The semiclassical theory of Bloch wave packet dynamics predicts a self-rotation angular momentum in asymmetric periodic potentials, which has never been observed. We show how this is manifested in Bose-Einstein condensed atoms in optical lattices. Displacing the wave packet to a corner of the Brillouin zone we obtain a current distribution with a non-quantized angular momentum, independent of the size of the distribution. A weak interatomic interaction does not modify the results, affecting only the rate of spreading in the lattice. A strong repulsive interaction results in a collapse of the wavefunction into matter-wave lattice solitons.The semiclassical theory of Bloch wave packet dynamics predicts a self-rotation angular momentum in asymmetric periodic potentials, which has never been observed. We show how this is manifested in Bose-Einstein condensed atoms in optical lattices. Displacing the wave packet to a corner of the Brillouin zone we obtain a current distribution with a non-quantized angular momentum, independent of the size of the distribution. A weak interatomic interaction does not modify the results, affecting only the rate of spreading in the lattice. A strong repulsive interaction results in a collapse of the wavefunction into matter-wave lattice solitons.

arXiv:cond-mat/0306184Jun 6, 20032 citations

The semiclassical evolution of wave packets

Robert G. Littlejohn

Physics ReportsMay 1, 1986593 citations

Mapping the Berry curvature from semiclassical dynamics in optical lattices

Hannah M. Price, Nigel R. Cooper

We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry curvature across the Brillouin zone. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wave packet undergoing Bloch oscillations. However, in two dimensions these trajectories may be complicated Lissajous-like figures, making it difficult to extract the effects of Berry curvature in general. We propose how this can be done using a ``time-reversal'' protocol. This compares the velocity of a wave packet under positive and negative external force, and allows a clean measurement of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three specific systems: the asymmetric hexagonal lattice and two ``optical flux'' lattices in which the Chern number is nonzero. Finally, we discuss general experimental considerations for observing Berry curvature effects in ultracold gases.We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry curvature across the Brillouin zone. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wave packet undergoing Bloch oscillations. However, in two dimensions these trajectories may be complicated Lissajous-like figures, making it difficult to extract the effects of Berry curvature in general. We propose how this can be done using a ``time-reversal'' protocol. This compares the velocity of a wave packet under positive and negative external force, and allows a clean measurement of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three specific systems: the asymmetric hexagonal lattice and two ``optical flux'' lattices in which the Chern number is nonzero. Finally, we discuss general experimental considerations for observing Berry curvature effects in ultracold gases.

arXiv:1112.5616Physical Review AMar 15, 2012201 citations

Dynamics of two interacting electrons in Anderson-Hubbard chains with long-range correlated disorder: Effect of a static electric field

Wandearley S. Dias, Elton Malta Nascimento, M. L. Lyra +1 more

We investigate the influence of the on-site Hubbard interaction $U$ on the eigenstates and dynamics of two electrons restricted to move in a linear chain with long-range correlated disorder. We solve the time-dependent Schr\"odinger equation to follow the time evolution of an initially localized Gaussian two-electron wave packet. In the regime of strongly correlated disorder, for which one-electron extended eigenstates emerge near the band center, the electron-electron coupling promotes the trapping of a finite portion of the wave packet. In the presence of a uniform electric field, the wave packet develops complex Bloch oscillations. The power spectrum of the centroid's velocity trace shows a splitting near the typical semiclassical Bloch frequency, as well as a frequency doubling phenomenon for intermediate couplings which is related to the bounded states components that are present in the wave packet. Finally, we show that localized and extended two-electron eigenstates coexist near the band center with the level spacing distribution showing a universal Poissonian form irrespective to the Hubbard coupling.We investigate the influence of the on-site Hubbard interaction $U$ on the eigenstates and dynamics of two electrons restricted to move in a linear chain with long-range correlated disorder. We solve the time-dependent Schr\"odinger equation to follow the time evolution of an initially localized Gaussian two-electron wave packet. In the regime of strongly correlated disorder, for which one-electron extended eigenstates emerge near the band center, the electron-electron coupling promotes the trapping of a finite portion of the wave packet. In the presence of a uniform electric field, the wave packet develops complex Bloch oscillations. The power spectrum of the centroid's velocity trace shows a splitting near the typical semiclassical Bloch frequency, as well as a frequency doubling phenomenon for intermediate couplings which is related to the bounded states components that are present in the wave packet. Finally, we show that localized and extended two-electron eigenstates coexist near the band center with the level spacing distribution showing a universal Poissonian form irrespective to the Hubbard coupling.

Physical Review BJan 13, 201018 citations

We investigate the influence of the on-site Hubbard interaction

U

on the eigenstates and dynamics of two electrons restricted to move in a linear chain with long-range correlated disorder. We solve the time-dependent Schr\"odinger equation to follow the time evolution of an initially localized Gaussian two-electron wave packet. In the regime of strongly correlated disorder, for which one-electron extended eigenstates emerge near the band center, the electron-electron coupling promotes the trapping of a finite portion of the wave packet. In the presence of a uniform electric field, the wave packet develops complex Bloch oscillations. The power spectrum of the centroid's velocity trace shows a splitting near the typical semiclassical Bloch frequency, as well as a frequency doubling phenomenon for intermediate couplings which is related to the bounded states components that are present in the wave packet. Finally, we show that localized and extended two-electron eigenstates coexist near the band center with the level spacing distribution showing a universal Poissonian form irrespective to the Hubbard coupling.