arXiv subjects

Gerard McCaul

Publications and source records attributed to Gerard McCaul.

At least 19 recordsLinked to original sources

arXiv2026

Mean-Force Hamiltonians from Influence Functionals

The Hamiltonian of mean force (HMF) provides the standard starting point for strong-coupling thermodynamics, yet explicit operator forms are known only in restricted settings. We present a quenched density framework that uses the Hubbard-Stratonovich transformation to rewrite the reduced equilibrium state as an average over local propagators in imaginary time. This approach rigorously separates the statistical definition of the environment from the algebraic structure of the system response. We apply this framework to the minimal case of a harmonic environment with a coupling commuting with the system Hamiltonian. In this scenario the correction to the HMF has an exact, closed-form expression. We validate this result against finite-bath trace-out calculations and stochastic imaginary-time sampling in a five-level projector-coupled model.

quant-ph↗

arXiv2025

Observables in Motion: A guide to simulating classical and quantum dynamics

We present a pedagogical work-in-progress. This textbook aims to introduce Hilbert space representations for quantum and classical dynamics, outlining the mathematical foundations, practical guidance, and Python implementation of dynamical simulations. Beginning with a historical survey, the book systematically develops the mathematical foundations, kinematic descriptions, and formal evolution theory needed to understand both classical and quantum systems. It then provides practical guidance for numerically simulating time-dependent Schr\"odinger evolution, classical dynamics through symplectic integrators, and open quantum systems including phase-space formulations and stochastic unravellings.

quant-ph↗

arXiv2025

Free Snacks in Quantum Complexity

Estimating ground-state energies is a cornerstone problem in Hamiltonian complexity, and in general requires exponential resources even on quantum computers. It is in this context we analyse the recently developed Imaginary-Time Quantum Dynamical Emulation (ITQDE). This method enables estimation of spectral densities, partition functions, and low-lying gaps, but requires only minimal coherent control, modest classical post-processing, and no state preparation. Using a quadrature-based formulation, we derive scaling and stability criteria that diagnose when its estimates are reliable, and introduce a controlled smoothing that yields a principled bias-variance trade off. The resulting picture preserves the hardness of exact eigenvalue resolution but reveals a practical regime - a "free snack" - here coarse-grained spectral information is obtainable with only polynomial resources. By recasting sampling costs as explicit bounds on resolvable bandwidths, the intermediate regime between trivial and intractable complexity becomes accessible on near-term quantum hardware.

quant-ph↗

arXiv2025

Bose-Einstein condensate sub-wavelength confinement via superoscillations

Optical lattices are essential tools in ultra-cold atomic physics. Here we demonstrate theoretically that sub-wavelength confinement can be achieved in these lattices through superoscillations. This generic wave phenomenon occurs when a local region of the wave oscillates faster than any of the frequencies in its global Fourier decomposition. To illustrate how sub-wavelength confinement can be achieved via superoscillations, we consider a one-dimensional tri-chromatic optical potential confining a spinless Bose-Einstein Condensate of $^{87}$Rb atoms. By numerical optimization of the relative phases and amplitudes of the optical trap's frequency components, it is possible to generate superoscillatory spatial regions. Such regions contain multiple density peaks at sub-wavelength spacing. This work establishes superoscillations as a viable route to sub-wavelength BEC confinement in blue-detuned optical lattices.

cond-mat.quant-gas↗

arXiv2025

Dynamical learning and quantum memory with non-Hermitian many-body systems

Non-Hermitian (NH) systems provide a fertile platform for quantum technologies, owing in part to their distinct dynamical phases. These systems can be characterized by the preservation or spontaneous breaking of parity-time reversal symmetry, significantly impacting the dynamical behavior of quantum resources such as entanglement and purity; resources which in turn govern the system's information processing and memory capacity. Here we investigate this relationship using the example of an interacting NH spin system defined on random graphs. We show that the onset of the first exceptional point - marking the real-to-complex spectral transition - also corresponds to an abrupt change in the system's learning capacity. We further demonstrate that this transition is controllable via local disorder and spin interactions strength, thereby defining a tunable learnability threshold. Within the learning phase, the system exhibits the key features required for memory-dependent reservoir computing. This makes explicit a direct link between spectral structure and computational capacity, further establishing non-Hermiticity, and more broadly engineered dissipation, as a dynamic resource for temporal quantum machine learning.

quant-ph↗

arXiv2025

Unwrapping photonic reservoirs: enhanced expressivity via random Fourier encoding over stretched domains

Photonic Reservoir Computing (RC) systems leverage the complex propagation and nonlinear interaction of optical waves to perform information processing tasks. These systems employ a combination of optical data encoding (in the field amplitude and/or phase), random scattering, and nonlinear detection to generate nonlinear features that can be processed via a linear readout layer. In this work, we propose a novel scattering-assisted photonic reservoir encoding scheme where the input phase is deliberately wrapped multiple times beyond the natural period of the optical waves $[0,2\pi)$. We demonstrate that, rather than hindering nonlinear separability through loss of bijectivity, wrapping significantly improves the reservoir's prediction performance across regression and classification tasks that are unattainable within the canonical $2\pi$ period. We demonstrate that this counterintuitive effect stems from the nonlinear interference between sets of random synthetic frequencies introduced by the encoding, which generates a rich feature space spanning both the feature and sample dimensions of the data. Our results highlight the potential of engineered phase wrapping as a computational resource in RC systems based on phase encoding, paving the way for novel approaches to designing and optimizing physical computing platforms based on topological and geometric stretching.

physics.optics↗

arXiv2025

Minimal Quantum Reservoirs with Hamiltonian Encoding

We investigate a minimal architecture for quantum reservoir computing based on Hamiltonian encoding, in which input data is injected via modulation of system parameters rather than state preparation. This approach circumvents many of the experimental overheads typically associated with quantum machine learning, enabling computation without feedback, memory, or state tomography. We demonstrate that such a minimal quantum reservoir, despite lacking intrinsic memory, can perform nonlinear regression and prediction tasks when augmented with post-processing delay embeddings. Our results provide a conceptually and practically streamlined framework for quantum information processing, offering a clear baseline for future implementations on near-term quantum hardware.

quant-ph↗

arXiv2024

Tuning the terahertz response of liquids by creating polar many-body excitations

A surprising result from the theory of quantum control is the degree to which the properties of a physical system can be manipulated. Both atomic and many-body solid state models admit the possibility of creating a 'driven imposter', in which the optical response of one material mimics that of a dynamically distinct system. Here we apply these techniques to polarons in polar liquids. Such quasiparticles describe solvated electrons interacting with many-body degrees of freedom of their environment. The polaron frequency, which depends on the electron concentration in the liquid, is controlled with a pump field, rendering the polaron frequency of three different liquids identical. The experiments demonstrate the feasibility of 'polar impostorons', a so far purely theoretical phenomenon.

quant-ph↗

arXiv2024

Quantum Dynamical Emulation of Imaginary Time Evolution

We introduce a constructive method for mapping non-unitary dynamics to a weighted set of unitary operations. We utilize this construction to derive a new correspondence between real and imaginary time, which we term Imaginary Time Quantum Dynamical Emulation (ITQDE). This correspondence enables an imaginary time evolution to be constructed from the overlaps of states evolved in opposite directions. We develop ITQDE as a tool for estimating the ground and thermal state properties associated with a given Hamiltonian. We additionally provide a prescription for leveraging ITQDE to estimate the complete Hamiltonian spectrum. We go on to develop a quantum algorithm for computing Hamiltonian spectra based on ITQDE, which we validate through numerical simulations and quantum hardware implementations. We conclude with a discussion of how ITQDE can be utilized more broadly to derive novel thermodynamic results, including a generalisation of the Hubbard-Stratonovich transformation.

quant-ph↗

arXiv2023

Super-sensing: 100-Fold enhancement in THz time-domain spectroscopy contrast via superoscillating waveform shaping

Superoscillations are a phenomenon where a band-limited wave may locally oscillate faster than its highest Fourier component. They are a product of destructive interference between the wave's constituent harmonics. In this article, we demonstrate that superoscillations enable a new functionality in linear optical sensing -- the 100-fold enhancement in the optical contrast of the terahertz wave passing through two similar samples. To achieve this enhancement, we optimize the optical contrast in the time domain in a short observation window by varying the relative phases between the fundamental harmonics that make up the input terahertz wave. We find that the contrast is maximized when the wave intensity is minimized locally within the observation window, which naturally leads to the emergence of the superoscillations. We observe the 100-fold contrast enhancement both in our numerical simulations with Gaussian time-domain harmonics and in our experimental realization with narrow-band quasi-sinusoidal terahertz harmonics. Our results will have profound influence on terahertz sensing and imaging applications in medicine, pharmaceuticals, stand-off hazard detection, and nondestructive evaluation.

physics.optics↗

arXiv2023

Spectral Gaps via Imaginary Time

The spectral gap occupies a role of central importance in many open problems in physics. We present an approach for evaluating the spectral gap of a Hamiltonian from a simple ratio of two expectation values, both of which are evaluated using a quantum state that is evolved in imaginary time. In principle, the only requirement is that the initial state is supported on both the ground and first excited states. We demonstrate this approach for the Fermi-Hubbard and transverse-field Ising models through numerical simulation. We then go on to explore avenues for its implementation on quantum computers using imaginary-time quantum dynamical emulation.

quant-ph↗

arXiv2023

The wave operator representation of quantum and classical dynamics

The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator representation of quantum dynamics, and explore its connection to standard methods of quantum dynamics. This method takes as its central object the square root of the density matrix, and consequently enjoys several unusual advantages over standard representations. By combining this with purification techniques imported from quantum information, we are able to obtain a number of results. Not only is this formalism able to provide a natural bridge between phase and Hilbert space representations of both quantum and classical dynamics, we also find the waveoperator representation leads to novel semiclassical approximations of both real and imaginary time dynamics, as well as a transparent correspondence to the classical limit. This is demonstrated via the example of quadratic and quartic Hamiltonians, while the potential extensions of the waveoperator and its application to quantum-classical hybrids is discussed. We argue that the wave operator provides a new perspective that links previously unrelated representations, and is a natural candidate model for scenarios (such as hybrids) in which positivity cannot be otherwise guaranteed.

quant-ph↗

arXiv2023

Dynamical Generation of Epsilon-Near-Zero Behaviour via Tracking and Feedback Control

To date, epsilon near zero (ENZ) responses, characterized by an infinite phase velocity, are primarily achieved by applying a monochromatic light source to a tailored metamaterial. Here, we derive the equations for inducing a dynamically generated broadband ENZ response in a large class of many-body systems via tracking and feedback control. We further find that this response leads to a current-energy relationship identical to that of an ideal inductor. Using a Fermi-Hubbard model, we numerically confirm these results which have the potential to advance optical computation on the nanoscale.

physics.optics↗

arXiv2022

Ultrafast laser-driven dynamics in metal-insulator interface

The nearly free electron metal next to a localized Mott insulating state has been recently proposed as a way to probe Kondo lattice physics and to gain insight into how the two extremes of localized and delocalized electron states interact (Sunko, et al, Science advances 6, 2020). Although high harmonic generation has been used extensively to investigate the gas phase, its extension to solids is relatively recent, and has not yet been applied to interfaces. Here, we investigate the field-induced dielectric break-down at the Mott-insulator/metal interface using high harmonic generation, emitted when the interface is subjected to an ultrafast laser pulse. We show that the intensity of high harmonic emission correlates closely with doublon production and the corresponding loss of short-range anti-ferromagnetic order. For strong interlayer coupling, the harmonic intensity is defined by a phase transition between states that do not exist in a pure Mott insulator case. For weak interlayer coupling, the threshold for dielectric breakdown is considerably lowered due to the presence of a metallic layer. This suggests that interlayer coupling can be used as an additional knob to control magnetic insulator break-down, with implications for using Mott insulators as memristors in neuromorphic circuits.

cond-mat.str-el↗

arXiv2022

Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics

It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time coordinate transformation. We demonstrate that an equivalent transformation can be performed for classical systems in the context of Koopman von-Neumann (KvN) dynamics. We further extend this mapping to dissipative evolutions in both the quantum and classical cases, and show that this mapping imparts an identical time-dependent scaling on the dissipation parameters for both types of dynamics. The derived classical procedure presents a number of opportunities to import squeezing dependent quantum procedures (such as Hamiltonian amplification) into the classical regime.

quant-ph↗

arXiv2022

Superoscillations Made Super Simple

In ordinary circumstances the highest frequency present in a wave is the highest frequency in its Fourier decomposition. It is however possible for there to be a spatial or temporal region of the wave which locally oscillates at a still greater frequency, in a phenomenon known as superoscillation. Superoscillations find application in wide range of disciplines, but at present their generation is based upon constructive approaches which are difficult to implement. Here we address this, exploiting the fact that superoscillations are a product of destructive interference to produce a prescription for generating superoscillations from the superposition of arbitrary waveforms. As a first test of the technique, we use it to combine four THz laser fields generated by periodically poled Lithium Niobate. From this, we are able to predict and observe for the first time THz optical superoscillations in the temporal domain. The ability to generate superoscillations in this manner has potential application in a wide range of fields. It may for example contribute to the experimental realization of the complex pulses required by quantum control, and the generation of attosecond pulses without resorting to nonlinear processes.

physics.optics↗

arXiv2022

Optical Distinguishability of Mott Insulators in Time vs Frequency Domain

High Harmonic Generation (HHG) promises to provide insight into ultrafast dynamics and has been at the forefront of attosecond physics since its discovery. One class of materials that demonstrate HHG are Mott insulators whose electronic properties are of great interest given their strongly-correlated nature. Here, we use the paradigmatic representation of Mott insulators, the half-filled Fermi-Hubbard model, to investigate the potential of using HHG response to distinguish these materials. We develop an analytical argument based on the Magnus expansion approximation to evolution by the Schrodinger equation that indicates decreased distinguishability of Mott insulators as lattice spacing, $a$, and the strength of the driving field, $F_0$, increase relative to the frequency, $\omega_0$. This argument is then bolstered through numerical simulations of different systems and subsequent comparison of their responses in both the time and frequency domain. Ultimately, we demonstrate reduced resolution of Mott insulators in both domains when the dimensionless parameter $g \equiv aF_0 / \omega_0$ is large, though the time domain provides higher distinguishability. Conductors are exempted from these trends, becoming much more distinguishable in the frequency domain at high $g$.

physics.optics↗

arXiv2022

Sequential optical response suppression for chemical mixture characterization

The characterization of mixtures of non-interacting, spectroscopically similar quantum components has important applications in chemistry, biology, and materials science. We introduce an approach based on quantum tracking control that allows for determining the relative concentrations of constituents in a quantum mixture, using a single pulse which enhances the distinguishability of components of the mixture and has a length that scales linearly with the number of mixture constituents. To illustrate the method, we consider two very distinct model systems: mixtures of diatomic molecules in the gas phase, as well as solid-state materials composed of a mixture of components. A set of numerical analyses are presented, showing strong performance in both settings.

quant-ph↗