes another nontrivial stability condition. These conditions determine the (local) stability of the system towards phase separation (or other ordered phases). We also study systematically the effects of finite temperature and the related pseudogap on the phase diagrams defined by our stability conditions.
Abstract Finite-temperature phase structures for asymmetric two-component D-wave fermion superfluids in the weak coupling BCS regime are investigated. The Fulde–Ferrell–Larkin-Ovchinnikov (FFLO) state becomes non-degenerate with the orientation of Cooper pair momentum due to the anisotropic pairing gap for D-wave pairing. The new parameter θ 0, corresponding to the orientation of Cooper pair momentum, greatly enriches the phase structures. Especially, the phase separation (PS) region in the phase diagram is significantly reduced comparing to that for S-wave pairing. Theoretically, the stability condition of solutions is equivalent to the positive definite Hessian matrix of free energy in the hyperplane defined by the number density constraints in the parameter space spanned by the average chemical potential μ, relative chemical potential h, paring gap Δ, pair momentum q, and θ 0. In addition, the stability condition of the superfluid density is essentially included in the positive definite Hessian matrix. Moreover, the positiveness of imbalance number susceptibility D δ ρ / D h is always equivalent to the positiveness of the smaller eigenvalue λ − of the number susceptibility matrix. While the criteria ∂2Ω/∂Δ2 and ∂ 2 Ω ∂ Δ 2 ∂ 2 Ω ∂ q 2 − ∂ 2 Ω ∂ Δ ∂ q 2 against PS in previous studies are equivalent to λ − only under the prerequisite that the solution is a local minimum in the corresponding hyperplane.