Coherent multiple-period states in a resonantly driven qubit

TL;DR

This paper explores how multiple-period states emerge in periodically driven qubits, revealing symmetry-breaking phenomena and topological properties in simple quantum systems and qubit chains.

Contribution

It demonstrates the emergence of multiple-period states in a single qubit and qubit chains, linking to topological Floquet systems and providing explicit solutions.

Findings

Multiple-period states break discrete time-translation symmetry.

A qubit chain with modulated coupling maps to the Kitaev chain.

Period doubling in long chains is topologically protected.

Abstract

We consider multiple-period states in systems of periodically modulated qubits. In such states the discrete time-translation symmetry imposed by the modulation is broken. We explicitly show how multiple-period states emerge in the simplest quantum system, a single qubit subjected to a pulsed resonant modulation and/or a pulsed modulation of the transition frequency. We also show that a qubit chain with the qubit coupling modulated at twice the qubit frequency has symmetry that allows mapping it on the Kitaev chain and thus provides an example of a topologically nontrivial Floquet system. An explicit solution for a two-qubit system illustrates the effect of resonant period doubling for coupled qubits, whereas in a long chain period doubling is topologically protected.