Applications of time-dependent spin wave theory: many-body Kapitza pendulum of long-range interacting spin chains and driven dissipative time crystals
This talk branches into two parts. The common ground is a method to implement Holstein-Primakoff expansion in strongly non-equilibrium conditions, resulting in a self-consistent theory of spin waves coupled to a dynamical order parameter. This technique is helpful in solving many-body problems far from equilibrium in a variety of physical platforms:
— in the first part of the talk, I will discuss results concerning dynamical phases of periodically driven quantum spin chains with long range interactions. Specifically, I will discuss the simultaneous dynamical stabilisation via periodic drive of the entire band of quantum many-body fluctuations of a model at hand for current experiments involving trapped ions. This constitutes an analog of the Kapitza pendulum for a driven quantum many body system.
— in the second part of the talk, I will present a many-body version of the Dicke model where atoms interact among each others via a short-range integrability breaking coupling, as well as collectively with the cavity mode. The energy inflow due to a periodic drive of the light-matter coupling is balanced by the outflow into the vacuum, modelled by incoherent one-body photon losses. This entails a rich dynamical phase diagram comprising regimes of synchronisation, heating and melting of the order parameter, as a result of the peculiar interplay between dissipation and many-body interactions. In particular, our platform can host both instances of long-lived and metastable discrete time crystals; the latter are stabilised by dissipation, exist only under periodically driven conditions, and escape conventional paradigms for pre-thermalization in many-body systems.