Controlling trapped-ion motional modes for precision measurement

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 progress towards generation of one-mode and two-mode squeezed states using parametric excitation. These operations help to create motional state interferometers and can be used to achieve Heisenberg-limited phase sensitivities. We present a preliminary implementation of an SU(1,1) interferometer using two motional modes of a ⁴⁰Ca⁺ ion in a Paul trap, and compare the performance to the more traditional SU(2) Mach-Zender interferometer. We also report on preliminary results for using single-mode squeezed states and coherent states as the interferometer inputs to further increase phase sensitivity. 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. The calculation of the Fisher information from experimental data can be used to quantify the phase sensitivity that we can achieve in our setup.