arXiv subjects

David A. W. Hutchinson

Publications and source records attributed to David A. W. Hutchinson.

13 recordsLinked to original sources

arXiv2023

Signatures of superradiance as a witness to multipartite entanglement

Generation and detection of entanglement is at the forefront of most quantum information technologies. There is a plethora of techniques that reveal entanglement on the basis of only partial information about the underlying quantum state, including entanglement witnesses. Superradiance refers to the phenomenon of highly synchronized photon emission from an ensemble of quantum emitters that is caused by correlations among the individual particles and has been connected by Dicke himself to the presence of multipartite entangled states. We investigate this connection in a quantitative way and discuss, whether or not signatures of superradiance from semiconductor nanolasers, manifesting themselves as a modification of the spontaneous-emission time, can be interpreted as a witness to detect entanglement in the underlying state of the emitters.

quant-ph↗

arXiv2023

Momentum-space signatures of the Anderson transition in a symplectic, two-dimensional, disordered ultracold gas

We study Anderson Localization in two dimensional (2D) disordered spin-orbit systems described by the Gaussian symplectic ensemble using momentum-space signatures such as the coherent backscattering (CBS) anti-peak, and the coherent forward scattering (CFS) peak. Significantly, these momentum-space features are readily accessible in ultracold atom experiments through absorption imaging after time-of-flight expansion. The critical exponent and mobility edge of the metal-insulator transition are successfully obtained in this model through a finite-time analysis of the CBS width. An anomalous residual diffusion, unique to 2D, is identified at the transition point where the system changes from a metal to an insulator. A spin localization phenomenon is also observed in the deep localized regime.

cond-mat.dis-nn↗

arXiv2022

Improving quantum annealing by engineering the coupling to the environment

A large class of optimisation problems can be mapped to the Ising model where all details are encoded in the coupling of spins. The task of the original mathematical optimisation is then equivalent to finding the ground state of the corresponding spin system which can be achieved via quantum annealing relying on the adiabatic theorem. Some of the inherent disadvantages of this procedure can be alleviated or resolved using a stochastic approach, and by coupling to the external environment. We show that careful engineering of the system-bath coupling at an individual spin level can further improve annealing.

quant-ph↗

arXiv2021

Effects of disorder upon transport and Anderson Localization in a finite, two dimensional Bose gas

Anderson localization in a two-dimensional ultracold Bose-gas has been demonstrated experimentally. Atoms were released within a dumbbell-shaped optical trap, where the channel of variable aspect ratio provided the only path for particles to travel between source and drain reservoirs. This channel can be populated with columnar (repulsive) optical potential spikes of square cross section with arbitrary pattern. These spikes constitute impurities, the scattering centres for the otherwise free propagation of the particles. This geometry does not allow for classical potential trapping which can be hard to exclude in other experimental setups. Here we add further theoretical evidence for Anderson localization in this system by comparing the transport processes within a regular and a random pattern of impurities. It is demonstrated that the transport within randomly distributed impurities is suppressed and the corresponding localization length becomes shorter than the channel length. However, if an equal density of impurities are distributed in a regular manner, the transport is only modestly disturbed. This observation corroborates the conclusions of the experimental observation: the localization is indeed attributed to the disorder. Beyond analysing the density distribution and the localization length, we also calculate a quantum `impedance' exhibiting qualitatively different behaviour for regular and random impurity patterns.

cond-mat.quant-gas↗

arXiv2020

Observation of two-dimensional Anderson localisation of ultracold atoms

Anderson localisation -- the inhibition of wave propagation in disordered media -- is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased. Here we report the results of an experiment measuring the 2D transport of ultracold atoms between two reservoirs, which are connected by a channel containing pointlike disorder. The design overcomes many of the technical challenges that have hampered observation of localisation in previous works. We experimentally observe exponential localisation in a 2D ultracold atom system.

cond-mat.quant-gas↗

arXiv2019

Environment mediated multipartite and multidimensional entanglement

Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.

cond-mat.quant-gas↗

arXiv2019

Peculiarities in the gravitational field of a filamentary ring

The gravitational field of a massive, filamentary ring is considered. We provide an analytic expression for the gravitational potential and demonstrate that the exact gravitational potential and its gradient, thus the gravitational force-field, is not central. Hence it is a good candidate to discuss the difference between the concepts of center of mass and center of gravity. We focus on other consequences of reduced symmetry, e.g., only the $z$-component of the angular momentum is conserved. However, the remnant high symmetry of this system also ensures that there are special classes of motions which are restricted to invariant subspaces, thus, depending on the initial condition, the dynamics of a point particle is integrable. We also show that periodic orbits in the equatorial plane external to the ring are possible, but only if the angular momentum is above a threshold value. In this case the orbits are stable.

cond-mat.soft↗

arXiv2014

A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms

Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.

quant-ph↗

arXiv2011

Rotons in interacting ultracold Bose gases

In three dimensions, non-interacting bosons undergo Bose-Einstein condensation at a critical temperature, $T_{c}$, which is slightly shifted by $ΔT_{\mathrm{c}}$, if the particles interact. We calculate the excitation spectrum of interacting Bose-systems, \sup{4}He and \sup{87}Rb, and show that a roton minimum emerges in the spectrum above a threshold value of the gas parameter. We provide a general theoretical argument for why the roton minimum and the maximal upward critical temperature shift are related. We also suggest two experimental avenues to observe rotons in condensates. These results, based upon a Path-Integral Monte-Carlo approach, provide a microscopic explanation of the shift in the critical temperature and also show that a roton minimum does emerge in the excitation spectrum of particles with a structureless, short-range, two-body interaction.

cond-mat.quant-gas↗

arXiv2011

Physics of the Riemann Hypothesis

Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here we choose a particular number theoretical function, the Riemann zeta function and examine its influence in the realm of physics and also how physics may be suggestive for the resolution of one of mathematics' most famous unconfirmed conjectures, the Riemann Hypothesis. Does physics hold an essential key to the solution for this more than hundred-year-old problem? In this work we examine numerous models from different branches of physics, from classical mechanics to statistical physics, where this function plays an integral role. We also see how this function is related to quantum chaos and how its pole-structure encodes when particles can undergo Bose-Einstein condensation at low temperature. Throughout these examinations we highlight how physics can perhaps shed light on the Riemann Hypothesis. Naturally, our aim could not be to be comprehensive, rather we focus on the major models and aim to give an informed starting point for the interested Reader.

math-ph↗

arXiv2009

Geometric scaling in the spectrum of an electron captured by a stationary finite dipole

We examine the energy spectrum of a charged particle in the presence of a {\it non-rotating} finite electric dipole. For {\emph{any}} value of the dipole moment $p$ above a certain critical value p_{\mathrm{c}}$ an infinite series of bound states arises of which the energy eigenvalues obey an Efimov-like geometric scaling law with an accumulation point at zero energy. These properties are largely destroyed in a realistic situation when rotations are included. Nevertheless, our analysis of the idealised case is of interest because it may possibly be realised using quantum dots as artificial atoms.

cond-mat.other↗

arXiv2008

Quantum mechanical potentials related to the prime numbers and Riemann zeros

Prime numbers are the building blocks of our arithmetic, however, their distribution still poses fundamental questions. Bernhard Riemann showed that the distribution of primes could be given explicitly if one knew the distribution of the non-trivial zeros of the Riemann $ζ(s)$ function. According to the Hilbert-P{ó}lya conjecture there exists a Hermitean operator of which the eigenvalues coincide with the real part of the non-trivial zeros of $ζ(s)$. This idea encourages physicists to examine the properties of such possible operators, and they have found interesting connections between the distribution of zeros and the distribution of energy eigenvalues of quantum systems. We apply the Mar{č}henko approach to construct potentials with energy eigenvalues equal to the prime numbers and to the zeros of the $ζ(s)$ function. We demonstrate the multifractal nature of these potentials by measuring the R{é}nyi dimension of their graphs. Our results offer hope for further analytical progress.

math-ph↗

arXiv2006

Thermodynamically activated vortex-dipole formation in a two-dimensional Bose-Einstein condensate

Three distinct types of behaviour have recently been identified in the two-dimensional trapped bosonic gas, namely; a phase coherent Bose-Einstein condensate (BEC), a Berezinskii-Kosterlitz-Thouless-type (BKT) superfluid and normal gas phases in order of increasing temperature. In the BKT phase the system favours the formation of vortex-antivortex pairs, since the free energy is lowered by this topological defect. We provide a simple estimate of the free energy of a dilute Bose gas with and without such vortex dipole excitations and show how this varies with particle number and temperature. In this way we can estimate the temperature for cross-over from the coherent BEC to the (only) locally ordered BKT-like phase by identifying when vortex dipole excitations proliferate. Our results are in qualitative agreement with recent, numerically intensive, classical field simulations.

cond-mat.stat-mech↗