Random Multipolar Driving: Tunably Slow Heating through Spectral Engineering

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the time-scale on which these persist. We study interacting many-body driven by random sequences with $n-$multipolar correlations, corresponding to a polynomially suppressed low frequency spectrum. For $n\geq1$, we find prethermal regime, lifetime of grows algebraically driving rate, exponent ${2n+1}$. A simple theory based Fermi's golden rule accounts for this behaviour. The quasiperiodic Thue-Morse sequence corresponds $n\to \infty$ limit, and accordingly exhibits an exponentially long-lived regime. Despite absence periodicity drive, spite its eventual heat death, regime host versatile non-equilibrium phases, illustrate multipolar discrete time crystal.