# Topological classes of quasi-periodically driven quantum dynamics, and the transitions between them

• Philip Crowley (Boston University)
• Thursday 11 July 2019, 14:00-15:00
• Theory Library.

Few level quantum systems driven by multiple incommensurate tones exhibit temporal analogues of non-interacting phenomena in spatial dimensions. Analogous to the bands of a two-dimensional lattice, for two drives the pre-thermal dynamics of a driven qudit can be classified according to a Chern number. We show that non-zero Chern numbers lead to dramatic dynamical signatures, including chaotic sensitivity to initial conditions, and aperiodic time dynamics of expectation values, and the integer-quantised pumping of energy from one drive to the other – a temporal analogue to the quantum hall effect.

We then study the transition between the non-trivial and trivial classes of pre-thermal dynamics. The transition is asymptotically sharp in the limit of zero frequency and is characterised by a Dirac point in the instantaneous band structure as a function of the drive phases. We show that the average pumping rate is half-integer quantised at the transition with a lifetime that diverges with the drive frequencies as $\omega_{1,2}^{-3/2}$. The drives also inject energy into the spin; we present universal Kibble-Zurek scaling functions for both energy transfer processes in the low frequency regime. This analysis of the transition provides an experimentally feasible route to observing the transport signatures of a Dirac point in a quasiperiodically driven qubit.

This talk is part of the Theoretical Physics Seminars series.