We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popovs hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is dete
rmined by saddle points of Popovs action, which, in particular, allows for weak solutions of the Gross-Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying {em within} the phonon part of the spectrum, contrary to traditional view.
We study the transport of ultracold impurity atoms immersed in a Bose-Einstein condensate (BEC) and trapped in a tight optical lattice. Within the strong-coupling regime, we derive an extended Hubbard model describing the dynamics of the impurities i
n terms of polarons, i.e. impurities dressed by a coherent state of Bogoliubov phonons. Using a generalized master equation based on this microscopic model we show that inelastic and dissipative phonon scattering results in (i) a crossover from coherent to incoherent transport of impurities with increasing BEC temperature and (ii) the emergence of a net atomic current across a tilted optical lattice. The dependence of the atomic current on the lattice tilt changes from ohmic conductance to negative differential conductance within an experimentally accessible parameter regime. This transition is accurately described by an Esaki-Tsu-type relation with the effective relaxation time of the impurities as a temperature-dependent parameter.
We investigate the influence of noise on a graph state generation scheme which exploits a mirror inverting spin chain. Within this scheme the spin chain is used repeatedly as an entanglement bus (EB) to create multi-partite entanglement. The noise mo
del we consider comprises of each spin of this EB being exposed to independent local noise which degrades the capabilities of the EB. Here we concentrate on quantifying its performance as a single-qubit channel and as a mediator of a two-qubit entangling gate, since these are basic operations necessary for graph state generation using the EB. In particular, for the single-qubit case we numerically calculate the average channel fidelity and whether the channel becomes entanglement breaking, i.e., expunges any entanglement the transferred qubit may have with other external qubits. We find that neither local decay nor dephasing noise cause entanglement breaking. This is in contrast to local thermal and depolarizing noise where we determine a critical length and critical noise coupling, respectively, at which entanglement breaking occurs. The critical noise coupling for local depolarizing noise is found to exhibit a power-law dependence on the chain length. For two qubits we similarly compute the average gate fidelity and whether the ability for this gate to create entanglement is maintained. The concatenation of these noisy gates for the construction of a five qubit linear cluster state and a Greenberger-Horne-Zeilinger state indicates that the level of noise that can be tolerated for graph state generation is tightly constrained.
