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We show how maximally correlated states of N two-level particles can be used in spectroscopy to yield a frequency uncertainty equal to (NT) Ϫ1 , 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. ͓S1050-2947͑96͒50712-2͔

The quantum Zeno effect is the inhibition of transitions between quant.ulll st.a.t.es by rrC'queul. measurements of the state. The inhibition arises because the measurement. causes a collapse (reduction) of the wave function. If the time between measurements is short enough, the wave function usually collapses back to the initial state. We have observed this effect. in an rf transition between two 9Be+ ground-state hyperfine levels. The iOlls were confined in a Penning trap and laser cooled. Short pulses of light, applied at the same time as the rf field, made the measurements. If an ion was in one state, it scattered a few photons; if it was in t.he other, it scattered no photons. In the latter case the wave-function collapse was due t.o a null measurement. Good agreement was found with calculations.

State-selected rubidium-87 molecules were created at rest in a dilute Bose-Einstein condensate of rubidium-87 atoms with coherent free-bound stimulated Raman transitions. The transition rate exhibited a resonance line shape with an extremely narrow width as small as 1.5 kilohertz. The precise shape and position of the resonance are sensitive to the mean-field interactions between the molecules and the atomic condensate. As a result, we were able to measure the molecule-condensate interactions. This method allows molecular binding energies to be determined with unprecedented accuracy and is of interest as a mechanism for the generation of a molecular Bose-Einstein condensate.