Tunnelling and the Born-Oppenheimer approximation in optical lattices

We study periodic well-to-well flopping of rubidium atoms in one-dimensional grey optical lattices using a nondestructive, real-time measurement technique and quantum Monte Carlo wavefunction simulations. The observed flopping rates as well as flopping rates extracted from exact band structure calculations can largely be reproduced using adiabatic models that employ the Born-Oppenheimer approximation. The adiabatic model is greatly improved by taking into account a gauge potential that is added to the usual adiabatic light-shift potential. The validity of the adiabatic model allows us to interpret the observed flopping phenomenon as periodic well-to-well tunnelling. At low intensities and in related far-off-resonant optical lattices the adiabatic model fails. There, a weak-coupling model becomes valid, which describes the well-to-well flopping as a Rabi oscillation between weakly coupled stales, but not as a tunnel effect.