Several recent studies have investigated the dynamics of cold atoms in optical lattices subject to AC forcing; the theoretically predicted renormalization of the tunneling amplitudes has been verified experimentally. Recent observations include globa
l motion of the atom cloud, such as giant Super-Bloch Oscillations (SBOs). We show that, in order to understand unexplained features of SBOs, in addition to the renormalization of the tunneling, a new and important phase correction must be included. For Fermionic systems with strong attractive interactions, one may engineer different types of collisions and recollisions between bound-pairs and unpaired atoms.
Numerous theoretical and experimental studies have investigated the dynamics of cold atoms subjected to time periodic fields. Novel effects dependent on the amplitude and frequency of the driving field, such as Coherent Destruction of Tunneling have
been identified and observed. However, in the last year or so, three distinct types of experiments have demonstrated for the first time, interesting behaviour associated with the driving phase: i.e. for systems experiencing a driving field of general form $V(x)sin (omega t + phi)$, different types of large scale oscillations and directed motion were observed. We investigate and explain the phenomenon of Super-Bloch Oscillations (SBOs) in relation to the other experiments and address the role of initial phase in general. We analyse and compare the role of $phi$ in systems with homogeneous forces ($V(x)= const$), such as cold atoms in shaken or amplitude-modulated optical lattices, as well as non-homogeneous forces ($V(x) eq const$), such as the sloshing of atoms in driven traps, and clarify the physical origin of the different $phi$-dependent effects.
We investigate the effect of periodic driving by an external field on systems with attractive pairing interactions. These include spin systems (like the ferromagnetic XXZ model) as well as ultracold fermionic atoms described by the attractive Hubbard
model. We show that a well-known phenomenon seen in periodically driven systems--the renormalization of the exchange coupling strength--acts selectively on bound-pairs of spins/atoms, relative to magnon/bare atom states. Thus one can control the direction and speed of transport of bound-pair relative to magnon/unpaired atom states, and thus coherently achieve spatial separation of these components. Applications to recent experiments on transport with fermionic atoms in optical lattices which consist of mixtures of bound-pairs and bare atoms are discussed.
We investigate for quantum dynamics in phase-space regions containing ``shearless tori. We show that the properties of these peculiar classical phase-space structures -- important to the dynamics of tokamaks -- may be exploited for quantum informatio
n applications. In particular we show that shearless tori permit the non-dispersive transmission of localized wavepackets. The quantum many-body Hamiltonian of a Heisenberg ferromagnetic spin chain, subjected to an oscillating magnetic field, can be reduced to a classical one-body ``image dynamical system which is the well-studied Harper map. The Harper map belongs to a class of Hamiltonian systems (non-twist maps) which contain shearless tori. We show that a variant with sinusoidal time driving ``driven Harper model produces shearless tori which are especially suitable for quantum state transfer. The behavior of the concurrence is investigated as an example.
