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Laser Physics Letters

Nonlinear effects in periodic potentials: asymmetric Landau-Zener tunnelling of a Bose-Einstein condensate

M. Jona-Lasinio, O. Morsch, Matteo Cristiani, Nicola Malossi, Jörg Helge Müller, E Courtade, Marco Anderlini, E. Arimondo

Published Feb 7, 2004• 5 citations
Publisher

Abstract

From a two-level model for nonlinear Landau-Zener tunnelling between two energy bands of a Bose-Einstein condensate in a periodic potential we obtain unequal tunnelling rates for the two directions of tunnelling. With increasing nonlinearity, tunnelling from the ground state to the excited state is enhanced, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunnelling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry. We discuss the limitations of our approach and possible future experiments.

DOI
10.1002/lapl.200310039

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From a two-level model for nonlinear Landau-Zener tunnelling between two energy bands of a Bose-Einstein condensate in a periodic potential we obtain unequal tunnelling rates for the two directions of tunnelling. With increasing nonlinearity, tunnelling from the ground state to the excited state is enhanced, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunnelling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry. We discuss the limitations of our approach and possible future experiments.
Using a simple model for nonlinear Landau-Zener tunneling between two energy bands of a Bose-Einstein condensate in a periodic potential, we find that the tunneling rates for the two directions of tunneling are not the same. Tunneling from the ground state to the excited state is enhanced by the nonlinearity, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunneling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry.
We present our experimental investigations on the subject of dynamical nonlinearity-induced instabilities and of nonlinear Landau-Zener tunneling between two energy bands in a Rubidium Bose-Einstein condensate in an accelerated periodic potential. These two effects may be considered two different regimes (for small and large acceleration) of the same physical system and studied with the same experimental protocol. Nonlinearity introduces an asymmetry in Landau-Zener tunneling; as a result, tunneling from the ground state to the excited state is enhanced whereas in the opposite direction it is suppressed. When the acceleration is lowered, the condensate exhibits an unstable behaviour due to nonlinearity. We also carried out a full numerical simulation of both regimes integrating the full Gross-Pitaevskii equation; for the Landau-Zener effect we also used a simple two-level model. In both cases we found good agreement with the experimental results.
In BECs, collisions between condensate atoms give rise to a nonlinear contribution to the dynamics which is typically included as a mean-field term in the Schrodinger equation. This nonlinearity leads to a modification of well-known effects associated with matter waves in periodic potentials and adds a number of phenomena that are absent in the linear problem. We focused on the dynamics of a BEC in an accelerated optical lattice. In the linear case, this gives rise to Bloch oscillations and, above a critical acceleration, to Landau-Zener tunneling. In the nonlinear case, the probability for Landau-Zener tunneling is modified depending on the direction in which it occurs between two bands. By varying the acceleration of the optical lattice and measuring the time-dependence of the interference contrast, we were able to identify the instability regime and the characteristic time in which the dynamical instability destroys the interference pattern. Furthermore, we observed an increase in the condensate dimensions perpendicular to the lattice direction when the unstable region was reached. This indicates a mechanism whereby the longitudinal instability leads to an increase in the transverse release energy
The nonlinear Landau—Zener tunneling and nonlinear Rabi oscillations of Bose—Einstein condensate (BEC) with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters (i.e., the modulation amplitude and frequency) and the strength of periodic potential.
In this paper, we develop a theory of the LZ tunneling between the lowest bands of a periodic potential. Our approach reveals the role of modulational instability (MI) on the atom transfer between zones as well as the effect of (partial) suppression of the MI by the lattice acceleration. Our consideration is based on the Gross-Pitaevskii equation, which in the two-zone approximation is reduced to the linearly coupled nonlinear Schrodinger equations. In the presence of nonlinearity, the Bloch states can become unstable and localized states can appear in the gaps between bands (gap-solitons) in which can dramatically affect the atomic transfer rate. The stability properties constitute the main reason of asymmetry of the LZ tunneling