Toward the preparation of sub-Poissonian states in a low frequency mechanical oscillator

Preparation of non-classical states of motion in a macroscopic object has been an ambition in the field of opto- and eletro-mechanics. We propose a protocol for the preparation of one type of non-classical state, the sub-Poissonian state. We dispersively couple a Cooper-pair box qubit to a 25 MHz aluminum drumhead mechanical oscillator, and enter the phonon number sensitive regime [1]. In this regime, the motion-induced AC Stark shift on the qubit allows us to address phonon populations with a number resolution of 7, and to extract the phonon distribution via the qubit lineshape. Using sideband transitions between the qubit and mechanics, we demonstrate progress towards preparing the mechanical oscillator in a sub-Poissonian state, where the variance in the phonon distribution is less than the mean phonon number.

[1] J.J.Viennot, X.Ma, K.W.Lehenrt, arXiv: 1808.02673, to appear in PRL.