No Arabic abstract
We investigate a three component fermion mixture in the presence of weak attractive interactions. We use a combination of the equation of motion and the Gaussian variational mean-field approaches, which both allow for simultaneous superfluid and magnetic ordering in an unbiased way, and capture the interplay between the two order parameters. This interplay significantly modifies the phase diagram, especially the superfluid-normal phase boundaries. In the close vicinity of the critical temperature and for small chemical potential imbalances, strong particle-hole symmetry breaking leads to a phase diagram similar to the one predicted by Cherng et al. [Phys. Rev. Lett. 99, 130406 (2007)], however, the overall phase diagram is markedly different: new chemical potential-driven first and second order transitions and triple points emerge as well as more exotic second order multicritical points, and bicritical lines with O(2,2) symmetry. We identify the terms which are necessary to capture this complex phase diagram in a Ginzburg-Landau approach, and determine the corresponding coefficients.
We investigate the formation of Bose-Einstein condensation and population imbalance in a three-component Fermi superfluid by increasing the U(3) invariant attractive interaction. We consider the system at zero temperature in three dimensions and also in two dimensions. Within the mean-field theory, we derive explicit formulas for number densities, gap order parameter, condensate density and condensate fraction of the uniform system, and analyze them in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of Cooper pairs to the Bose-Einstein Condensate (BEC) of strongly-bound molecular dimers. In addition, we study this Fermi mixture trapped by a harmonic potential: we calculate the density profiles of the three components and the condensate density profile of Cooper pairs in the BCS-BEC crossover.
Sliding phases have been long sought after in the context of coupled XY-models, as they are of relevance to various many-body systems such as layered superconductors, freestanding liquid-crystal films, and cationic lipid-DNA complexes. Here we report an observation of a dynamical sliding phase superfluid that emerges in a nonequilibrium setting from the quantum dynamics of a three-dimensional ultracold atomic gas loaded into the P-band of a one-dimensional optical lattice. A shortcut loading method is used to transfer atoms into the P-band at zero quasimomentum within a very short time duration. The system can be viewed as a series of pancake-shaped atomic samples. For this far-out-of-equilibrium system, we find an intermediate time window with a lifetime around tens of milliseconds, where the atomic ensemble exhibits robust superfluid phase coherence in the pancake directions, but no coherence in the lattice direction, which implies a dynamical sliding phase superfluid. The emergence of the sliding phase is attributed to a mechanism of cross-dimensional energy transfer in our proposed phenomenological theory, which is consistent with experimental measurements. This experiment potentially opens up a novel venue to search for exotic dynamical phases by creating high-band excitations in optical lattices.
We theoretically investigate one-dimensional three-component spin-orbit-coupled Fermi gases in the presence of Zeeman field. By solving the Bogoliubov-de-Gennes equations, we obtain the phase diagram at given chemical potential and order parameter. We show that the system undergoes a phase transition from Bardeen-Cooper-Schrieffer superfluid to topological superfluid as increasing the intensity of Zeeman field. By comparing to the two-component system, we find, besides the topological phase transition from the trivial superfluid to nontrivial topological superfluid, the system can always be in a nontrivial topological superfluid, and there are two Majorana zero energy regions while increasing the magnetic field. We find the three-component spin-orbit-coupled Fermi gases in certain parameter range is more optimizing for experimental realization due to the smaller magnetic field needed. We therefore propose a promising candidate for realizing topological superfluid.
We consider the problem of spin-triplet p-wave superfluid pairing with total spin projection $m_s=0$ in atomic Fermi gas across the Feshbach resonance. We allow for imbalanced populations and take into account the effects due to presence of a parabolic trapping potential. Within the mean-field approximation for the one- and two-channel pairing models we show that depending on the distance from the center of a trap at least two superfluid states will have the lowest energy. Superfluid shells which emerge in a trap may have two out of three angular components of the p-wave superfluid order parameter equal to zero.
Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space as well as in a harmonic trapping potential of frequency $omega$. Using the three-body problem to renormalize, we report analytic results for the change in the fourth- and fifth-order virial coefficients $Delta b_4$ and $Delta b_5$ as functions of $Delta b_3$. Additionally, we argue that in the $omega to 0$ limit the relationship $b_n^text{T} = n^{-d/2} b_n$ holds between the trapped (T) and homogeneous coefficients for arbitrary temperature and coupling strength (not merely in scale-invariant regimes). Finally, we point out an exact, universal (coupling- and frequency-independent) relationship between $Delta b_3^text{T}$ in 1D with three-body forces and $Delta b_2^text{T}$ in 2D with two-body forces.