arXiv subjects

Sophie S. Shamailov

Publications and source records attributed to Sophie S. Shamailov.

7 recordsLinked to original sources

arXiv2026

Quantum and classical noise characteristics of parametrically driven cavity solitons in dispersive Kerr resonators

Temporal cavity solitons generated in monochromatically driven dispersive Kerr resonators offer an attractive avenue for on-chip optical frequency comb generation. Key to many of their applications is to understand how noise -- both technical and quantum -- affects the soliton states, which has accordingly been extensively investigated. Here, we report on a comprehensive theoretical study that elucidates how technical and quantum fluctuations impact a new type of soliton structure that has very recently been predicted and observed in dispersive Kerr resonators under conditions of bichromatic driving: the pure-Kerr parametrically driven cavity soliton (PDCS). We examine how classical laser phase noise transfers from the two pump fields onto the soliton frequency comb, and we calculate the solitons' fundamental quantum-limited timing jitter and two-mode squeezing spectra. In each case, we find that PDCSs can out-perform conventional cavity solitons with comparable characteristics, even when driven by two uncorrelated lasers. Our results demonstrate that pure-Kerr PDCSs can offer unprecedented performance in noise-sensitive photonic applications and as a quantum resource

physics.optics↗

arXiv2021

Comment on "Observation of two-dimensional Anderson localisation of ultracold atoms"

Here I provide additional experimental information and criticise the analysis, modelling, interpretation and claims presented in the recent paper [Nature Communications 11, 4942 (2020)]. I argue that the authors have no clear experimental evidence of Anderson localisation (as they claim) and their numerical simulations are very far indeed from reproducing the experiment, as stated in their article. Furthermore, some effects that are ascribed to real physical mechanisms are revealed to be simply artefacts.

cond-mat.quant-gas↗

arXiv2021

Anderson localisation in two dimensions: insights from Localisation Landscape Theory, exact diagonalisation, and time-dependent simulations

Motivated by experimental progress in cold atomic systems, we use and advance Localisation Landscape Theory (LLT), to examine two-dimensional systems with point-like random scatterers. We begin by showing that exact eigenstates cannot be efficiently used to extract the localisation length. We then provide a comprehensive review of known LLT, and confirm that the Hamiltonian with the effective potential of LLT has very similar low energy eigenstates to that with the physical potential. Next, we use LLT to compute the localisation length for very low-energy, maximally localised eigenstates and test our method against exact diagonalisation. Furthermore, we propose a transmission experiment that optimally detects Anderson localisation, and demonstrate how one may extract a length scale which is correlated with (and in general smaller than) the localisation length. In addition, we study the dimensional crossover from one to two dimensions, providing a new explanation to the established trends. The prediction of a mobility edge coming from LLT is tested by direct Schrödinger time evolution and is found to be unphysical. Moreover, we investigate expanding wavepackets, to find that these can be useful in detecting and quantifying Anderson localisation in a transmission experiment, with the only disadvantage being the inability to resolve the energy dependence of the localisation length. Then, we utilise LLT to uncover a connection between the Anderson model for discrete disordered lattices and continuous two-dimensional disordered systems, which provides powerful new insights. From here, we demonstrate that localisation can be distinguished from other effects by a comparison to dynamics in an ordered potential with all other properties unchanged. Finally, we thoroughly investigate the effect of acceleration and repulsive interparticle interactions, as relevant for current experiments.

cond-mat.quant-gas↗

arXiv2021

Computing the eigenstate localisation length at very low energies from Localisation Landscape Theory

While Anderson localisation is largely well-understood, its description has traditionally been rather cumbersome. A recently-developed theory -- Localisation Landscape Theory (LLT) -- has unparalleled strengths and advantages, both computational and conceptual, over alternative methods. To begin with, we demonstrate that the localisation length cannot be conveniently computed starting directly from the exact eigenstates, thus motivating the need for the LLT approach. Then, we confirm that the Hamiltonian with the effective potential of LLT has very similar low energy eigenstates to that with the physical potential, justifying the crucial role the effective potential plays in our new method. We proceed to use LLT to calculate the localisation length for very low-energy, maximally localised eigenstates, as defined by the length-scale of exponential decay of the eigenstates, (manually) testing our findings against exact diagonalisation. We then describe several mechanisms by which the eigenstates spread out at higher energies where the tunnelling-in-the-effective-potential picture breaks down, and explicitly demonstrate that our method is no longer applicable in this regime. We place our computational scheme in context by explaining the connection to the more general problem of multidimensional tunnelling and discussing the approximations involved. Our method of calculating the localisation length can be applied to (nearly) arbitrary disordered, continuous potentials at very low energies.

cond-mat.dis-nn↗

arXiv2019

Quantum dark solitons in the one-dimensional Bose gas

Dark and grey soliton-like states are shown to emerge from numerically constructed superpositions of translationally-invariant eigenstates of the interacting Bose gas in a toroidal trap. The exact quantum many-body dynamics reveals a density depression with superdiffusive spreading that is absent in the mean-field treatment of solitons. A simple theory based on finite-size bound states of holes with quantum-mechanical center-of-mass motion quantitatively explains the time-evolution of the superposition states and predicts quantum effects that could be observed in ultra-cold gas experiments. The soliton phase step is shown to be a key ingredient of an accurate finite size approximation, which enables us to compare the theory with numerical simulations. The fundamental soliton width, an invariant property of the quantum dark soliton, is shown to deviate from the Gross-Pitaevskii predictions in the interacting regime and vanishes in the Tonks-Girardeau limit.

cond-mat.quant-gas↗

arXiv2018

Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves

Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.

cond-mat.quant-gas↗

arXiv2017

Dark-soliton-like excitations in the Yang-Gaudin gas of attractively interacting fermions

Yrast states are the lowest energy states at given non-zero momentum and provide a natural extension of the concept of dark solitons to strongly-interacting one-dimensional quantum gases. Here we study the yrast states of the balanced spin-$\frac{1}{2}$ Fermi gas with attractive delta-function interactions in one dimension with the exactly solvable Yang-Gaudin model. The corresponding Bethe-ansatz equations are solved for finite particle number and in the thermodynamic limit. Properties corresponding to the soliton-like nature of the yrast excitations are calculated including the missing particle number, phase step, and inertial and physical masses. The inertial to physical mass ratio, which is related to the frequency of oscillations in a trapped gas, is found to be unity in the limits of strong and weak attraction and falls to $\approx 0.78$ in the crossover regime. This result is contrasted by one-dimensional mean field theory, which predicts a divergent mass ratio in the weakly attractive limit. By means of an exact mapping our results also predict the existence and properties of dark-soliton-like excitations in the super Tonks-Girardeau gas. The prospects for experimental observations are briefly discussed.

cond-mat.quant-gas↗