F. VIENNOT “Non-classical energy squeezing of a macroscopic mechanical oscillator”

The ability to access a broad range of quantum states 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. This linear interaction limits the accessible range of motional states to gaussian states. To go beyond this limitation, we quadratically couple the displacement of a mechanical oscillator to the energy levels of a superconducting charge qubit ¹J.J. Viennot, , X. Ma, & K.W. Lehnert, PRL 121, 183601 (2018) [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 ²X. Ma, J.J. Viennot, S. Kotler, J.D. Teufel, K.W. Lehnert, Nature Physics 17, 322-326 (2021)[2], characterized by 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] J.J. Viennot, , X. Ma, & K.W. Lehnert, PRL 121, 183601 (2018) 
[2] X. Ma, J.J. Viennot, S. Kotler, J.D. Teufel, K.W. Lehnert, Nature Physics 17, 322-326 (2021)