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arXiv:1104.2535

Tunneling of ultracold atoms in time-independent potentials

E. Arimondo, Sandro Wimberger

Published Apr 13, 2011• 0 citations
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Abstract

We present theoretical as well as experimental results on resonantly enhanced quantum tunneling of Bose-Einstein condensates in optical lattices both in the linear case of single particle dynamics and in the presence of atom-atom interactions. Our results demonstrate the usefulness of condensates in optical lattices for the dynamical control of tunneling and for simulating Hamiltonians originally used for describing solid state phenomena.

DOI
10.48550/arxiv.1104.2535

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We present theoretical as well as experimental results on resonantly enhanced quantum tunneling of Bose-Einstein condensates in optical lattices both in the linear case of single particle dynamics and in the presence of atom-atom interactions. Our results demonstrate the usefulness of condensates in optical lattices for the dynamical control of tunneling and for simulating Hamiltonians originally used for describing solid state phenomena.
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Collective quantum tunneling of a Bose-Einstein condensate between two parts of an optical lattice separated by an energy barrier is theoretically investigated. We show that by a pulsewise change of the barrier height, it is possible to switch between a tunneling regime and a self-trapped one. This property of the system is explained by effectively reducing the nonlinear dynamics of the system to that of a particle moving in a double square well potential. The analysis is performed for both attractive and repulsive interatomic forces, and emphasizes the experimental relevance of our findings.
We have observed tunneling suppression and photon-assisted tunneling of Bose-Einstein condensates in an optical lattice subjected to a constant force plus a sinusoidal shaking. For a sufficiently large constant force, the ground energy levels of the lattice are shifted out of resonance and tunneling is suppressed; when the shaking is switched on, the levels are coupled by low-frequency photons and tunneling resumes. Our results agree well with theoretical predictions and demonstrate the usefulness of optical lattices for studying solid-state phenomena.
The similarity between matter waves in periodic potential and solid-state physics processes has triggered the interest in quantum simulation using Bose-Fermi ultracold gases in optical lattices. The present work evidences the similarity between electrons moving under the application of oscillating electromagnetic fields and matter waves experiencing an optical lattice modulated by a frequency difference, equivalent to a spatially shaken periodic potential. We demonstrate that the tunneling properties of a Bose-Einstein condensate in shaken periodic potentials can be precisely controlled. We take additional crucial steps towards future applications of this method by proving that the strong shaking of the optical lattice preserves the coherence of the matter wavefunction and that the shaking parameters can be changed adiabatically, even in the presence of interactions. We induce reversibly the quantum phase transition to the Mott insulator in a driven periodic potential.
A proof-of-principle experiment simulating effects predicted by relativistic wave equations with ultracold atoms in a bichromatic optical lattice that allows for a tailoring of the dispersion relation is reported. We observe the analog of Klein tunneling, the penetration of relativistic particles through a potential barrier without the exponential damping that is characteristic for nonrelativistic quantum tunneling. Both linear (relativistic) and quadratic (nonrelativistic) dispersion relations are investigated, and significant barrier transmission is observed only for the relativistic case.