arXiv subjects

D. J. Saunders

Publications and source records attributed to D. J. Saunders.

At least 19 recordsLinked to original sources

arXiv2022

Covariant derivatives for Ehresmann connections

We deal with the construction of covariant derivatives for some quite general Ehresmann connections on fibre bundles. We show how the introduction of a vertical endomorphism allows construction of covariant derivatives separately on both the vertical and horizontal distributions of the connection which can then be glued together on the total space. We give applications across an important class of tangent bundle cases, frame bundles and the Hopf bundle.

math.DG↗

arXiv2021

Linear connections and shape maps for second order ODEs with and without constraints

We deal with the construction of linear connections associated with second order ordinary differential equations with and without first order constraints. We use a novel method allowing glueing of submodule covariant derivatives to produce new, closed form expressions for the Massa-Pagani connection and our extension of it to the constrained case.

math.DG↗

arXiv2020

Preparing Narrow Velocity Distributions for Quantum Memories in Room-Temperature Alkali Vapours

Quantum memories are a crucial technology for enabling large-scale quantum networks through synchronisation of probabilistic operations. Such networks impose strict requirements on quantum memory, such as storage time, retrieval efficiency, bandwidth, and scalability. On- and off-resonant ladder protocols on warm atomic vapour platforms are promising candidates, combining efficient high-bandwidth operation with low-noise on-demand retrieval. However, their storage time is severely limited by motion-induced dephasing caused by the broad velocity distribution of atoms comprising the vapour. In this paper, we demonstrate velocity selective optical pumping to overcome this decoherence mechanism. This will increase the achievable memory storage time of vapour memories. This technique can also be used for preparing arbitrarily shaped absorption profiles, for instance, preparing an atomic frequency comb absorption feature.

quant-ph↗

arXiv2019

Unsupervised Machine Learning to Teach Fluid Dynamicists to Think in 15 Dimensions

An autoencoder is used to compress and then reconstruct three-dimensional stratified turbulence data in order to better understand fluid dynamics by studying the errors in the reconstruction. The original single data set is resolved on approximately $6.9\times10^{10}$ grid points, and 15 fluid variables in three spatial dimensions are used, for a total of about $10^{12}$ input quantities in three dimensions. The objective is to understand which of the input variables contains the most relevant information about the local turbulence regimes in stably stratified turbulence (SST). This is accomplished by observing flow features that appear in one input variable but then `bleed over' to multiple output variables. The bleed over is shown to be robust with respect to the number of layers in the autoencoder. In this proof of concept, the errors in the reconstruction include information about the spatial variation of vertical velocity in most of the components of the reconstructed rate-of-strain tensor and density gradient, which suggests that vertical velocity is an important marker for turbulence features of interest in SST. This result is consistent with what fluid dynamicists already understand about SST and, therefore, suggests an approach to understanding turbulence based on more detailed analyses of the reconstruction on errors in an autoencoding algorithm.

physics.flu-dyn↗

arXiv2019

Optimal Coherent Filtering for Single Noisy Photons

We introduce a filter using a noise-free quantum buffer with large optical bandwidth that can both filter temporal-spectral modes, as well as inter-convert them and change their frequency. We show that such quantum buffers optimally filter out temporal-spectral noise; producing identical single-photons from many distinguishable noisy single-photon sources with the minimum required reduction in brightness. We then experimentally demonstrate a noise-free quantum buffer in a warm atomic system that is well matched to quantum dots and can outperform all intensity (incoherent) filtering schemes for increasing indistinguishability.

quant-ph↗

arXiv2018

High-speed noise-free optical quantum memory

Quantum networks promise to revolutionise computing, simulation, and communication. Light is the ideal information carrier for quantum networks, as its properties are not degraded by noise in ambient conditions, and it can support large bandwidths enabling fast operations and a large information capacity. Quantum memories, devices that store, manipulate, and release on demand quantum light, have been identified as critical components of photonic quantum networks, because they facilitate scalability. However, any noise introduced by the memory can render the device classical by destroying the quantum character of the light. Here we introduce an intrinsically noise-free memory protocol based on two-photon off-resonant cascaded absorption (ORCA). We consequently demonstrate for the first time successful storage of GHz-bandwidth heralded single photons in a warm atomic vapour with no added noise; confirmed by the unaltered photon statistics upon recall. Our ORCA memory platform meets the stringent noise-requirements for quantum memories whilst offering technical simplicity and high-speed operation, and therefore is immediately applicable to low-latency quantum networks.

quant-ph↗

arXiv2017

High Efficiency Raman Memory by Suppressing Radiation Trapping

Raman interactions in alkali vapours are used in applications such as atomic clocks, optical signal processing, generation of squeezed light and Raman quantum memories for temporal multiplexing. To achieve a strong interaction the alkali ensemble needs both a large optical depth and a high level of spin-polarisation. We implement a technique known as quenching using a molecular buffer gas which allows near-perfect spin-polarisation of over $99.5\%$ in caesium vapour at high optical depths of up to $\sim 2 \times 10^5$; a factor of 4 higher than can be achieved without quenching. We use this system to explore efficient light storage with high gain in a GHz bandwidth Raman memory.

quant-ph↗

arXiv2016

In Situ Characterisation of an Optically Thick Atom-Filled Cavity

A means for precise experimental characterization of the dielectric susceptibility of an atomic gas inside and optical cavity is important for design and operation of quantum light matter interfaces, particularly in the context of quantum information processing. Here we present a numerically optimised theoretical model to predict the spectral response of an atom-filled cavity, accounting for both homogeneous and inhomogeneous broadening at high optical densities. We investigate the regime where the two broadening mechanisms are of similar magnitude, which makes the use of common approximations invalid. Our model agrees with an experimental implementation with warm caesium vapour in a ring cavity. From the cavity response, we are able to extract important experimental parameters, for instance the ground state populations, total number density and the magnitudes of both homogeneous and inhomogeneous broadening.

physics.atom-ph↗

arXiv2016

Theory of noise suppression in Λ-type quantum memories by means of a cavity

Quantum memories, capable of storing single photons or other quantum states of light, to be retrieved on-demand, offer a route to large-scale quantum information processing with light. A promising class of memories is based on far-off-resonant Raman absorption in ensembles of $Λ$-type atoms. However at room temperature these systems exhibit unwanted four-wave mixing, which is prohibitive for applications at the single-photon level. Here we show how this noise can be suppressed by placing the storage medium inside a moderate-finesse optical cavity, thereby removing the main roadblock hindering this approach to quantum memory.

quant-ph↗

arXiv2015

Tangent bundle geometry induced by second order partial differential equations

We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold of independent variables, together with a transverse local vector field. The resulting decomposition provides several natural curvature operators. The harmonic map equation is examined, and in this case both the 1-form and the vector field arise naturally.

math.DG↗

arXiv2015

Shape maps for second order partial differential equations

We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri's equation. We develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. Explicit computations are given, along with a nontrivial example.

math.DG↗

arXiv2015

A Cavity-Enhanced Room-Temperature Broadband Raman Memory

Broadband quantum memories hold great promise as multiplexing elements in future photonic quantum information protocols. Alkali vapour Raman memories combine high-bandwidth storage, on-demand read-out, and operation at room temperature without collisional fluorescence noise. However, previous implementations have required large control pulse energies and suffered from four-wave mixing noise. Here we present a Raman memory where the storage interaction is enhanced by a low-finesse birefringent cavity tuned into simultaneous resonance with the signal and control fields, dramatically reducing the energy required to drive the memory. By engineering anti-resonance for the anti-Stokes field, we also suppress the four-wave mixing noise and report the lowest unconditional noise floor yet achieved in a Raman-type warm vapour memory, $(15\pm2)\times10^{-3}$ photons per pulse, with a total efficiency of $(9.5\pm0.5)$%.

quant-ph↗

arXiv2015

Broadband, noise-free optical quantum memory with neutral nitrogen-vacancy centers in diamond

It is proposed that the ground-state manifold of the neutral nitrogen-vacancy center in diamond could be used as a quantum two-level system in a solid-state-based implementation of a broadband, noise-free quantum optical memory. The proposal is based on the same-spin $Λ$-type three-level system created between the two E orbital ground states and the A$_1$ orbital excited state of the center, and the cross-linear polarization selection rules obtained with the application of transverse electric field or uniaxial stress. Possible decay and decoherence mechanisms of this system are discussed, and it is shown that high-efficiency, noise-free storage of photons as short as a few tens of picoseconds for at least a few nanoseconds could be possible at low temperature.

quant-ph↗

arXiv2014

Interfacing GHz-bandwidth heralded single photons with a room-temperature Raman quantum memory

Photonics is a promising platform for quantum technologies. However, photon sources and two-photon gates currently only operate probabilistically. Large-scale photonic processing will therefore be impossible without a multiplexing strategy to actively select successful events. High time-bandwidth-product quantum memories - devices that store and retrieve single photons on-demand - provide an efficient remedy via active synchronisation. Here we interface a GHz-bandwidth heralded single-photon source and a room-temperature Raman memory with a time-bandwidth product exceeding 1000. We store heralded single photons and observe a clear influence of the input photon statistics on the retrieved light, which agrees with our theoretical model. The preservation of the stored field's statistics is limited by four-wave-mixing noise, which we identify as the key remaining challenge in the development of practical memories for scalable photonic information processing.

quant-ph↗

arXiv2013

Hilbert forms for a Finsler metrizable projective class of sprays

The projective Finsler metrizability problem deals with the question whether a projective-equivalence class of sprays is the geodesic class of a (locally or globally defined) Finsler function. In this paper we use Hilbert-type forms to state a number of different ways of specifying necessary and sufficient conditions for this to be the case, and we show that they are equivalent. We also address several related issues of interest including path spaces, Jacobi fields, totally-geodesic submanifolds of a spray space, and the equivalence of path geometries and projective-equivalence classes of sprays.

math.DG↗

arXiv2012

Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole

Demonstrating nonclassical effects over longer and longer distances is essential for both quantum technology and fundamental science. The main challenge is loss of photons during propagation, because considering only those cases where photons are detected opens a "detection loophole" in security whenever parties or devices are untrusted. Einstein-Podolsky-Rosen (EPR) steering is equivalent to an entanglement-verification task in which one party (device) is untrusted. We derive arbitrarily loss-tolerant tests, enabling us to perform a detection-loophole-free demonstration of EPR-steering with parties separated by a coiled 1 km optical fiber, with a total loss of 8.9 dB (87%).

quant-ph↗

arXiv2012

The multiplier approach to the projective Finsler metrizability problem

This paper is concerned with the problem of determining whether a projective-equivalence class of sprays is the geodesic class of a Finsler function. We address both the local and the global aspects of this problem. We present our results entirely in terms of a multiplier, that is, a type (0,2) tensor field along the tangent bundle projection. In the course of the analysis we consider several related issues of interest including the positivity and strong convexity of positively-homogeneous functions, the relation to the so-called Rapcsák conditions, some peculiarities of the two-dimensional case, and geodesic convexity for sprays.

math.DG↗

arXiv2011

Homogeneity and projective equivalence of differential equation fields

We propose definitions of homogeneity and projective equivalence for systems of ordinary differential equations of order greater than two, which allow us to generalize the concept of a spray (for systems of order two). We show that the Euler-Lagrange fields of parametric Lagrangians of order greater than one which are regular (in a natural sense that we define) form a projective equivalence class of homogeneous systems. We show further that the geodesics, or base integral curves, of projectively equivalent homogeneous differential equation fields are the same apart from orientation-preserving reparametrization; that is, homogeneous differential equation fields determine systems of paths.

math.DG↗