Engineering Landau-Zener Tunneling of Ultra-cold Atoms in Tilted Lattices

A comprehensive study of the coherent control of the time-resolved
Landau–Zener tunneling of a Bose–Einstein condensate in a periodic po-
tential subjected to an additional static force is presented. This system en-
joys a continuing popularity in many experimental and theoretical groups
[1, 2]. In excellent agreement with experimental results, our theoretical
calculations, based on a mean-field effective theory for a many-particle
condensate, explain the temporal behavior of the Landau-Zener tunneling
[3]. While for a typical initial state of a BEC being strongly localized in
momentum space, we observe a step-like structure in the survival proba-
bility as a function of time (resembling the periodic Bloch oscillation), this
structure is gradually washed out by increasing either atom-atom interac-
tion together with other observed time-dependent structures in the profile
of the survival probability. This clarifies to what extend we can expect
deviation from a purely exponential decay in the studied Landau-Zener
tunneling process. We go also beyond and propose a possibility to ma-
nipulate the tunneling probability of ultracold atoms loaded into a tilted
quasi-1D geometry supporting a stochastic potential. Our theoretical and
numerical results show that the tunneling in such a disordered potential
can be controlled by adding different types of colored noise. A scaling
law is introduced, which effectively reduces the parameter-dependence of
the tunneling and enables us to universally characterize the effect of the
noise.

References:

[1] C. Sias et al., Phys. Rev. Lett. 98, 120403 (2007).

[2] M. Gustavsson et al., Phys. Rev. Lett. 100, 080404 (2008); M. Fattori et al.,
Phys. Rev. Lett. 100, 080405 (2008); T. Schulte et al., Phys. Rev. A, 77, 023610
(2008), B. Deissler et al., Nature Phys. 6, 354 - 358 (2010) .

[3] A. Zenesini et al., Phys. Rev. Lett 103, 090403 (2009), G.Tayebirad et al., Phys.
Rev. A 82, 013633 (2010).