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Physical Review A

Bloch oscillations of cold atoms in two-dimensional optical lattices

Andrey R. Kolovsky, H. J. Korsch

Published Jun 4, 2003• 73 citations
Publisher

Abstract

Bloch oscillations of cold atoms in two-dimensional optical lattices are studied. The cases of separable and nonseparable potentials are compared by simulating the wave-packet dynamics. For these two classes of optical potential, the Bloch oscillations were found to be qualitatively the same in the case of a weak static field but fundamentally different in the case of a strong field. In addition, the dynamics of the atoms in a double-period potential (which can easily be realized in two dimensions) is studied for the regime of a weak static field.

DOI
10.1103/physreva.67.063601

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Bloch oscillations of cold atoms in two-dimensional optical lattices are studied. The cases of separable and nonseparable potentials are compared by simulating the wave-packet dynamics. For these two classes of optical potential, the Bloch oscillations were found to be qualitatively the same in the case of a weak static field but fundamentally different in the case of a strong field. In addition, the dynamics of the atoms in a double-period potential (which can easily be realized in two dimensions) is studied for the regime of a weak static field.
This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.
Quantum dynamics of a charged particle in a two-dimensional (2D) lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations (the case of vanishing electric field) and Bloch oscillations (zero magnetic field), details of which has not yet been completely understood. In the present work we suggest to study this problem by using cold atoms in optical lattices. We introduce a one-dimensional (1D) model which can be easily realized in laboratory experiments with quasi-1D optical lattices and show that this model captures many features of the cyclotron-Bloch dynamics of the quantum particle in 2D square lattices.
This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.
We study the Bloch dynamics of a Bose-Einstein condensate of cold atoms by using the formalism of the discrete nonlinear Schroedinger equation. Depending on the static force magnitudes the system is shown to exhibit two qualitatively different regimes of Bloch oscillations - exponential decay for the static force magnitude less than some critical value (defined by the condensate density) and quasiperiodic oscillations in the opposite case. The relation of these regimes to the onset of chaos in the system is discussed.
Optical lattices are formed when cold atoms get trapped in the periodic array of optical potential wells created by a number of traveling light waves. Exact periodicity is guaranteed when the number of traveling waves exceeds the number of dimensions by no more than one. We present a few simple exactly solvable models for the transport of atoms over a lattice in the tight-binding limit. One model concerns the spreading of an atom by tunneling through the barriers and by momentum recoil induced by optical pumping. Another model gives results for the amplitude of Bloch oscillations, which occur when a uniform is added to the periodic potential. Finally the dissipative spreading of the quasimomentum due to optical pumping is modeled.
The early quantum theory of electrical conductivity in crystal lattices by Bloch and Zener [1,2] led to the striking prediction that a homogeneous static electric field induces an oscillatory rather than uniform motion of the electrons. These so-called Bloch oscillations have never been observed in natural crystals because the scattering time of the electrons by the lattice defects is much shorter than the Bloch period. In semiconductor superlattices the larger spatial period leads to a much shorter Bloch period (,600 fs) and Bloch oscillations have recently been observed through the emission of THz radiation by the electrons [3]. Here we present Bloch oscillations of atoms in the fundamental energy band of a periodic optical potential. We directly measure the atomic momentum distribution evolving in time under the influence of a constant inertial force for various potential depths. We experimentally observe oscillation periods in the millisecond range as well as positive and negative effective masses. Bloch oscillations are a pure quantum effect which can be explained in a simple one-dimensional model. The periodicity of the lattice (period d) leads to a band structure (Fig. 1) of the energy spectrum of the particle and the corresponding eigenenergies Ensqd and eigenstates jn, ql (Bloch states) are labeled by the discrete band index n and the continuous quasimomentum q; Ensqd and jn, ql are periodic functions of q with period 2pyd and q is conventionally restricted to the first Brillouin zone g2pyd, pydg [4]. Under the influence of a constant external force F, weak enough not to induce interband transitions, a given Bloch state jn, qs0dl evolves (up to a phase factor) into the state jn, qstdl according to qstd ­ qs0d 1 Ftyh . (1) This evolution is periodic with a period tB ­ hyjFjd corresponding to the time required for the quasimomentum to scan a full Brillouin zone. The mean velocity in jn, qstdl