Quantum harmonic oscillator state synthesis and analysis

Experiments are described in which a single, harmonically bound, beryllium ion in a Paul trap is put into Fock, thermal, coherent, squeezed, and Schroedinger cat states. Experimental determinations of the density matrix and the Wigner function are described. A simple calculation of the decoherence of a superposition of coherent states due to an external electric field is given.Comment: 13 pages, LaTeX2e, special style file spie.sty included, 11 eps figures included using epsfig, graphicx, subfigure, floatflt macros. To appear in Proc. Conf. on Atom Optics, San Jose, CA, Feb. 1997, edited by M. G. Prentiss and W. D. Phillips, SPIE Proc. # 299

Optimal frequency measurements with maximally correlated states

We show how maximally correlated states of N two-level particles can be used in spectroscopy to yield a frequency uncertainty equal to (NT) �1, where T is the time of a single measurement. From the time-energy uncertainty relation we show that this is the best precision possible. We rephrase these results in the language of particle interferometry and obtain a state and detection operator which can be used to achieve a phase uncertainty exactly equal to the 1/N Heisenberg limit, where N is the number of particles used in the measurement. �S1050-2947�96�50712-2� PACS number�s�: 42.50.Dv, 06.30.Ft, 03.65.Bz, 39.30.�w Quantum limits to noise in spectroscopy �1–4 � and interferometry �5–13 � have been a subject of fundamental, and to an increasing degree, practical interest. This is especially true for spectroscopy on trapped atoms or ions where the number of particles N is fixed and kept small to reduce undesired perturbations. Naively, the uncertainty of a spectroscopic or interferometric measurement is limited by counting statistics to be inversely proportional to N 1/2. However, a number o