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arXiv:1007.1326 · Physical Review A

Time-resolved measurement of Landau-Zener tunneling in different bases

G. Tayebirad, Alessandro Zenesini, D. Ciampini, R. Mannella, O. Morsch, E. Arimondo, Niels Lörch, Sandro Wimberger

Published Jul 26, 2010• 45 citations
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Abstract

A comprehensive study of the tunneling dynamics of a Bose-Einstein condensate in a tilted periodic potential is presented. We report numerical and experimental results on time-resolved measurements of the Landau-Zener tunneling of ultracold atoms introduced by the tilt, which experimentally is realized by accelerating the lattice. The use of different protocols enables us to access the tunneling probability, numerically as well as experimentally, in two different bases, namely, the adiabatic basis and the diabatic basis. The adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic one to the free-particle momentum eigenstates. Our numerical and experimental results are compared with existing two-state Landau-Zener models.

DOI
10.1103/physreva.82.013633

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A comprehensive study of the tunneling dynamics of a Bose-Einstein condensate in a tilted periodic potential is presented. We report numerical and experimental results on time-resolved measurements of the Landau-Zener tunneling of ultracold atoms introduced by the tilt, which experimentally is realized by accelerating the lattice. The use of different protocols enables us to access the tunneling probability, numerically as well as experimentally, in two different bases, namely, the adiabatic basis and the diabatic basis. The adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic one to the free-particle momentum eigenstates. Our numerical and experimental results are compared with existing two-state Landau-Zener models.
A comprehensive study of the time-resolved Landau–Zener tunneling of a Bose– Einstein condensate in a tilted periodic potential is presented in this thesis. Several ways are discussed how to control the tunneling. In the first collection of our results, the tunneling from the ground band to the continuum is shown to depend crucially on the initial condition and system parameters, and also on the strength of atom-atom interactions. The use of different protocols enables us to access the tunneling probability in two different bases, namely, the adiabatic basis (eigenstates of the Hamiltonian with the potential) and the diabatic basis (free-particle momentum eigenstates). The structure of the survival probability and the measure of the tunneling time depend on the chosen basis. All these possibilities have been checked and proved in experiments. We go also beyond and propose a possibility to manipulate the tunneling probability of ultracold atoms in the tilted time-dependent stochastic potentials. Our theoretical and numerical results show that the tunneling in such a potential can be controlled by adding different types of colored noise. A scaling law is introduced for these results, which effectively reduces the parameter-dependence of the tunneling and leads to a better understanding of dynamics in the proposed noisy system.
We report time-resolved measurements of Landau-Zener tunneling of Bose-Einstein condensates in accelerated optical lattices, clearly resolving the steplike time dependence of the band populations. Using different experimental protocols we were able to measure the tunneling probability both in the adiabatic and in the diabatic bases of the system. We also experimentally determine the contribution of the momentum width of the Bose condensates to the temporal width of the tunneling steps and discuss the implications for measuring the jump time in the Landau-Zener problem.
The time it takes a quantum system to complete a tunneling event (which in the case of cross-barrier tunneling can be viewed as the time spent in a classically forbidden area) is related to the time required for a state to evolve to an orthogonal state, and an observation, i.e., a quantum mechanical projection on a particular basis, is required to distinguish one state from another. We have performed time-resolved measurements of Landau-Zener tunneling of Bose-Einstein condensates in accelerated optical lattices, clearly resolving the steplike time dependence of the band populations. The use of different protocols enabled us to access the tunneling probability, in two different bases, namely, the adiabatic basis and the diabatic basis. The adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic one to the free-particle momentum eigenstates. Our findings pave the way towards more quantitative studies of the tunneling time for LZ transitions, which are of current interest in the context of optimal quantum control and the quantum speed limit.
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 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. Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied. In order to allow in-trap measurements of these phenomena, we dynamically compensated for the intrinsic micromotion of the atoms in our time-orbiting potential trap.