Nonclassical energy squeezing with quadratic electromechanics

The ability to access a broad range of quantum state of motion with massive mechanical oscillators has been an enduring ambition in the field of opto- and electromechanics. Despite achieving many landmarks, the often exploited radiation pressure coupling between these
mechanical oscillators and microwave or optical light relies on a linearized interaction that limits possible quantum effects. To go beyond this limitation, we quadratically couple the displacement of a mechanical oscillator to the energy levels of a superconducting charge qubit[1]. Through microwave frequency drives that change both the state of the oscillator and the qubit, we dissipatively stabilize the oscillator in a non-classical state with a large mean phonon number of 43 and sub-Poissonian number fluctuations of approximately 3. In this number squeezed state, we observe a striking feature of the quadratic coupling, the two phonon recoils of the mechanical oscillator due to qubit transitions. These are closely analogous to the vibronic transitions in molecules, heralding entry into a new regime of artificial systems with fast electrons coupled strongly to slow vibrations.

[1] Viennot, J. J., Ma, X. & Lehnert, K. W. Phonon-Number-Sensitive Electromechanics. PRL121, 183601(2018)