Quantum projection noise limited spectroscopy with ions in a Penning-Malmberg trap. ---Progress toward spin squeezed states.

We describe plans and summarize initial progress towards making spin squeezed states with up to $\sim$100 $^{9}$Be$^{+}$ ions in a Penning-Malmberg trap. We use the ground-state electron spin-flip transition, which in the 4.5 T magnetic field of the trap has a transition frequency of 124 GHz, as the ion qubit. With a 30 mW Gunn diode oscillator we have observed Rabi flopping rates as high as $\sim$7 kHz. We will summarize experimental progress on realizing projection noise limited spectroscopy on this transition, which is a prerequisite for demonstrating spin squeezing. For entangling the ions we plan to use a generalization of the few ion qubit phase gate developed at NIST \footnote{D. Leibfried, et al., Nature {\bf 438}, 639 (2005).} to generate an $\exp{(i\chi {J_{z}}^2 t)}$ interaction between all of the ion qubits. This interaction can be implemented on a single plane of ions \footnote{T.B. Mitchell, et al., Science {\bf 282}, 1290 (1998).} with a motional sideband, stimulated Raman transition.