We study the dynamics of a one-dimensional spin-orbit coupled Schrodinger particle with two internal components moving in a random potential. We show that this model can be implemented by the interaction of cold atoms with external lasers and additio
nal Zeeman and Stark shifts. By direct numerical simulations a crossover from an exponential Anderson-type localization to an anomalous power-law behavior of the intensity correlation is found when the spin-orbit coupling becomes large. The power-law behavior is connected to a Dyson singularity in the density of states emerging at zero energy when the system approaches the quasi-relativistic limit of the random mass Dirac model. We discuss conditions under which the crossover is observable in an experiment with ultracold atoms and construct explicitly the zero-energy state, thus proving its existence under proper conditions.
We study the short-time evolution of the bipartite entanglement in quantum lattice systems with local interactions in terms of the purity of the reduced density matrix. A lower bound for the purity is derived in terms of the eigenvalue spread of the
interaction Hamiltonian between the partitions. Starting from an initially separable state the purity decreases as $1 - (t/tau)^2$, i.e. quadratically in time, with a characteristic time scale $tau$ that is inversly proportional to the boundary size of the subsystem, i.e., as an area-law. For larger times an exponential lower bound is derived corresponding to the well-known linear-in-time bound of the entanglement entropy. The validity of the derived lower bound is illustrated by comparison to the exact dynamics of a 1D spin lattice system as well as a pair of coupled spin ladders obtained from numerical simulations.
We describe a method to create effective gauge potentials for stationary-light polaritons in two or three spatial dimensions. When stationary light is created in the interaction with a uniformly rotating ensemble of coherently driven double $Lambda$
atoms, the equation of motion is that of a massive Schrodinger particle in an effective magnetic field. In addition a repulsive scalar potential emerges which can however be compensated by a space-dependent detuning. Since the effective interaction area for the polaritons can be made large, degenerate Landau levels can be created with degeneracy well above 100. This opens the possibility to study the bosonic analogue of the fractional quantum Hall effect for interacting stationary-light polaritons.
We present a general proof that Dirac particles cannot be localized below their Compton length by symmetric but otherwise arbitrary scalar potentials. This proof does not invoke the Heisenberg uncertainty relation and thus does not rely on the nonrel
ativistic linear momentum relation. Further it is argued that the result is also applicable for more general potentials, as e.g. generated by nonlinear interactions. Finally a possible realisation of such a system is proposed.
