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Mark G. Kuzyk

Publications and source records attributed to Mark G. Kuzyk.

At least 19 recordsLinked to original sources
arXiv2024

Deterministic Shaping of Quantum Light Statistics

We propose a theoretical method for the deterministic shaping of quantum light via photon number state selective interactions. Nonclassical states of light are an essential resource for high precision optical techniques that rely on photon correlations and noise reshaping. Notable techniques include quantum enhanced interferometry, ghost imaging, and generating fault tolerant codes for continuous variable optical quantum computing. We show that a class of nonlinear-optical resonators can transform many-photon wavefunctions to produce structured states of light with nonclassical noise statistics. The devices, based on parametric down conversion, utilize the Kerr effect to tune photon number dependent frequency matching, inducing photon number selective interactions. With a high amplitude coherent pump, the number selective interaction shapes the noise of a two-mode squeezed cavity state with minimal dephasing, illustrated with simulations. We specify the requisite material properties to build the device and highlight the remaining material degrees of freedom which offer flexible material design.

quant-ph↗
arXiv2020

Quantum Origins of the Density Operator

Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a new set of probabilities in addition to those that are built into the wave function. This paper brings attention to the fact that the density matrix can be reconciled with the underlying quantum-mechanical description using a two-particle entangled state with a one-particle subsystem as the simplest illustration of the basic principle. The extra-quantum probabilities are traced to the coefficients of superposition of the quantum state vector and the seemingly irreversible exponential population decay is shown to be compatible with the unitary time evolution of a pure state when the two particles interact. The two-particle universe thus provides the student with a tool for understanding how the density operator, with all its richness, emerges from quantum mechanics.

physics.gen-ph↗
arXiv2020

Collecting data with a mobile phone: Studies of mechanical laws such as energy and momentum conservation

We use videos taken with a mobile phone to study conservation of energy, conservation of momentum, and the work-energy theorem by analyzing the collision of a cue ball and the eight ball. A video of the full time sequence, starting from before the cue ball is struck until well after the collision, is recorded with a mobile phone. The video is imported into Origin (free to teachers and students taking a class) [OriginLab Corporation, Origin, Version 2020 (OriginLab Corporation, Northampton, MA, USA, 2020)], where the coordinates of the balls are digitized frame-by-frame using the free Video Extractor app. From these data, the velocities are determined as a function of time and used to determine the energy and momentum of each ball. The data suggest that the balls slip through part of their motion when rotating at an angular velocity different than the rolling angular velocity, so angular momentum and frictional torque must be considered. Such experiments require no specialized equipment other than a device to take a video, and the act of digitizing the data provides the student with visual reinforcement of the physics. Experimentation by students outside of campus can be fun for them and provides a useful alternative to classes when in-lab experiments are not practical. Use of a mobile phone in this way is generally applicable to any other mechanical phenomena that involve motion.

physics.ed-ph↗
arXiv2020

Length as a Paradigm for Understanding the Classical Limit

It is regrettable that the quantum length of an object is rarely if ever discussed, because it provides an ideal pedagogical paradigm for understanding how a physicist uses classical intuition to define quantum properties and how such quantum properties behave as one would expect in the classical limit. It also provides for a way to understand many-particle states, and leads to interesting quantum behavior that challenges our intuition of measurement.

quant-ph↗
arXiv2020

Topological control of the nonlinear-optical response of hybrid quantum systems

We map the topological properties of a one dimensional superlattice to the optical properties of an electronic system. We find that the nonlinear-optical response is optimized for electrons that live in the transitional morphology between topologically protected edge states and delocalized eigenstates. This provides a novel means of tuning the nonlinear-optical response of hybrid quantum systems. We show how these characteristics can be used to mimic saturable absorption and illustrate how `quantum cords' can be used to build an efficient all-optical switch.

physics.optics↗
arXiv2020

Quantum Limits on Material Response Factors for Optimized Radiative Heat Transfer

Through quantum mechanical considerations, we optimize the material response factor $|χ|^2/\text{Im}\left[χ\right]$, which plays a pivotal role in the fundamental limits of near-field radiative heat transfer (RHT). A comparison of the limits obtained to experimental data for select materials shows that current materials fall several orders of magnitude short of the optimized values, suggesting the possibility of significant improvement in the rate of radiative heat transfer between two bodies. This work informs material design efforts that seek to optimize RHT, as well as provides insights into the quantum origins of RHT and the theory of fundamental limits.

physics.optics↗
arXiv2019

Theoretical and experimental studies of photomechanical materials

After a brief introduction to the field of light-responsive materials, this paper provides a general theory for modeling the photomechanical response of a material, applies it to the two best-known mechanisms of photothermal heating and photo-isomerization, and then describes an experimental apparatus for quantitative measurements of the stress response. Several different materials are characterized to illustrate how the experiments and theory can be used to isolate the contributing mechanisms both through photomechanical measurements and auxiliary measurements of laser heating and thermal expansion. The efficiency and figure of merit of the photomechanical response is defined on several scales form the molecule to the bulk, and the photomorphon -- the basic material element that determines the bulk response -- is introduced. The photomorphon provides a conceptual model that can be expressed in terms of viscoelastic elements such as springs in series and parallel with the photoactive molecule. The photomechanical response, figure of merit, and the deduced microscopic photomechanical properties are tabulated and proposals for new materials classes are made.

physics.optics↗
arXiv2018

Using a proxy state to improve the accuracy of truncated hyperpolarizability calculations

We have developed a simple algorithm for defining a single proxy state which accounts for state truncation in the sum-over-states calculations of the dispersion of the molecular hyperpolarizabilities. The transition strengths between the proxy state and the truncated set of states are determined using the Thomas-Reiche-Kuhn sum rules. In addition to the sum rules, this method requires as an input the off-resonant polarizability. This proxy state method can augment experimentally determined parameters or finite-state theories to allow for a more accurate prediction of the nonlinear optical properties of molecular systems. We benchmark this approach by comparison with exact perturbation calculations of one-dimensional power law potentials.

physics.optics↗
arXiv2017

Exact fundamental limits of the first and second hyperpolarizabilities

This letter calculates the exact fundamental limits of the first (β) and second (γ) hyperpolarizabilities using Monte-Carlo sampling of energy spectra and transition moments constrained by the diagonal Thomas-Reiche-Kuhn (TRK) sum rules and filtered by the off-diagonal TRK sum rules. The upper bounds of β and γ are determined from these quantities by applying error-refined extrapolation to perfect compliance to the sum rules. The method yields the largest diagonal component of the hyperpolarizabilities for an arbitrary number of interacting electrons in any number of dimensions without the necessity for exotic interactions or unconventional spectra. The results show that the fundamental limits agree with those achieved by potential optimization and direct solution of mechanical Hamiltonians, about 30% (40%) below original estimates of the limits for β (γ), and show that the special cases that lead to divergent nonlinearities in the many-state catastrophe are not physically realizable. Thus, this letter shows for the first time that the fundamental limits are rigorously exact and are achievable without exotic material designs.

physics.optics↗
arXiv2016

Self-healing properties of 1-amino, 2,4-dibromo anthraquinone dye doped in PMMA polymer

We used fluorescence spectroscopic measurements as a probe to study the self-healing properties of anthraquinone derivative molecules doped in poly(methyl methacrylate) (PMMA). 2,4-dibromo anthraquinone dye doped in PMMA recovers after photodegradation. Its dynamics differs from other anthraquinone derivative molecules. This could be due to the relatively heavier bromine atom attached to one of the carbon atoms of the benzene ring. In this paper, we will discuss the self-healing properties of 2,4-dibromo anthraquinone doped in PMMA matrix. We also tested the correlated chromophore domain model (CCrDM) and have characterized the self-healing properties by determining the CCrDM parameters. We also estimated the self-absorption of fluorescence signal by the dye molecule without which the analysis of the self-recovery of the molecule would be incomplete.

cond-mat.soft↗
arXiv2016

Polynomial potentials determined from the energy spectrum and transition dipole moments that give the largest hyperpolarizabilities

We attempt to get a polynomial solution to the inverse problem, that is, to determine the form of the mechanical Hamiltonian when given the energy spectrum and transition dipole moment matrix. Our approach is to determine the potential in the form of a polynomial by finding an approximate solution to the inverse problem, then to determine the hyperpolarizability for that system's Hamiltonian. We find that the largest hyperpolarizabilities approach the apparent limit of previous potential optimization studies, but we do not find real potentials for the parameter values necessary to exceed this apparent limit. We also explore half potentials with positive exponent, which cannot be expressed as a polynomial except for integer powers. This yields a simple closed potential with only one parameter that scans nearly the full range of the intrinsic hyperpolarizability. The limiting case of vanishing exponent yields the largest intrinsic hyperpolarizability.

quant-ph↗
arXiv2016

General solution to nonlinear optical quantum graphs using Dalgarno-Lewis summation techniques

We develop an algorithm to apply the Dalgarno-Lewis (DL) perturbation theory to quantum graphs with multiple, connected edges. We use it to calculate the nonlinear optical hyperpolarizability tensors for graphs and show that it replicates the sum over states computations, but executes ten to fifty times faster. DL requires only knowledge of the ground state of the graph, eliminating the requirement to determine all possible degeneracies of a complex network. The algorithm is general and may be applied to any quantum graph.

quant-ph↗
arXiv2016

Dalgarno-Lewis perturbation theory for nonlinear optics

We apply the quadrature-based perturbation method of Dalgarno and Lewis to the evaluation of the nonlinear optical response of quantum systems. This general operator method for perturbation theory allows us to derive exact expressions for the first three electronic polarizabilities which require only a good estimate of the ground state wave function, makes no explicit reference to the underlying potential, and avoids complexities arising from excited state degeneracies. We apply this method to simple examples in 1D quantum mechanics for illustration, exploring the sensitivity of this method to variational solutions as well as poor numerical sampling. Finally, to the best of our knowledge, we extend the Dalgarno-Lewis method for for the first time to time-harmonic perturbations, allowing dispersion characteristics to be determined from the unperturbed ground state wave function alone.

physics.optics↗
arXiv2016

Hybrid quantum systems for enhanced nonlinear optical susceptibilities

Significant effort has been expended in the search for materials with ultra-fast nonlinear-optical susceptibilities, but most fall far below the fundamental limits. This work applies a theoretical materials development program that has identified a promising new hybrid made of a nanorod and a molecule. This system uses the electrostatic dipole moment of the molecule to break the symmetry of the metallic nanostructure that shifts the energy spectrum to make it optimal for a nonlinear-optical response near the fundamental limit. The structural parameters are varied to determine the ideal configuration, providing guidelines for making the best structures.

physics.optics↗
arXiv2016

Fundamental limits on the electro-optic device figure of merit

Device figures of merit are commonly employed to assess bulk material properties for a particular device class, yet these properties ultimately originate in the linear and nonlinear susceptibilities of the material which are not independent of each other. In this work, we calculate the electro-optic device figure of merit based on the half-wave voltage and linear loss, which is important for phase modulators and serves as the simplest example of the approach. This figure of merit is then related back to the microscopic properties in the context of a dye-doped polymer, and its fundamental limits are obtained to provide a target. Surprisingly, the largest figure of merit is not always associated with a large nonlinear-optical response, the quantity that is most often the focus of optimization. An important lesson to materials design is that the figure of merit alone should be optimized. The best device materials can have low nonlinearity provided that the loss is low; or, near resonance high loss may be desirable because it is accompanied by resonantly-enhanced, ultra-large nonlinear response so device lengths are short. Our work shows which frequency range of operation is most promising for optimizing the material figure of merit for electro-optic devices.

physics.optics↗
arXiv2016

Molecular structure and reversible photodegradation in anthraquinone dyes

Reversible photodegradation is a process that has been observed in several dye molecules, but the underlying mechanisms are not still well understood. In this contribution, we characterize a series of anthraquinone dyes to determine how self-healing depends on molecular structure. Past studies have used probing techniques that rely on linear absorption, two-photon fluorescence, and amplified spontaneous emission. Each of these probes provide an indirect measure of the populations of the damaged and undamaged species, requiring calibrations or assumptions to be made that might affect the accuracy of the results. The present studies use fluorescence as a probe, which is shown to directly measure the undamaged population. It is found that certain anthraquinone classes share common structural features that are associated with self healing. Furthermore, the time and temperature dependence of photodegradation and self-healing is found to be consistent with the domain model of self healing.

physics.chem-ph↗
arXiv2016

Applying universal scaling laws to identify the best molecular design paradigms for third-order nonlinear optics

The scaling of the fundamental limits of the second hyperpolarizability is used to define the intrinsic second hyperpolarizability, which aids in identifying material classes with ultralarge nonlinear-optical response per unit of molecular size. The intrinsic nonlinear response is a size-independent metric that we apply to comparing classes of molecular homologues, which are made by adding repeat units to extend their lengths. Several new figures of merit are proposed that quantify not only the intrinsic nonlinear response, but also how the second hyperpolarizability increases with size within a molecular class. Scaling types can be classified into sub-scaling, nominal scaling that follows the theory of limits, and super-scaling behavior. Super-scaling homologues that have large intrinsic nonlinearity are the most promising because they efficiently take advantage of increased size. We apply our approach to data in the literature to identify the best super-scaling molecular paradigms and articulate the important underlying parameters.

physics.optics↗