Abstract
We present theoretical and numerical results on the dynamics of ultracold atoms in an accelerated single- and double-periodic optical lattice. In the single-periodic potential Bloch oscillations can be used to generate fast directed transport with very little dispersion. The dynamics in the double-periodic system is dominated by Bloch–Zener oscillations, i.e. the interplay of Bloch oscillations and Zener tunnelling between the subbands. Apart from directed transport, the latter system permits various interesting applications, such as widely tunable matter wave beam splitters and Mach–Zehnder interferometry. As an application, a method for efficient probing of small nonlinear mean-field interactions is suggested. Furthermore, the influence of the nonlinearity onto the Bloch bands, the breakdown of adiabaticity and the stability of the dynamics is discussed and analysed by numerical results.
Highlights
DEUTSCHE PHYSIKALISCHE GESELLSCHAFT tunnelling between minibands has been observed in different systems as, e.g. in optical superlattices for light waves [11]
We investigate the dynamics of cold atoms in a one-dimensional (1D) doubleperiodic potential, which is governed by the Schrödinger equation
D denotes the fundamental period, F is the strength of the external field and U and εU are the amplitudes of the two optical lattices, where the double-periodic potential is weak, ε 1
Summary
A wave packet in the ground band is accelerated in real space by the external field and reflected at the edges of the band, which gives rise to an oscillating motion. Within this picture, the spatial extension of these oscillations can be estimated as. The dynamics in momentum space shown in figure 1 is understood: the function C(k) moves under an envelope given by the Wannier–Stark function ψ0,0(k) In real space, this periodic motion yields the familiar Bloch oscillations. A stronger influence of higher bands due to a stronger external force would increase the dispersion This transport mechanism has some remarkable features that can be analysed in the singleband tight-binding approximation. We want to point out, that the presented transport mechanism differs from the transport in a quantum ratchet (see, e.g. [21, 22]) since the underlying double-periodic lattice is spatially symmetric and the direction of the transport depends on the initial sign of F and the initial state
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