The admixture of spin-singlet and spin-triplet pairing states in superconductors can be typically induced by breaking spatial inversion symmetry. Employing the numerically exact auxiliary-field quantum Monte Carlo method, we study such mixed-parity pairing phenomena of attractive fermions with Rashba spin-orbit coupling (SOC) in a two-dimensional optical lattice at finite temperature. We systematically explore the evolution of the essential pairing structure in both singlet and triplet channels versus the temperature, fermion filling, and SOC and interaction strengths, via computing the finite-size results of the condensate fraction and pair wave function. Our numerical results reveal that the singlet channel dominates in the fermion pairing and the triplet pairing has a relatively small contribution to the superfluidity for physically relevant parameters. In contrast to the singlet channel mainly consisting of the on-site Cooper pairs, the triplet pairing has plentiful patterns in real space with the largest contributions from several nearest neighbors. As the SOC strength increases, the pairing correlation is first enhanced and then suppressed for triplet pairing while it is simply weakened in the singlet channel. We have also obtained the Berezinskii-Kosterlitz-Thouless transition temperatures through the finite-size analysis of the condensate fraction. Our results can serve as a quantitative guide for future optical lattice experiments as well as accurate benchmarks for theories and other numerical methods.
The method of singlet-triplet level anticrossing has been extended to the
n=61,3D levels of He. Measurement of this anticrossing gives a highly accurate determination of the zero-field singlet-triplet separation and a less accurate determination of the antisymmetric part of the spin-orbit coupling perturbation between the
n=61,3D states. The zero-field separation for
n=6, although considerably more accurate, is in essential agreement with previous optical results, confirming the accuracy of the intercombination line measurements. The singlettriplet intervals calculated by many-body perturbation theory are also found to be in very good agreement with the experimental results.
In the singlet-triplet qubit architecture, the two-qubit interactions required in universal quantum computing can be implemented by capacitative coupling, by exploiting the charge distribution differences of the singlet and triplet states. The efficiency of this scheme is limited by decoherence, that can be mitigated by stronger coupling between the qubits. In this paper, we study the capacitative coupling of singlet-triplet qubits in different geometries of the two-qubit system. The effects of the qubit-qubit distance and the relative orientation of the qubits on the capacitative coupling strength are discussed using an accurate microscopic model and exact diagonalization of it. We find that trapezoidal quantum dot formations allow strong coupling with low charge distribution differences between the singlet and triplet states. The analysis of geometry on the capacitative coupling is also extended to the many-qubit case and the creation of cluster states.