One-dimensional Lattice Potential Research Articles

Relativistic motion of an Airy wave packet in a lattice potential

We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its velocity, and so the acceleration cannot continue indefinitely. Instead, we show that the wavepacket's motion is described by relativistic equations of motion, which surprisingly, arise naturally from evolution under the standard non-relativistic Schr\"odinger equation. The presence of the lattice potential allows the wavepacket's motion to be controlled by means of Floquet engineering. In particular, in the deep relativistic limit when the wavepacket's motion is photon-like, this form of control allows it to mimic both standard and negative refraction. Airy wavepackets held in lattice potentials can thus be used as powerful and flexible simulators of relativistic quantum systems.

Bloch oscillations in lattice potentials with controlled aperiodicity

We numerically investigate the damping of Bloch oscillations in a one-dimensional lattice potential whose translational symmetry is broken in a systematic manner, either by making the potential bichromatic or by introducing scatterers at distinct lattice sites. We find that the damping strongly depends on the ratio of lattice constants in the bichromatic potential and that even a small concentration of scatterers can lead to strong damping. Moreover, collisional interparticle interactions are able to counteract aperiodicity-induced damping of Bloch oscillations. The discussed effects should readily be observable for ultracold atoms in optical lattices.

Nonequilibrium dynamics of condensates in a lattice with the two-particle-irreducible effective action in the1∕Nexpansion

The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a case where the gas is strongly interacting. This is realized by an appropriate choice of the parameters in the Hamiltonian, and by starting with an initial state, where one lattice well contains a Bose-Einstein condensate while all other wells are empty. Oscillations of the condensate as well as noncondensate fractions of the gas between the different sites of the lattice are found to be damped as a consequence of the collisional interactions between the atoms. Functional integral techniques involving self-consistently determined mean fields as well as two-point correlation functions are used to derive the two-particle-irreducible (2PI) effective action. The action is expanded in inverse powers of the number of field components $\mathcal{N}$, and the dynamic equations are derived from it to next-to-leading order in this expansion. This approach reaches considerably beyond the Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the exact quantum dynamics obtained by Rey et al. [Phys. Rev. A 69, 033610 (2004)] for small atom numbers.