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Physical Review Letters

Tunneling Dynamics and Gauge Potentials in Optical Lattices

Sangit Dutta, Boon-Keng Kevin Teo, Georg A. Raithel

Published Sep 6, 1999• 52 citations
Publisher

Abstract

We study periodic well-to-well tunneling of ${}^{87}\mathrm{Rb}$ atoms on adiabatic potential surfaces of a 1D optical lattice. The observed dependence of the lowest-band tunneling period on the depth of the adiabatic potential can only be explained by an additional intensity-independent gauge potential predicted by Dum et al. The experimental data are in excellent agreement with our quantum Monte Carlo wave-function simulations and band structure calculations.

DOI
10.1103/physrevlett.83.1934

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We study periodic well-to-well tunneling of 87Rb{}^{87}\mathrm{Rb}87Rb atoms on adiabatic potential surfaces of a 1D optical lattice. The observed dependence of the lowest-band tunneling period on the depth of the adiabatic potential can only be explained by an additional intensity-independent gauge potential predicted by Dum et al. The experimental data are in excellent agreement with our quantum Monte Carlo wave-function simulations and band structure calculations.
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.
Summary form only given. It has been predicted that topological potentials play a significant role in gray optical lattices. However, so far there has been no direct experimental demonstration of their existence. Unlike light-shift potentials, which, in the case of low saturation, scale as the laser intensity, topological (or gauge) potentials are intensity independent and solely depend on the topology of the lattice, which is determined by the detuning, beam geometry and magnetic fields. In our experiment, /sup 87/Rb atoms are collected in a standard magneto-optic trap and loaded into a 1D optical lattice. The lattice is formed by counterpropagating, orthogonally polarized laser beams. The minima of the trapping potential form at the antinodes of the standing waves and, as a result of optical pumping, the wells are alternately occupied. When an atom tunnels from one type of well to another, it must then flip its magnetic spin state. The gauge potential is associated with the energy needed for this change. In this gray lattice, the potential wells are shallow due to the weak interaction with the light field. Shallow potentials are necessary for tunneling. We use two schemes to observe tunneling. In the first, we use an auxiliary weak laser pulse to selectively depopulate one of the two types of wells. We observe tunneling by measuring the population in each type of well as a function of time. The second way we study tunneling is to create atomic wave-packets within the wells and to observe their motion as they oscillate. The wave-packets are created by diabatically displacing the trapped atoms in either position or momentum space. Tunneling occurs when the wave-packets run against barriers provided by the maxima of the trapping potential.
We report experimental results on the properties of Bose-Einstein condensates in one-dimensional optical lattices. By accelerating the lattice, we observed Bloch oscillations of the condensate in the lowest band, as well as Landau-Zener (LZ) tunneling into higher bands when the lattice depth was reduced and/or the acceleration of the lattice was increased. The dependence of the LZ tunneling rate on the condensate density was then related to mean-field effects modifying the effective potential acting on the condensate, yielding good agreement with recent theoretical work. We also present several methods for measuring the lattice depth and discuss the effects of the micromotion in the time-orbiting-potential trap on our experimental results.
We have loaded Bose-Einstein condensates into one-dimensional, off-resonant optical lattices and accelerated them by chirping the frequency difference between the two lattice beams. For small values of the lattice well depth, Bloch oscillations were observed. Reducing the potential depth further, Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied and used as a probe for the effective potential resulting from mean-field interactions as predicted by Choi and Niu [Phys. Rev. Lett. 82, 2022 (1999)]. The effective potential was measured for various condensate densities and trap geometries, yielding good qualitative agreement with theoretical calculations.
We study Rydberg atoms in ponderomotive optical lattices. Unlike for ground-state atoms, for Rydberg atoms in an optical lattice the extent of the electronic wave-function can approach the lattice period. This leads to state-dependent adiabatic trapping potentials that are unique to Rydberg atoms. We first discuss a theoretical model of adiabatic lattice potentials of Rydberg atoms. Then, we use microwave spectroscopy to experimentally demonstrate and investigate the state-dependence of the adiabatic potentials of S1/2 Rydberg states of rubidium. The observed microwave spectra depend strongly on both the principal quantum number and the depth of the lattice. A semi-classical simulation is used to explain the features seen in the spectra. Based on the results, we estimate the trapping efficiency of the ponderomotive optical lattice.
We study the dynamics of bosonic atoms in a tilted one-dimensional optical lattice and report on the first direct observation of density-induced tunneling. We show that the interaction affects the time evolution of the doublon oscillation via density-induced tunneling and pinpoint its density and interaction dependence. The experimental data for different lattice depths are in good agreement with our theoretical model. Furthermore, resonances caused by second-order tunneling processes are studied, where the density-induced tunneling breaks the symmetric behavior for attractive and repulsive interactions predicted by the Hubbard model.