Structure and consequences of vortex-core states in p-wave superfluids

It is now well established that in two-dimensional chiral $p$-wave paired superfluids, the vortices carry zero-energy

modes which obey non-abelian exchange statistics and can potentially be used for topological quantum computation.

In such superfluids there may also exist other excitations below the bulk gap inside the cores of vortices.

We study the properties of these subgap states, and argue that their

presence affects the topological protection of the zero modes.

In conventional superconductors where the chemical potential is of the order of the Fermi energy

of a non-interacting Fermi gas, there is a large number of subgap states and the mini-gap

towards the lowest of these states is a small fraction of the Fermi energy. It is therefore difficult

to cool the system to below the mini-gap and at experimentally available temperatures, transitions

between the subgap states, including the zero modes, will occur and can alter the quantum

states of the zero-modes. Consequently, qubits defined uniquely in terms of the zero-modes

do not remain coherent.

We show that compound qubits involving the zero-modes and the parity of the occupation number

of the subgap states on each vortex are still well defined. However, practical schemes taking into

account all subgap states would nonetheless be difficult to achieve.

We propose to avoid this difficulty by working in the regime of small chemical potential $\mu$, near the transition

to a strongly paired phase, where the number of subgap states is reduced. We develop the theory to describe

this regime of strong pairing interactions and we show how the subgap states are ultimately absorbed into the bulk gap.

Since the bulk gap also vanishes as $\mu\to 0$ there is an optimum value $\mu_c$ which maximises the combined gap.

We propose cold atomic gases as candidate systems where the regime of strong interactions can be explored,

and explicitly evaluate $\mu_c$ in a Feshbach resonant $^{40}$K gas.