Nonlinear atom-optical $\delta$-kicked harmonic oscillator using a Bose-Einstein condensate

We experimentally investigate the atom-optical $\delta$-kicked harmonic oscillator for the case of nonlinearity due to collisional interactions present in a Bose-Einstein condensate. A Bose condensate of rubidium atoms tightly confined in a static harmonic magnetic trap is exposed to a one-dimensional optical standing-wave potential that is pulsed on periodically. We focus on the quantum antiresonance case for which the classical periodic behavior is simple and well understood. We show that after a small number of kicks the dynamics are dominated by dephasing of matter wave interference due to the finite width of the condensate’s initial momentum distribution. In addition, we demonstrate that the nonlinear mean-field interaction in a typical harmonically confined Bose condensate is not sufficient to give rise to chaotic behavior.

Figure 1

Energy plotted vs kick number for the quantum antiresonance condition, $\stackrel{-}{k}=2\pi$ with mean-field interactions. The solid circles are the measured mean energies and the error bars include shot-to-shot variation and systematic uncertainty in the calculation of the energy. The open circles are the corresponding theoretical values computed using Eq. (2) and the solid line is to guide the eye.

Figure 2

Momentum distribution vs kick number for the numerical simulation in Fig. 1

Figure 3

Numerical simulations of energy vs kick number for the quantum antiresonance condition, $\stackrel{-}{k}=2\pi$. (a) No collisional interaction $(C=0)$, (b) collisional interaction corresponding to the experiment $(C=50)$, and (c) strong collisional interaction $(C=1000)$.