Asymmetric Landau-Zener Tunneling in a Periodic Potential

Abstract

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.

Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures

“…This effect was first predicted by Pitaevskii in 1959 for the phonon excitation in superfluid 4 He [45]. The two created excitations have the same quasi-momentum q c /2 and energy E qc/2 at q = q c .…”

“…For α ≤ 6, the excitation energy E q bends up before bending over, as q approaches the BZ boundary. This behavior is analogous to the so called "anomalous dispersion" of the phonon spectrum in superfluid 4 He [22,23,32]. For α > 6, in contrast, the spectrum simply bends over as one leaves the low q (phonon) region.…”

“…We find that the Bogoliubov-Popov excitation spectrum E q must exhibit "anomalous dispersion" for damping processes to occur. This is analogous to the case of phonon damping in superfluid 4 He. In the absense of this "bending-up" of the low q spectrum, energy conservation cannot be satisfied.…”

“…An optical lattice is an ideal system for studying a variety of solid state physics phenomena, such as Bloch oscillations [1,2], Landau-Zener tunneling [3,4], and Josephson oscillations [5]. An optical lattice is an ideal crystal without lattice imperfections or impurities, and parameters can be changed easily over a wide range.…”

Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids

“…We make reference to the two-mode mean-field and Bose-Hubbard schemes inherited from the Gross-Pitaevskii and full quantum approaches [4][5][6][7][8][9]. As a result of incorporating the linear variation in time between the two levels, all of those treatments suggested a breakdown of the adiabatic limit, that is, that the LZ transition probability does not vanish even in the adiabatic limit.…”