Tunneling and the Born-Oppenheimer Approximation in Optical Lattices

Jeremy B. Reeves, Ludwig Krinner, M. K. Stewart +2 more

S K Dutta, Georg A. Raithel

Abstract. 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 states, but not as a tunnel effect.

Dirk-Soeren Luehmann, Ole Jürgensen, K. Sengstock

Kirk W. Madison

Ole Søe Sørensen, Klaus Mølmer

We analyze the quantum states of two identical bosons in a combined harmonic oscillator and periodic lattice trap in one spatial dimension. In the case of tight-binding and only nearest-neighbor tunneling, the equations of motion are conveniently represented in the momentum representation. We show that in the case of strong attraction between the particles, the different time scales of relative and center-of-mass motions validate a separation of the problem similar to the Born-Oppenheimer approximation applied in the description of electronic and nuclear motions in molecules.

Boon-Keng Kevin Teo, Jeffrey R. Guest, Georg A. Raithel