The nonlinear dynamics of two ions in a Paul trap is known to show chaos or condensation into a regular ‘‘crystal.’’ We present the first observations of frequency locking of two microspheres (diameter 10 μm) in a Paul trap, in close agreement with theoretical predictions. This system reproduces the main features of our earlier work on two-ion chaos. The phase space is fragmented, and chaotic transients can converge to several regular attractors. Damping, including laser cooling, can extinguish frequency-locked attractors, explaining their absence in ion trap experiments. Study of two weakly coupled circle maps shows that this is a general phenomenon when three frequencies are present.

• Received 19 May 1993

DOI:https://doi.org/10.1103/PhysRevLett.71.1828