Topological signatures of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-wave superconducting wire through light

We show how the ${\mathbb{Z}}_{2}$ topological index of a one-dimensional topological $p$-wave superconductor can be revealed when driving with a classical vector potential, i.e., an electromagnetic wave, through the light-induced transition probabilities and the profile of the induced quasiparticle population. As a function of driving frequency $\ensuremath{\omega}$, it is possible to obtain a measure of this topological invariant from the resonance envelope classifying the two distinct topological phases of the short-range Kitaev wire. We propose to probe the topological phase transition in the model through the responses of the global capacitance in the presence of the light field and through the Josephson current between the wire and the proximity coupled bulk superconductor. The system may also be implemented on the Bloch sphere allowing alternative ways to measure the $\mathbb{Z}$ and ${\mathbb{Z}}_{2}$ topological invariants through circuit or cavity quantum electrodynamics.