New states of matter can arise when a system is exposed to a periodic drive, such as by irradiating a solid with light or by mechanically shaking a gas of ultracold atoms. While experiments have validated this method, the target often exhibits a drastically reduced lifetime because it continuously absorbs energy from the drive. Moreover, in systems of bosonic particles the periodic drive can trigger the rapid growth of collective excitations, known as parametric instabilities, which typically decay and result in additional heating. Here, ...
