Emil A. Yuzbashyan

We determine the exact asymptotic many-body wavefunction of a spin-$s$ Richardson-Gaudin model with a coupling inversely proportional to time, for time evolution starting from the ground state at $t = 0^+$ and for arbitrary $s$. Contrary to common belief, the resulting wavefunction cannot be derived from the spin-$1/2$ case by merging spins, but instead requires independent treatment for each spin size. The steady state is non-thermal and, in contrast to the spin-$1/2$ case, does not conform to a natural Generalized Gibbs Ensemble. We show that mean-field theory is exact for any product of a finite number of spin operators on different sites. We discuss how these findings can be probed in cavity QED and trapped ion experiments.

Two-dimensional $p+ i p$ superconductors and superfluids are systems that feature chiral behavior emerging from the Cooper pairing of electrons or neutral fermionic atoms with non-zero angular momentum. Their realization has been a longstanding goal because they offer great potential utility for quantum computation and memory. However, they have so far eluded experimental observation both in solid state systems as well as in ultracold quantum gases. Here, we propose to leverage the tremendous control offered by rotating two-dimensional trapped-ion crystals in a Penning trap to simulate the dynamical phases of two-dimensional $p+ip$ superfluids. This is accomplished by mapping the presence or absence of a Cooper pair into an effective spin-1/2 system encoded in the ions' electronic levels. We show how to infer the topological properties of the dynamical phases, and discuss the role of beyond mean-field corrections. More broadly, our work opens the door to use trapped ion systems to explore exotic models of topological superconductivity and also paves the way to generate and manipulate skyrmionic spin textures in these platforms.