We study the dynamics of a soliton-impurity system modeled in terms of a binary Bose-Einstein condensate. This is achieved by `switching off one of the two self-interaction scattering lengths, giving a two component system where the second component
is trapped entirely by the presence of the first component. It is shown that this system possesses rich dynamics, including the identification of unusual `weak dimers that appear close to the zero inter-component scattering length. It is further found that this system supports quasi-stable trimers in regimes where the equivalent single-component gas does not, which is attributed to the presence of the impurity atoms which can dynamically tunnel between the solitons, and maintain the required phase differences that support the trimer state.
Deterministically aperiodic sequences are an intermediary between periodic sequences and completely random sequences. Materials which are translationally periodic have Bloch-like extended states, while random media exhibit Anderson localisation. Mate
rials constructed on the basis of deterministic aperiodic sequences such as Fibonacci, Thue-Morse, and Rudin-Shapiro exhibit different properties, which can be related to their spectrum. Here, by investigating the dynamics of discrete-time quantum walks using different aperiodic sequences of coin operations in position space and time we establish the role of the diffraction spectra in characterizing the spreading of the wavepacket.
Vortex lattices in rapidly rotating Bose-Einstein condensates lead to a periodic modulation of the superfluid density with a triangular symmetry. Here we show that this symmetry can be combined with an external perturbation in order to create super-l
attice structures with two or more periodicities. Considering a condensate which is kicked by an optical lattice potential, we find the appearance of transient moire lattice structures, which can be identified using the kinetic energy spectrum.
The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two regions with
different topological numbers, can, for example, be effectively modelled using different coin parameters for the walk on either side of the interface. Depending on the neighbouring numbers, this can lead to localized states in one-dimensional configurations and here we carry out a detailed study into the strength of such localized states. We show that it can be related to the amount of entanglement created by the walks, with minima appearing for strong localizations. This feature also persists in the presence of small amounts of $sigma_x$ (bit flip) noise.
Optical detection of structures with dimensions smaller than an optical wavelength requires devices that work on scales beyond the diffraction limit. Here we present the possibility of using a tapered optical nanofiber as a detector to resolve indivi
dual atoms trapped in an optical lattice in the Mott Insulator phase. We show that the small size of the fiber combined with an enhanced photon collection rate can allow for the attainment of large and reliable measurement signals.
Adiabatic radio frequency (RF) potentials are powerful tools for creating advanced trapping geometries for ultra-cold atoms. While the basic theory of RF trapping is well understood, studies of more complicated setups involving multiple resonant freq
uencies in the limit where their effects cannot be treated independently are rare. Here we present an approach based on Floquet theory and show that it offers significant corrections to existing models when two RF frequencies are near degenerate. Furthermore it has no restrictions on the dimension, the number of frequencies or the orientation of the RF fields. We show that the added degrees of freedom can, for example, be used to create a potential that allows for easy creation of ring vortex solitons.
Photons in optical networks can be used in multi-path interferometry and various quantum information processing and communication protocols. Large networks, however, are often not free from defects, which can appear randomly between the lattice sites
and are caused either by production faults or deliberate introduction. In this work we present numerical simulations of the behaviour of a single photon injected into a regular lattice of beam-splitting components in the presence of defects that cause perfect backward reflections. We find that the photon dynamics is quickly dominated by the backscattering processes, and a small fraction of reflectors in the paths of the beam-splitting array strongly affects the percolation probability of the photon. We carefully examine such systems and show an interesting interplay between the probabilities of percolation, backscattering and temporary localization. We also discuss the sensitivity of these probabilities to lattice size, timescale, injection point, fraction of reflectors and boundary conditions.
A universal definition of non-Markovianity for open systems dynamics is proposed. It is extended from the classical definition to the quantum realm by showing that a `transition from the Markov to the non-Markov regime occurs when the correlations be
tween the system and the environment, generated by their joint evolution, can no longer be neglected. The suggested definition is based on the comparison between measured correlation functions and those built by assuming that the system is in a Markov regime thus giving a figure of merit of the error coming from this assumption. It is shown that the knowledge of the dynamical map and initial condition of the system is not enough to fully characterise the non-Markovian dynamics of the reduced system. The example of three exactly solvable models, i.e. decoherence and spontaneous emission of the qubit in a bosonic bath and decoherence of the photons polarization induced by interaction with its spacial degrees of freedom, reveals that previously proposed Markovianity criteria and measures which are based on dynamical map analysis fail to recognise non-Markov behaviour.
We examine the stability and dynamics of a family of crossed dark solitons in a harmonically confined Bose-Einstein condensate in two dimensions. Working in a regime where the fundamental snake instability is suppressed, we show the existence of an i
nstability which leads to an interesting collapse and revival of the initial state for the fundamental case of two crossed solitons. The instability originates from the singular point where the solitons cross, and we characterise it by examining the Bogoliubov spectrum. Finally, we extend the treatment to systems of higher symmetry.
We investigate trapping geometries for cold, neutral atoms that can be created in the evanescent field of a tapered optical fibre by combining the fundamental mode with one of the next lowest possible modes, namely the HE21 mode. Counter propagating
red-detuned HE21 modes are combined with a blue-detuned HE11 fundamental mode to form a potential in the shape of four intertwined spirals. By changing the polar- ization from circular to linear in each of the two counter-propagating HE21 modes simultaneously the 4-helix configuration can be transformed into a lattice configuration. The modification to the 4-helix configuration due to unwanted excitation of the the T E01 and T M01 modes is also discussed.
