We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.
We determine the zero-temperature quantum phase diagram of a
px+ipy pairing model based on the exactly solvable hyperbolic Richardson-Gaudin model. We present analytical and large-scale numerical results for this model. In the continuum limit, the exact solution exhibits a third-order quantum phase transition, separating a strong-pairing from a weak-pairing phase. The mean-field solution allows to connect these results to other models with
px+ipy pairing order. We define an experimentally accessible characteristic length scale, associated with the size of the Cooper pairs, that diverges at the transition point, indicating that the phase transition is of a confinement-deconfinement type without local order parameter. We propose an experimental measurement to detect the transition. We show that this phase transition is not limited to the
px+ipy pairing model but can be found in any representation of the hyperbolic Richardson-Gaudin model and is related to a symmetry that is absent in the rational Richardson-Gaudin model.
We discuss the possibility of a quantum phase transition in ultracold spin polarized fermionic gases which exhibit a p-wave Feshbach resonace. We show that when fermionic atoms form a condensate that can be externally tuned between the BCS and BEC limits, the zero temperature compressibility and the spin susceptibility of the fermionic gas are non-analytic functions of the two-body bound state energy. This non-analyticity is due to a massive rearrangement of the momentum distribution in the ground state of the system. Furthermore, we show that the low temperature superfluid density is also non-analytic, and exibits a dramatic change in behavior when the critical value of the bound state energy is crossed.
We systematically study the BCS-BEC crossover and the quantum phase transition in ultracold
6Li and
40K atoms across a wide Feshbach resonance. The background scattering lengths for
6Li and
40K have opposite signs, which lead to very different behaviors for these two types of atoms. For
40K, both the two-body and the many-body calculations show that the system always has two branches of solutions: one corresponds to a deeply bound molecule state; and the other, the one accessed by the current experiments, corresponds to a weakly bound state with population always dominantly in the open channel. For
6Li, there is only a unique solution with the standard crossover from the weakly bound Cooper pairs to the deeply bound molecules as one sweeps the magnetic field through the crossover region. Because of this difference, for the experimentally accessible state of
40K, there is a quantum phase transition at zero temperature from the superfluid to the normal Fermi gas at the positive detuning of the magnetic field where the
s-wave scattering length passes its zero point. For
6Li, however, the system changes continuously across the zero point of the scattering length. For both types of atoms, we also give a detailed comparison between the results from the two-channel and the single-channel model over the whole region of the magnetic field detuning.
In this Rapid Communication a generalization of the BEC-BCS crossover theory to a multicomponent superfluid is presented by studying a three-species mixture of Fermi gas across two Feshbach resonances. At the BEC side of resonances, two kinds of molecules are stable which gives rise to a two-component Bose condensate. This two-component superfluid state can be experimentally identified from the radio-frequency spectroscopy, density profile, and short noise measurements. As approaching the BCS side of resonances, the superfluidity will break down at some point and yield a first-order quantum phase transition to normal state, due to the mismatch of three Fermi surfaces. Phase separation instability will occur around the critical regime.
The continuous crossover between a Bardeen-Cooper-Schrieffer (BCS)-type superfluid of fermion pairs and a Bose-Einstein condensate (BEC) of tightly bound bosonic molecules can be attributed to the spontaneous breaking of global
U(1) gauge symmetry which underlies both quantum condensation phenomena. Recently much attention has been paid to this problem, since Feshbach resonances allow for an experimental implementation of crossover physics in cold fermion gases. The strong interactions close to resonance call for an analysis beyond Mean Field Theory. We develop a systematic functional integral approach for the description of this phenomenon. Starting from a Yukawa-type atom-molecule model, a symmetry analysis allows to both construct the equation of state and to classify the thermodynamic phases in a unified way. The onset of superfluidity is signalled by the emergence of a massless Goldstone mode associated with the broken continuous U(1) symmetry. Beyond Mean Field, we include fluctuations of the molecule field self-consistently via the solution of suitable Schwinger-Dyson equations. The phase diagram is computed, and a variety of universal features are established. A new form of crossover from an exactly solvable narrow resonance limit to broad resonances or pointlike interactions is found. At low temperature our results agree well with quantum Monte Carlo simulations and recent experiments. Our approach is further developed in the frame of functional renormalization group equations. While the effective bosonic theory in the BEC regime shows the characteristics of a Bogoliubov theory for small temperatures, the phase transition is of second order.