A two-mode thermomechanically squeezed phonon laser.

Lasers find ubiquitous use in physics due to their coherence, spectral purity and high intensity. However, the output of a laser does not carry crucial resources such as squeezing and entanglement, and the generation of such properties requires the use of nonlinear media. In the electromagnetic domain, the nonlinearities are weak, resulting in sources of squeezing and entanglement that are not bright. In this work, we exploit the fact that strong nonlinearities can be readily implemented in a mechanical system to enable simultaneous lasing and two-mode squeezing, producing a bright and coherent source of classically correlated phonons: a two-mode thermomechanically squeezed phonon laser. Our device is experimentally implemented by combining nonlinear damping with parametric modulation of the coupling between two center-of-mass oscillation modes of an optically levitated nanoparticle at the sum of their mechanical frequencies. Above the linear stability threshold of the system, we observe parametrically sustained oscillation and subthermal two-mode squeezing coexisting with mechanical lasing. Our device is a substantial addition to the ongoing revolution in optical tweezer physics, important to studies of nonequilibrium systems in mesoscopic classical thermodynamics, and a necessary stepping stone in the longer-term development of a quantum mechanical extension.