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arXiv:quant-ph/0603093 · New Journal of Physics

Bloch–Zener oscillations

B M Breid, D Witthaut, H J Korsch

Published Jul 5, 2006• 121 citations
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Abstract

It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two sub-bands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunnelling between the sub-bands, a Bloch–Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian which is a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker–Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach–Zehnder interferometer is briefly discussed.

DOI
10.1088/1367-2630/8/7/110

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It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two sub-bands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunnelling between the sub-bands, a Bloch–Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian which is a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker–Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach–Zehnder interferometer is briefly discussed.
It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two subbands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunneling between the subbands, a Bloch-Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian, a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker-Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach-Zehnder interferometer is briefly discussed. PACS numbers: 03.65.-w, 03.75.Be, 03.75.LmBloch-Zener oscillations 2 1.
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 tunneling 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. PACS numbers: 03.65.-w, 03.75.Be, 03.75.Dg, 03.75.LmManipulation of matter waves using Bloch and Bloch-Zener oscillations 2 1.
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.
It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.
The effect of an additional high frequency alternating field on the Bloch-Zener oscillation of a quantum particle is investigated theoretically. The effective magnitude of the band gap is reduced by the ac field, and even collapsed to zero by appropriately tuning the amplitude and the frequency of the oscillation. This results in the enhancement of the Zener tunneling with dramatic changes of the Bloch-Zener oscillation. The temporal behavior of the wave packet is clarified as due to the interplay of the Landau-Zener interference in the repeated level crossings with two different time scales, namely, the period of the Bloch oscillation, and the period of the high frequency ac field.
Stimulated by the experimental realization of spin-dependent tunneling via a gradient magnetic field [C. J. Kennedy et al., Phys. Rev. Lett. 111, 225301 (2013); M. Aidelsburger et al., Phys. Rev. Lett. 111, 185301 (2013)], we investigate the dynamics of Bloch oscillations and Landau-Zener tunneling of single spin-half particles in a periodic potential under the influence of a spin-dependent constant force. In analogy to the Wannier-Stark system, we call our system the Wannier-Zeeman system. If there is no coupling between the two spin states, the system can be described by two crossing Wannier-Stark ladders with opposite tilts. The spatial crossing between two Wannier-Stark ladders becomes a spatial anticrossing if the two spin states are coupled by external fields. For a wave packet away from the spatial anticrossing, due to the spin-dependent constant force, it will undergo spatial Landau-Zener transitions assisted by the intrinsic intraband Bloch oscillations, which we call the Bloch-Landau-Zener dynamics. If the interspin coupling is sufficiently strong, the system undergoes adiabatic Bloch-Landau-Zener dynamics, in which the spin dynamics follows the local dressed states. Otherwise, for nonstrong interspin couplings, the system undergoes nonadiabatic Bloch-Landau-Zener dynamics.