Bloch oscillations in two-dimensional lattices

Witthaut, Dirk; Keck, Frédéric; Korsch, Hans Jürgen; Mossmann, S.

doi:10.1088/1367-2630/6/1/041

Cited by 48 publications

(57 citation statements)

References 26 publications

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“…A drastically different scenario has been predicted [14] for an input beam which is initially very narrow, comparable in its size with a single site of the 2D lattice. Such a beam excites simultaneously waves with wavevectors distributed over the whole Brillouin zone.…”

mentioning

confidence: 97%

“…All direct experimental observations of Bloch oscillations and Zener tunneling performed so far were limited to one-dimensional geometries. New effects may be associated with these phenomena in systems of higher dimensionality [13,14]. In a two-dimensional periodic potential the wave follows complex Lissajous-type trajectories when the direction of the static force does not coincide with a principal axis of the lattice.…”

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confidence: 99%

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Bloch Oscillations and Zener Tunneling in Two-Dimensional Photonic Lattices

et al. 2006

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We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square photonic lattice superimposed on a refractive index ramp, and demonstrate the tunneling of light from the first to the higher-order transmission bands of the lattice bandgap spectrum, associated with the spectral dynamics inside the first Brillouin zone and corresponding oscillations of the primary beam.

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confidence: 97%

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confidence: 99%

Bloch Oscillations and Zener Tunneling in Two-Dimensional Photonic Lattices

et al. 2006

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“…Especially, the velocity of the directed motion is given by equation (55). But, one has to keep in mind that for realistic potentials, as investigated for example in [9], the factors g (u,v) decrease exponentially with increasing |u| + |v| so that the directed motion and the dispersion are very small compared to the oscillation.…”

Section: Single-band Modelsmentioning

confidence: 99%

“…Bose-Einstein condensates in optical lattices has motivated new theoretical studies in this field (see [4] and the references given there). Bloch oscillations are one of the striking phenomena in such systems and an example for a counterintuitive behaviour in quantum mechanics [4][5][6][7][8][9][10][11]. While [4][5][6][7] discuss the one-dimensional case analytically in a single-band tight-binding model, in [8][9][10][11] two-dimensional Bloch oscillations are considered, however, only partially in an analytical treatment.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional Bloch oscillations: a Lie-algebraic approach

Mossmann¹,

Schulze²,

Witthaut³

et al. 2005

J. Phys. A: Math. Gen.

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A Lie-algebraic approach successfully used to describe one-dimensional Bloch oscillations in a tight-binding approximation is extended to two dimensions. This extension has the same algebraic structure as the one-dimensional case while the dynamics shows a much richer behaviour. The Bloch oscillations are discussed using analytical expressions for expectation values and widths of the operators of the algebra. It is shown under which conditions the oscillations survive in two dimensions and the centre of mass of a wave packet shows a Lissajous like motion. In contrast to the one-dimensional case, a wavepacket shows systematic dispersion that depends on the direction of the field and the dispersion relation of the field free system.

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“…Nowadays one observes a growing interest in BO in multidimensional lattices [10][11][12][13][14][15]. In the single-particle approach this problem was considered in references [11,12]. It was shown that an increase of the lattice dimensionality introduces new effects not present in the 1D lattice.…”

Section: Introductionmentioning

confidence: 99%

Effect of the lattice alignment on Bloch oscillations of a Bose-Einstein condensate in a square optical lattice

Chung

Kolovsky

2008

Eur. Phys. J. D

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Abstract. We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the force. We study stability of these oscillations for non-vanishing interactions, which is shown to depend on an alignment of the force vector with respect to the lattice crystallographic axes. If the force is aligned along any of the axes, the mean field approach can be used to identify the stability conditions. On the contrary, for a misaligned force one has to employ the microscopic approach, which predicts periodic modulation of Bloch oscillations in the limit of a large forcing.PACS. 03.75.Lm Bose-Einstein condensates in periodic potentials -03.75.Kk Dynamic properties of condensates

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Bloch oscillations in two-dimensional lattices

Cited by 48 publications

References 26 publications

Bloch Oscillations and Zener Tunneling in Two-Dimensional Photonic Lattices

Bloch Oscillations and Zener Tunneling in Two-Dimensional Photonic Lattices

Two-dimensional Bloch oscillations: a Lie-algebraic approach

Effect of the lattice alignment on Bloch oscillations of a Bose-Einstein condensate in a square optical lattice

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