Gerard McCaul
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View article: Observables in Motion: A guide to simulating classical and quantum dynamics
Observables in Motion: A guide to simulating classical and quantum dynamics Open
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…
View article: Free Snacks in Quantum Complexity
Free Snacks in Quantum Complexity Open
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 Dy…
View article: Unwrapping photonic reservoirs: Enhanced expressivity via random Fourier encoding over stretched domains
Unwrapping photonic reservoirs: Enhanced expressivity via random Fourier encoding over stretched domains Open
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 amplit…
View article: Super-sensing: 100-fold enhancement in THz time-domain spectroscopy contrast via superoscillating waveform shaping
Super-sensing: 100-fold enhancement in THz time-domain spectroscopy contrast via superoscillating waveform shaping Open
Superoscillations, where a band-limited wave oscillates locally faster than its highest Fourier harmonic, result from destructive interference between the harmonics. Here, we demonstrate that superoscillations enable a 100-fold contrast en…
View article: Unwrapping photonic reservoirs: enhanced expressivity via random Fourier encoding over stretched domains
Unwrapping photonic reservoirs: enhanced expressivity via random Fourier encoding over stretched domains Open
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 amplit…
View article: Minimal Quantum Reservoirs with Hamiltonian Encoding
Minimal Quantum Reservoirs with Hamiltonian Encoding Open
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 e…
View article: Tuning the terahertz response of liquids by creating polar many-body excitations
Tuning the terahertz response of liquids by creating polar many-body excitations Open
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 wh…
View article: Quantum Dynamical Emulation of Imaginary Time Evolution
Quantum Dynamical Emulation of Imaginary Time Evolution Open
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 …
View article: Super-sensing: 100-Fold enhancement in THz time-domain spectroscopy contrast via superoscillating waveform shaping
Super-sensing: 100-Fold enhancement in THz time-domain spectroscopy contrast via superoscillating waveform shaping Open
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 demo…
View article: Spectral Gaps via Imaginary Time
Spectral Gaps via Imaginary Time Open
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 usi…
View article: Spectral Gaps via Imaginary Time
Spectral Gaps via Imaginary Time Open
View article: The wave operator representation of quantum and classical dynamics
The wave operator representation of quantum and classical dynamics Open
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 representati…
View article: Correction to: Towards single atom computing via high harmonic generation
Correction to: Towards single atom computing via high harmonic generation Open
View article: Dynamical Generation of Epsilon-Near-Zero Behaviour via Tracking and Feedback Control
Dynamical Generation of Epsilon-Near-Zero Behaviour via Tracking and Feedback Control Open
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 g…
View article: Ultrafast laser-driven dynamics in metal-insulator interface
Ultrafast laser-driven dynamics in metal-insulator interface Open
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…
View article: Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics
Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics Open
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 …
View article: Superoscillations Made Super Simple
Superoscillations Made Super Simple Open
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 gr…
View article: Optical Distinguishability of Mott Insulators in Time vs Frequency Domain
Optical Distinguishability of Mott Insulators in Time vs Frequency Domain Open
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 pr…
View article: Sequential optical response suppression for chemical mixture characterization
Sequential optical response suppression for chemical mixture characterization Open
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 allo…
View article: Non-Uniqueness of Non-Linear Optical Response
Non-Uniqueness of Non-Linear Optical Response Open
In recent years, non-linear optical phenomena have attracted much attention, with a particular focus on the engineering and exploitation of non-linear responses. Comparatively little study has however been devoted to the driving fields tha…
View article: Optical Indistinguishability via Twinning Fields
Optical Indistinguishability via Twinning Fields Open
Here we introduce the concept of the twinning field-a driving electromagnetic pulse that induces an identical optical response from two distinct materials. We show that for a large class of pairs of generic many-body systems, a twinning fi…
View article: How to win friends and influence functionals: deducing stochasticity from deterministic dynamics
How to win friends and influence functionals: deducing stochasticity from deterministic dynamics Open
View article: Towards Single Atom Computing via High Harmonic Generation
Towards Single Atom Computing via High Harmonic Generation Open
The development of alternative platforms for computing has been a longstanding goal for physics, and represents a particularly pressing concern as conventional transistors approach the limit of miniaturization. A potential alternatice para…
View article: Fast computation of dissipative quantum systems with ensemble rank truncation
Fast computation of dissipative quantum systems with ensemble rank truncation Open
We introduce a new technique for the simulation of dissipative quantum\nsystems. This method is composed of an approximate decomposition of the\nLindblad equation into a Kraus map, from which one can define an ensemble of\nwavefunctions. U…
View article: Diffusion Fails to Make a Stink
Diffusion Fails to Make a Stink Open
In this work we consider the question of whether a simple diffusive model can explain the scent tracking behaviors found in nature. For such tracking to occur, both the concentration of a scent and its gradient must be above some threshold…
View article: Scalable single-shot mixture characterization
Scalable single-shot mixture characterization Open
The characterization of mixtures of non-interacting, spectroscopically similar quantum components has important applications in chemistry, biology, and materials science. We introduce a scalable approach for determining concentrations in a…
View article: Single-shot mixture characterization
Single-shot mixture characterization Open
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 allo…
View article: Controlling arbitrary observables in correlated many-body systems
Controlling arbitrary observables in correlated many-body systems Open
Here we present an expanded analysis of a model for the manipulation and\ncontrol of observables in a strongly correlated, many-body system, which was\nfirst presented in [McCaul et al., eprint: arXiv:1911.05006]. A field-free,\nnon-linear…
View article: Driven Imposters: Controlling Expectations in Many-Body Systems
Driven Imposters: Controlling Expectations in Many-Body Systems Open
We present a framework for controlling the observables of a general correlated electron system driven by an incident laser field. The approach provides a prescription for the driving required to generate an arbitrary predetermined evolutio…
View article: Entropy nonconservation and boundary conditions for Hamiltonian dynamical systems
Entropy nonconservation and boundary conditions for Hamiltonian dynamical systems Open
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new dyn…