Tuning towards dynamic freezing using a two-rate protocol

TL;DR

This paper investigates how two-frequency periodic driving can induce near-perfect wavefunction freezing in quantum systems, identifying parameter regions for optimal freezing and analyzing correlations, with implications for experimental realization.

Contribution

It introduces a two-rate driving protocol to tune towards dynamical freezing in various quantum models, both integrable and non-integrable, supported by numerical and semi-analytic analysis.

Findings

Regions of near-perfect wavefunction overlap identified in parameter space

Correlation functions exhibit characteristic features in freezing regions

Experimental setups like optical lattices can test the predicted phenomena

Abstract

We study periodically driven closed quantum systems where two parameters of the system Hamiltonian are driven with frequencies $\omega_1$ and $\omega_2=r \omega_1$. We show that such drives may be used to tune towards dynamics induced freezing where the wavefunction of the state of the system after a drive cycle at time $T= 2\pi/\omega_1$ has almost perfect overlap with the initial state. We locate regions in the $(\omega_1 ,r)$ plane where the freezing is near exact for a class of integrable and a specific non-integrable model. The integrable models that we study encompass Ising and XY models in $d=1$, Kitaev model in $d=2$, and Dirac fermions in graphene and atop a topological insulator surface whereas the non-integrable model studied involves the experimentally realized one-dimensional (1D) tilted Bose-Hubbard model in an optical lattice. In addition, we compute the relevant correlation functions of such driven systems and describe their characteristics in the region of $(\omega_1,r)$ plane where the freezing is near-exact. We supplement our numerical analysis with semi-analytic results for integrable driven systems within adiabatic-impulse approximation and discuss experiments which may test our theory.