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Physical Review Letters

How Landau-Zener Tunneling Takes Time

Qian Niu, Mark G. Raizen

Published Apr 20, 1998• 81 citations
Publisher

Abstract

We calculate the time evolution of Landau-Zener tunneling for atoms in an accelerating optical lattice. Analytical expressions are obtained that are in good agreement with a recent observation of nonexponential decay. We identify new experimental regimes that show a crossover from strong coherent oscillations to exponential decay in the temporal evolution of the survival probability. We establish the time scale of this crossover, and make connection to a tunneling time of Zener breakdown.

DOI
10.1103/physrevlett.80.3491

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We calculate the time evolution of Landau-Zener tunneling for atoms in an accelerating optical lattice. Analytical expressions are obtained that are in good agreement with a recent observation of nonexponential decay. We identify new experimental regimes that show a crossover from strong coherent oscillations to exponential decay in the temporal evolution of the survival probability. We establish the time scale of this crossover, and make connection to a tunneling time of Zener breakdown.
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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.
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We observe quantum tunneling of cold sodium atoms from an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. For sufficiently large values of the acceleration, we observe an exponential decay in the number of atoms that remain trapped as a function of the interaction time. We show that this loss is due to quantum tunneling, and compare the decay rates with Landau-Zener theory. We also observe oscillations in the tunneling rate as a function of the acceleration which are due to quantum interference effects.
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