Abstract:

Optomechanics and electromechanics have made it possible to prepare macroscopic mechanical oscillators in their quantum ground states1, in quadrature-squeezed states2 and in entangled states of motion3. However, the effectively linear interaction between motion and light or electricity precludes access to the broader class of quantum states of motion, such as cat states or energy-squeezed states. Strong quadratic coupling of motion to light could allow a way around this restriction4–6. Although there have been experimental demonstrations of quadratically coupled optomechanical systems5,7,8, these have not yet accessed non-classical states of motion. Here we create non-classical states by quadratically coupling motion to the energy levels of a Cooper-pair box qubit. Through microwave-frequency drives that change the state of both the oscillator and qubit, we then dissipatively stabilize the oscillator in a state with a large mean phonon number of 43 and sub-Poissonian number fluctuations of approximately 3. In this energy-squeezed state, we observe a striking feature of the quadratic coupling: the recoil of the mechanical oscillator caused by qubit transitions, closely analogous to the vibronic transitions in molecules9,10.