We show that fermionic dipoles in a two-layer geometry form Cooper pairs with both singlet and triplet components when they are tilted with respect to the normal of the planes. The mixed parity pairing arises because the interaction between dipoles in the two different layers is not inversion symmetric. We use an efficient eigenvalue approach to calculate the zero-temperature phase diagram of the system as a function of the dipole orientation and the layer distance. The phase diagram contains purely triplet as well as mixed singlet and triplet superfluid phases. We show in detail how the pair wave function for dipoles residing in different layers smoothly changes from singlet to triplet symmetry as the orientation of the dipoles is changed. Our results indicate that dipolar quantum gases can be used to unambiguously observe mixed parity pairing.
We study the ground-state phase diagram of an interacting staggered Su-Schrieffer-Heeger (SSH) ladder in the vicinity of the Gaussian quantum critical point. The corresponding effective field theory, which nonperturbatively treats correlation effects in the ladder, is a double-frequency sine-Gordon (DSG) model. It involves two perturbations at the Gaussian fixed point: the deviation from criticality, and umklapp scattering processes. While massive phases with broken symmetries are identified by means of local order parameters, a topological distinction between thermodynamically equivalent phases becomes feasible only when nonlocal fermionic fields, parity, and the string order parameter are included in consideration. We prove that a noninteracting fermionic staggered SSH ladder is exactly equivalent to an O(2)-symmetric model of two decoupled Kitaev-Majorana chains, or two one-dimensional
p-wave superconductors. Close to the Gaussian fixed point, the SSH ladder maps to an Ashkin-Teller-like system when interactions are included. Thus, the topological order in the SSH ladder is related to broken-symmetry phases of the associated quantum spin-chain degrees of freedom. The obtained phase diagram includes a Tomonaga-Luttinger liquid state that, due to umklapp processes, can become unstable against either spontaneous dimerization or the onset of a charge-density wave (CDW). In these gapped phases, elementary bulk excitations are quantum kinks carrying the charge
QF=1/2. For sufficiently strong, long-range interactions, the phase diagram of the model exhibits a bifurcation of the Gaussian critical point into two outgoing Ising criticalities. The latter sandwich a mixed phase in which dimerization coexists with a site-diagonal CDW. In this phase, elementary bulk excitations are represented by two types of topological solitons carrying different fermionic charges, which continuously interpolate between 0 and 1. This phase has also mixed topological properties with coexisting parity and string order parameters.