Supplemental Data

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Observation of Chaos-Assisted Tunneling Between Islands of Stability
Daniel A. Steck, Windell H. Oskay, Mark G. Raizen

Supplementary Material

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  • Movie 1
    Phase-space motion of the classical islands of stability. This movie illustrates the continuous evolution of the classical phase space presented in Fig. 5B.An individual phase space describes the classical dynamics when stroboscopically sampled once each period of the external modulation. The frames in this movie correspond to choosing different phases of the sampling.The symmetry-related islands (large blue spots) move towards and away from each other in a synchronous manner.

  • Movie 2
    High temporal resolution tunneling measurement. This movie shows the individual momentum distributions for the data presented in Fig. 5A. The data presented in this movie are the result of sampling the momentum distribution each microsecond (20 times per modulation period)for the first 200 microseconds of the CAT experiment, corresponding to the first half-oscillation seen in Fig. 1C. Atoms are initially loaded in the classical island at positive momentum, and tunnel to the island at negative momentum. While this process is occuring, however, it is possible to see the motion of the classical islands. The atoms trapped in the two symmetry-related islands can be seen to move towards and away from each other in unison.

  • Movie 3
    Observation of chaos-assisted tunneling. This movie shows the individual momentum distributions for the data presented in Fig. 1C. The data are sampled every 40 microseconds (every 2 modulation periods). During the course of the interaction, a large fraction of the initial atomic sample coherently tunnels to the opposite momentum. Four complete oscillations are visible in this animation.

Supplemental Figure 1. Dependence of the tunneling signal on the width of the initial momentum selection. The standard state preparation sequence involves a long (800 microsecond) stimulated Raman velocity selection pulse. Shorter selection times result in wider slices in momentum. The contrast in the tunneling oscillations then decreases because fewer of the atoms have the reflection symmetry that is necessary for tunneling to occur. We also performed the experiment in the absence of Raman velocity selection by exposing the atoms to the interaction potential immediately after cooling in the three-dimensional optical lattice. In this case, the momentum distribution is nearly uniform over the scale of a photon recoil momentum, and no coherent oscillations are observed.The widths of the momentum slices for these data are quantified by their half-widths at half maximum (HWHM).

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