arXiv subjects

Simon A. Gardiner

Publications and source records attributed to Simon A. Gardiner.

At least 19 recordsLinked to original sources

arXiv2025

Thermometry of simulated Bose--Einstein condensates using machine learning

Precise determination of thermodynamic parameters in ultracold Bose gases remains challenging due to the destructive nature of conventional measurement techniques and inherent experimental uncertainties. We demonstrate a machine learning approach for rapid, non-destructive estimation of the chemical potential and temperature from a single image of an \emph{in situ} imaged density profiles of finite-temperature Bose gases. Our convolutional neural network is trained exclusively on quasi-2D `pancake' condensates in harmonic trap configurations. It achieves parameter extraction within fractions of a second. The model also demonstrates {some} zero-shot generalisation across both trap geometry and thermalisation dynamics, successfully estimating the temperature (although not the chemical potential) for toroidally trapped condensates with errors of only a few nanokelvin despite no prior exposure to such geometries during training, and maintaining predictive accuracy during dynamic thermalisation processes after a relatively brief evolution without explicit training on non-equilibrium states. These results suggest that supervised learning can overcome traditional limitations in ultracold atom thermometry, with extension to broader geometric configurations, temperature ranges, and additional parameters potentially enabling comprehensive real-time analysis of quantum gas experiments. Such capabilities could significantly streamline experimental workflows whilst improving measurement precision across a range of quantum fluid systems.

cond-mat.quant-gas↗

arXiv2024

Solving physics-based initial value problems with unsupervised machine learning

Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach to solve physics-based initial value problems using unsupervised machine learning. We propose a deep learning framework that models the dynamics of a variety of mechanical systems through neural networks. Our framework is flexible, allowing us to solve non-linear, coupled, and chaotic dynamical systems. We demonstrate the effectiveness of our approach on systems including a free particle, a particle in a gravitational field, a classical pendulum, and the Hénon--Heiles system (a pair of coupled harmonic oscillators with a non-linear perturbation, used in celestial mechanics). Our results show that deep neural networks can successfully approximate solutions to these problems, producing trajectories which conserve physical properties such as energy and those with stationary action. We note that probabilistic activation functions, as defined in this paper, are required to learn any solutions of initial value problems in their strictest sense, and we introduce coupled neural networks to learn solutions of coupled systems.

physics.comp-ph↗

arXiv2021

Soliton interferometry with very narrow barriers obtained from spatially dependent dressed states

Bright solitons in atomic Bose--Einstein condensates are strong candidates for high precision matter-wave interferometry, as their inherent stability against dispersion supports long interrogation times. An analog to a beam splitter is then a narrow potential barrier. A very narrow barrier is desirable for interferometric purposes, but in a typical realisation using a blue-detuned optical dipole potential, the width is limited by the laser wavelength. We investigate a soliton interferometry scheme using the geometric scalar potential experienced by atoms in a spatially dependent dark state to overcome this limit. We propose a possible implementation and numerically probe the effects of deviations from the ideal configuration.

cond-mat.quant-gas↗

arXiv2021

Collective effects in the photon statistics of thermal atomic ensembles

We investigate the collective scattering of coherent light from a thermal alkali-metal vapor with temperatures ranging from 350 to 450 K, corresponding to average atomic spacings between $0.7 λ$ and $0.1 λ$. We develop a theoretical model treating the atomic ensemble as coherent, interacting, radiating dipoles. We show that the two-time second-order correlation function of a thermal ensemble can be described by an average of randomly positioned atomic pairs. Our model illustrates good agreement with the experimental results. Furthermore, we show how fine-tuning of the experimental parameters may make it possible to explore several photon statistics regimes.

quant-ph↗

arXiv2020

Splitting of two-component solitary waves from collisions with narrow potential barriers

We consider the interaction of two-component bright-bright solitons with a narrow potential barrier (splitter) in the framework of a system of two Gross-Pitaevskii (nonlinear-Schrödinger) equations modeling a binary Bose-Einstein condensate, with self-attraction in each component and cross-attraction between them. The objective is to study splitting of composite solitons, which may be used in the design of two-component soliton-interferometer schemes. We produce approximate analytic results, assuming a weak barrier and applying the perturbation theory in the limit in which the system is integrable and the solitary waves may be considered as exact solitons. We do this in the case of negligible interspecies interactions, and also when the nonlinearities are strongly asymmetric, allowing one to neglect the self-interaction in one of the species. Then, we use systematic simulations to study the transmissions of both components in regions outside these approximations and, in particular, to compare numerical results with their analytical countertparts. We concluded that there is an appreciable parameter range where one component is almost entirely transmitted through the barrier, while the other one is reflected. Excitation of internal vibrations in the passing and rebounding solitons is explored too, with a conclusion that it is weak in the regime of high-quality splitting.

nlin.PS↗

arXiv2020

Spin-orbit coupling in the presence of strong atomic correlations

We explore the influence of contact interactions on a synthetically spin-orbit coupled system of two ultracold trapped atoms. Even though the system we consider is bosonic, we show that a regime exists in which the competition between the contact and spin-orbit interactions results in the emergence of a ground state that contains a significant contribution from the anti-symmetric spin state. This ground state is unique to few-particle systems and does not exist in the mean-field regime. The transition to this state is signalled by an inversion in the average momentum from being dominated by centre-of-mass momentum to relative momentum and also affects the global entanglement shared between the real- and pseudo-spin spaces. Indeed, competition between the interactions can also result in avoided crossings in the groundstate which further enhances these correlations. However, we find that correlations shared between the pseudo-spin states are strongly depressed due to the spin-orbit coupling and therefore the system does not contain spin-spin entanglement.

cond-mat.quant-gas↗

arXiv2020

Quantum and Nonlinear Effects in Light Transmitted through Planar Atomic Arrays

We identify significant quantum many-body effects, robust to position fluctuations and strong dipole--dipole interactions, in the forward light scattering from planar arrays and uniform-density disks of cold atoms, by comparing stochastic electrodynamics simulations of a quantum master equation and of a semiclassical model that neglects quantum fluctuations. Quantum effects are pronounced at high atomic densities, light close to saturation intensity, and around subradiant resonances. We show that such conditions also maximize spin--spin correlations and entanglement of formation for the atoms, revealing the microscopic origin of light-induced quantum effects. In several regimes of interest, an enhanced semiclassical model with a single-atom quantum description reproduces light transmission remarkably well, and permits analysis of otherwise numerically inaccessible large ensembles, in which we observe collective many-body analogues of resonance power broadening, vacuum Rabi splitting, and significant suppression in cooperative reflection from atomic arrays.

quant-ph↗

arXiv2019

Splitting and recombination of bright-solitary-matter waves

Solitons are long-lived wavepackets that propagate without dispersion and exist in a wide range of one-dimensional (1D) nonlinear systems. A Bose-Einstein condensate trapped in a quasi-1D waveguide can support bright-solitary-matter waves (3D analogues of solitons) when interatomic interactions are sufficiently attractive that they cancel dispersion. Solitary-matter waves are excellent candidates for a new generation of highly sensitive interferometers, as their non-dispersive nature allows them to acquire phase shifts for longer times than conventional matter-waves interferometers. However, such an interferometer is yet to be realised experimentally. In this work, we demonstrate the splitting and recombination of a bright-solitary-matter wave on a narrow repulsive barrier, which brings together the fundamental components of an interferometer. We show that both interference-mediated recombination and classical velocity filtering effects are important, but for a sufficiently narrow barrier interference-mediated recombination can dominate. We reveal the extreme sensitivity of interference-mediated recombination to the experimental parameters, highlighting the potential of soliton interferometry.

cond-mat.quant-gas↗

arXiv2019

Lattice-depth measurement using continuous grating atom diffraction

We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, which leads to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a simplified model yielding an analytic formula describing such oscillations for a gas assumed to be at zero temperature. This model is extended to include atoms with initial momenta detuned from our chosen initial value, before analyzing the full finite-temperature response of the system. Finally we present a steady-state solution to the finite-temperature system, which in principle makes possible the measurement of both the lattice depth, and initial temperature of the atomic gas simultaneously.

quant-ph↗

arXiv2018

Lattice-depth measurement using multi-pulse atom diffraction in and beyond the weakly diffracting limit

Precise knowledge of optical lattice depths is important for a number of areas of atomic physics, most notably in quantum simulation, atom interferometry and for the accurate determination of transition matrix elements. In such experiments, lattice depths are often measured by exposing an ultracold atomic gas to a series of off-resonant laser-standing-wave pulses, and fitting theoretical predictions for the fraction of atoms found in each of the allowed momentum states by time of flight measurement, after some number of pulses. We present a full analytic model for the time evolution of the atomic populations of the lowest momentum-states, which is sufficient for a "weak" lattice, as well as numerical simulations incorporating higher momentum states for both relatively strong and weak lattices. Finally, we consider the situation where the initial gas is explicitly assumed to be at a finite temperature.

quant-ph↗

arXiv2017

Spin-orbit coupled interferometry with ring-trapped Bose--Einstein condensates

We propose a method of atom-interferometry using a spinor Bose-Einstein condensate (BEC) with a time-varying magnetic field acting as a coherent beam-splitter. Our protocol creates long-lived superpositional counterflow states, which are of fundamental interest and can be made sensitive to both the Sagnac effect and magnetic fields on the sub-micro-G scale. We split a ring-trapped condensate, initially in the $m_f=0$ hyperfine state, into superpositions of internal $m_f=\pm1$ states and condensate superflow, which are spin-orbit coupled. After interrogation, relative phase accumulation can be inferred from a population transfer to the $m_f=\pm1$ states. The counterflow generation protocol is adiabatically deterministic and does not rely on coupling to additional optical fields or mechanical stirring techniques. Our protocol can maximise the classical Fisher information for any rotation, magnetic field, or interrigation time, and so has the maximum sensitivity available to uncorrelated particles. Precision can increase with the interrogation time, and so is limited only by the lifetime of the condensate.

cond-mat.quant-gas↗

arXiv2017

Resonant transfer of large momenta from finite duration pulse sequences

We experimentally investigate the atom optics kicked particle at quantum resonance using finite duration kicks. Even though the underlying process is quantum interference it can be well described by an $ε$-pseudoclassical model. The $ε$-pseudoclassical model agrees well with our experiments for a wide range of parameters. We investigate the parameters yielding maximal momentum transfer to the atoms and find that this occurs in the regime where neither the short pulse approximation nor the Bragg condition is valid. Nonetheless, the momentum transferred to the atoms can be predicted using a simple scaling law, which provides a powerful tool for choosing optimal experimental parameters. We demonstrate this in a measurement of the Talbot time (from which $h/M$ can be deduced), in which we coherently split atomic wave-functions into superpositions of momentum states that differ by 200 photon recoils. Our work may provide a convenient way to implement large momentum difference beam splitters in atom interferometers.

quant-ph↗

arXiv2017

Superballistic center-of-mass motion in one-dimensional attractive Bose gases: Decoherence-induced Gaussian random walks in velocity space

We show that the spreading of the center-of-mass density of ultracold attractively interacting bosons can become superballistic in the presence of decoherence, via single-, two- and/or three-body losses. In the limit of weak decoherence, we analytically solve the numerical model introduced in [Phys. Rev. A 91, 063616 (2015)]. The analytical predictions allow us to identify experimentally accessible parameter regimes for which we predict superballistic spreading of the center-of-mass density. Ultracold attractive Bose gases form weakly bound molecules; quantum matter-wave bright solitons. Our computer-simulations combine ideas from classical field methods ("truncated Wigner") and piecewise deterministic stochastic processes. While the truncated Wigner approach to use an average over classical paths as a substitute for a quantum superposition is often an uncontrolled approximation, here it predicts the exact root-mean-square width when modeling an expanding Gaussian wave packet. In the superballistic regime, the leading-order of the spreading of the center-of-mass density can thus be modeled as a quantum superposition of classical Gaussian random walks in velocity space.

cond-mat.quant-gas↗

arXiv2016

Temperatures are not useful to characterise bright-soliton experiments for ultra-cold atoms

Contrary to many other translationally invariant one-dimensional models, the low-temperature phase for an attractively interacting one-dimensional Bose-gas (a quantum bright soliton) is stable against thermal fluctuations. However, treating the thermal properties of quantum bright solitons within the canonical ensemble leads to anomalous fluctuations of the total energy that indicate that canonical and micro-canonical ensembles are not equivalent. State-of-the-art experiments are best described by the micro-canonical ensemble, within which we predict a co-existence between single atoms and solitons even in the thermodynamic limit - contrary to strong predictions based on both the Landau hypothesis and the canonical ensemble. This questions the use of temperatures to describe state-of-the-art bright soliton experiments that currently load Bose-Einstein condensates into quasi-one-dimensional wave guides without adding contact to a heat bath.

cond-mat.quant-gas↗

arXiv2016

An $\mathbfε$-pseudoclassical model for quantum resonances in a cold dilute atomic gas periodically driven by finite-duration standing-wave laser pulses

Atom interferometers are a useful tool for precision measurements of fundamental physical phenomena, ranging from local gravitational field strength to the atomic fine structure constant. In such experiments, it is desirable to implement a high momentum transfer "beam-splitter," which may be achieved by inducing quantum resonance in a finite-temperature laser-driven atomic gas. We use Monte Carlo simulations to investigate these quantum resonances in the regime where the gas receives laser pulses of finite duration, and demonstrate that an $ε$-classical model for the dynamics of the gas atoms is capable of reproducing quantum resonant behavior for both zero-temperature and finite-temperature non-interacting gases. We show that this model agrees well with the fully quantum treatment of the system over a time-scale set by the choice of experimental parameters. We also show that this model is capable of correctly treating the time-reversal mechanism necessary for implementing an interferometer with this physical configuration.

quant-ph↗

arXiv2016

Enhanced optical cross section via collective coupling of atomic dipoles in a 2D array

Enhancing the optical cross section is an enticing goal in light-matter interactions, due to its fundamental role in quantum and non-linear optics. Here, we show how dipolar interactions can suppress off-axis scattering in a two-dimensional atomic array, leading to a subradiant collective mode where the optical cross section is enhanced by almost an order of magnitude. As a consequence, it is possible to attain an optical depth which implies high fidelity extinction, from a monolayer. Using realistic experimental parameters, we also model how lattice vacancies and the atomic trapping depth affect the transmission, concluding that such high extinction should be possible, using current experimental techniques.

physics.atom-ph↗

arXiv2016

Formation of Bose-Einstein condensates

The problem of understanding how a coherent, macroscopic Bose-Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly-interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation, and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases.

cond-mat.quant-gas↗

arXiv2015

Cooperative Ordering in Lattices of Interacting Two-Level Dipoles

We investigate the cooperative behavior of regular monolayers of driven two-level dipoles, using classical electrodynamics simulations. The dipolar response results from the interference of many cooperative eigenmodes, each frequency-shifted from the single resonant dipole case, and with a modified lifetime, due to the interactions between dipoles. Of particular interest is the kagome lattice, where the semiregular geometry permits simultaneous excitation of two dominant modes, one strongly subradiant, leading to an electromagnetically-induced-transparency-like interference in a two-level system. The interfering modes are associated with ferroelectric and antiferroelectric ordering in alternate lattice rows with long range interactions.

physics.atom-ph↗