Quantum projection noise and squeezing with ions in a Penning-Malmberg trap.

We summarize initial progress towards making spin squeezed states with $\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 trap magnetic field has a 124 GHz transition frequency, as the ion qubit. With a 30 mW Gunn diode oscillator we have observed $\pi$-times as short as 100 $\mu$s. We have realized projection noise limited spectroscopy\footnote{W.M. Itano, et al., Phys. Rev. A{\bf 47}, 3554 (1993).} 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. We have observed fast ($\sim$1 ms) magnetic field fluctuations of our magnet through spin-echo spectroscopy. These fluctuations limit the amount of time that can be used to apply the squeezing.