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Prethermal quantum many-body Kapitza phases of periodically driven spin systems

As realised by Kapitza long ago, a rigid pendulum can be stabilised upside down by periodically driving its suspension point with tuned amplitude and frequency. While this dynamical stabilisation is feasible in a variety of instances in systems with few degrees of freedom, it is natural to search for generalizations to multi-particle systems. In particular, a fundamental question is whether, by periodically driving a single parameter in a many-body system, one can stabilise an otherwise unstable phase of matter against all possible fluctuations of its microscopic degrees of freedom. In this work we show that such stabilisation occurs in experimentally realisable quantum many-body systems: a periodic modulation of a transverse magnetic field can make ferromagnetic spin systems with long-range interactions stably trapped around unstable paramagnetic configurations as well as in other unconventional dynamical phases with no equilibrium counterparts. These quantum Kapitza phases, characterized by a long lifetime, are within reach of current experiments.