QUANTUM PROJECTION NOISE - POPULATION FLUCTUATIONS IN 2-LEVEL SYSTEMS

Measurements of internal energy states of atomic ions confined in trap s can be used to illustrate fundamental properties of quantum systems, because long relaxation times and observation times are available. In the experiments described here, a single ion or a few identical ions were prepared in well-defined superpositions of two internal energy ei genstates. The populations of the energy levels were then measured. Fo r an individual ion, the outcome of the measurement is uncertain, unle ss the amplitude for one of the two eigenstates is zero, and is comple tely uncertain when the magnitudes of the two amplitudes are equal. In one experiment, a single Hg-199+ ion, confined in a linear rf trap, w as prepared in various superpositions of two hyperfine states. In anot her experiment, groups of Be-9+ ions, ranging in size from about 5 to about 400 ions, were confined in a Penning trap and prepared in variou s superposition states. The measured population fluctuations were grea ter when the state amplitudes were equal than when one of the amplitud es was nearly zero, in agreement with the predictions of quantum mecha nics. These fluctuations, which we call quantum projection noise, are the fundamental source of noise for population measurements with a fix ed number of atoms. These fluctuations are of practical importance, si nce they contribute to the errors of atomic frequency standards.