Bosonic toolbox in trapped ions for sensing of motional and spin degrees of freedom

Motional modes of trapped ions have been shown to be a useful tool for quantum sensing, making use of time reversal protocols. This application requires the ability to prepare well-defined motional states with high fidelity. Many of these states can be generated from motional ground states without the use of laser fields. We report our results in generating one-mode and two-mode squeezed states using parametric excitation. These operations help to create motional state interferometers and can be used to achieve sensitivities approaching the Cramér-Rao bound. We present an implementation of an SU(1,1) interferometer using one and two motional modes of a ⁴⁰Ca⁺ ion in a Paul trap, and compare the performance to the more traditional SU(2) Mach-Zender interferometer. To characterize the input and output motional states of the interferometers, the ions’ motion is coupled to internal ‘spin’ states, which are distinguishable through spin-dependent fluorescence. For more than one ion, coupling of the motional and spin degrees of freedom enables a transfer protocol of the motional squeezed state into a spin squeezed state. This protocol also enables increased sensitivity to qubit phase rotations. We present preliminary results of implementing this protocol and initial phase sensitivity estimates using two ions.