Abstract

We derive, from the microscopic Hamiltonian, a laser-cooling theory for the small vibrations in an arbitrary cluster of trapped ions. If either the interference of light scattered by different ions is ignored or all vibration modes are assumed to retain a common temperature during the cooling, then a collective vibration mode obeys essentially the same cooling theory as a single ion with the same mechanical-oscillation frequency. We also study both analytically and numerically the frequency spectrum of the small vibrations. In a harmonic trap the scale of the spectrum is determined solely by the three oscillation frequencies that a single ion would have in the trap. Ignoring many-particle heating phenomena of real traps, the qualitative conclusion emerges that if a single ion can be cooled in a given trap, then so can an ion cluster.

© 1988 Optical Society of America

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