arXiv subjects

Scott Parkins

Publications and source records attributed to Scott Parkins.

At least 19 recordsLinked to original sources

arXiv2026

Concentration-compactness for the geometric polyharmonic heat flow

We develop a concentration-compactness theory for geometric evolution equations of arbitrarily high order, using the geometric polyharmonic heat flow of closed immersed surfaces in $\R^3$ as the model case. The flow is the $(2p+2)$-order normal evolution \[ \partial_t f=(-1)^{p+1}\Delta^p H\,\nu,\qquad p\geq1, \] which includes the surface diffusion flow when $p=1$. We prove localised energy estimates with sharp cut-off bookkeeping, interior estimates, a lifespan/concentration alternative, tracefree-curvature $\varepsilon$-regularity estimates, and a gap theorem for stationary solutions. These tools are then combined with a blowup argument, the preservation of signed enclosed volume, and the monotonicity of area to rule out singularities below a small tracefree-curvature threshold. Consequently, for connected initial immersions satisfying $\|A^o\|_2^2<\varepsilon$, where $\varepsilon>0$ depends only on the order of the flow, the solution exists for all time and converges exponentially in $C^\infty$ to a round sphere with the preserved enclosed volume.

math.AP↗

arXiv2026

Heintze-Karcher and Reverse Alexandrov-Fenchel Inequalities via Focal Geometry

We prove a collection of reverse Alexandrov-Fenchel type inequalities in anisotropic, Euclidean, spherical, and hyperbolic settings. The unifying principle is that the relevant deficit is controlled by curvature radius data, or equivalently by the signed volume of an associated evolute or focal map. For smooth simple strictly convex curves in a smooth Minkowski plane we prove an anisotropic Hurwitz-type inequality: the anisotropic isoperimetric deficit is bounded above by the signed Euclidean area of the Minkowski evolute. For smooth closed strictly convex hypersurfaces in $\mathbb R^{n+1}$, with $E_k$ denoting the normalised $k$-th mean curvature, we establish the sharp reverse Alexandrov-Fenchel estimate \[ 0\le \frac{1}{|\mathbb S^{n}|} \left(\int_{M}E_{n-1}\,d\mu\right)^{2} -\int_{M}E_{n-2}\,d\mu \le \frac{n}{2(n+1)} \int_{M}\frac{E_{n-1}^{2}-E_{n-2}E_{n}}{E_{n}}\,d\mu . \] We also relate the deficit of the Minkowski inequality to the oriented volumes of the two focal maps. In space forms we derive a normal-graph formula for oriented volume and use it to give focal-map interpretations of the deficit of an unweighted Heintze--Karcher inequality. In dimension two this recovers evolute-area formulae. We then prove exact reverse isoperimetric identities for curves on $\mathbb S^{2}$ and strictly horoconvex curves in $\mathbb H^{2}$, in which the remainders are explicit nonnegative integrals measuring the oscillation of geodesic curvature. In the spherical case, for every smooth simple closed curve $\gamma\subset\mathbb S^2$ with length $L$ and enclosed area $A$, if $k_E$ denotes the ambient Euclidean curvature of $\gamma$, then \[ L^{2}-A(4\pi-A) \le \left(\int_{\gamma}k_E\,ds\right)^{2}-4\pi^{2}, \] with equality if and only if $\gamma$ is a geodesic circle. This relates the spherical isoperimetric deficit with the Euclidean Fenchel deficit.

math.DG↗

arXiv2026

Spin-entanglement of an atomic pair through coupling to their thermal motion

The spin-dynamics of two alkali atoms in an optical tweezer is driven by spin-changing collisions that couple the spin-state of the atoms to their relative motion. This paper experimentally studies the resulting spin-states when the relative motion is in a thermal state with k B T much larger than the energies of the spin-states that take part in the dynamics. We find that an initially unentangled spin-state can evolve into an entangled state. This is contrary to the common case when coupling a quantum system to hot degrees of freedom leads to loss of entanglement and not its generation. Moreover, we show that the generated entanglement is technologically useful as it, in principle, can enhance the sensitivity of measurements beyond the standard quantum limit. This may provide a promising avenue for robust entanglement generation for future technologies.

quant-ph↗

arXiv2026

Steady-State Emission of Quantum-Correlated Light in the Telecom Band from a Single Atom

We propose and investigate a scheme for the steady-state emission of quantum-correlated, telecom-band light from a single multilevel atom. By appropriately tuning the frequency of a pair of lasers, a two-photon transition is continually driven to an atomic excited state that emits photons at the desired wavelength. We show that resonantly coupling a cavity mode to the telecom transition can enhance the rate of emission while retaining the antibunched counting statistics that are characteristic of atomic light sources. We also explore coupling a second, independent cavity mode to the atom, which increases the telecom emission rate and introduces quantum correlations between the cavity modes. A model for the hyperfine structure of a single cesium atom is then described and numerically integrated to demonstrate the viability of implementing the scheme with a modern cavity QED system.

quant-ph↗

arXiv2025

Quantum-correlated photons from spectrally-separated modes of a cavity coupled to a strongly-driven two-level atom

Photon counting statistics are explored, theoretically, from a pair of cavity modes coupled to the fluorescent transitions in a strongly-driven two-level atom. We show that the cavity modes acquire nonclassical photon statistics that are representative of dressed-state picture atomic transitions. In particular, the modes are shown to be antibunched, while simultaneously having a cross-correlation value greater than unity. Furthermore, we propose an implementation of the system with a nanofiber cavity QED system, based on a strongly-driven cesium atom.

quant-ph↗

arXiv2025

Detecting entanglement between quantum emitters using directional emission

Recently, it was shown that quantum interference in a system containing a polarized and unpolarized emitter can allow directional emission of photons into a circulating cavity. Here, we ask whether high directionality of photon emission in this system implies a high degree of quantum correlation between the two emitters. We show that the answer is a qualified "yes", with photon emission directionality and emitter-emitter entanglement showing a monotonic relationship over a broad parameter range. The relationship only breaks down in the limit of perfect directionality. Furthermore, under reasonable assumptions for experimental parameters and stability, we show that the statistics of measured directionality allow a reliable estimate of the concurrence. This result implies that directionality of photon emission in the state preparation stage can be used to determine the entanglement between the emitters, with potential applications to more generic cases including quantum networks.

quant-ph↗

arXiv2025

Study of the EPR-type entanglement characteristics of a NDPA with time-delayed coherent feedback

An open non-degenerate parametric oscillator (NDPO) is studied below threshold in the undepleted pump regime with time-delayed coherent feedback (TDCF). The figure of merit is the two-mode squeezing spectrum measuring the strength of continuous-valued Einstein-Podolsky-Rosen-type (EPR-type) entanglement between the down-converted modes in the output field. Exploring different areas of the parameter space reveals the possibility of significantly enhanced entanglement with tunable characteristic frequency. These resonance-like features are closely related to the unique dynamics emerging as a result of delayed feedback. The system is very sensitive to phase matching, which can be adjusted by various parameters of the setup. Further advantage of the current scheme is that significant enhancement of entanglement can be achieved even with finite extraneous losses.

quant-ph↗

arXiv2025

Two-Photon Resonance Fluorescence in a Three-Level Ladder-Type Atom

In this work, we consider a three-level ladder-type atom driven by a coherent field, inspired by the experimental work of Gasparinetti et al. [Phys. Rev. A 100, 033802 (2019)]. When driven on two-photon resonance, the atom is excited into its highest energy state $| f \rangle$ by absorbing two photons simultaneously. The atom then de-excites via a cascaded decay $| f \rangle \rightarrow | e \rangle \rightarrow | g \rangle$. Here we present a theoretical study of the atomic fluorescence spectrum where, upon strong coherent driving, the spectrum exhibits seven distinct frequencies corresponding to transitions amongst the atomic dressed states. We characterize the quantum statistics of the emitted photons by investigating the second-order correlation functions of the emitted field. We do so by considering the total field emitted by the atom and focusing on each of the dressed-state components, taking in particular a secular-approximation and deriving straightforward, transparent analytic expressions for the second-order auto- and cross-correlations.

quant-ph↗

arXiv2025

Nonlinear Dynamics of a Dicke Model for V-Type Atoms

We study the nonlinear, semiclassical dynamics of an open spin-1 (three-level) variant of the traditional Dicke model. In particular, we focus on V-type energy-level configurations with varying degrees of energy-level asymmetry. We also allow for unbalanced coupling -- where co-rotating and counter-rotating Hamiltonian terms are independently tunable. We characterise the system with a dynamical systems approach, where different behaviors map to definite dynamical objects, and phase transitions to bifurcations. We find the emergence of both periodic and two-frequency oscillations, as well as multistability and chaotic dynamics.

quant-ph↗

arXiv2024

Long-distance cascaded fluorescence of cold Cesium atoms coupled to an optical nanofiber

We demonstrate the first experimental realization of cascaded resonance fluorescence over a 64-meter propagation delay time between two spatially and temporally independent ensembles of laser-cooled Cesium atoms coupled to an optical nanofiber. Spontaneously emitted photons from a strongly driven first ensemble are guided through a standard fiber, reflected by a fiber Bragg grating mirror, and interact with a second ensemble, producing a unidirectional two-node cascaded system. The cascaded fluorescence spectrum is broadened and blue-shifted relative to the original fluorescence spectrum. Our simple model reproduces the power broadening and the cascaded fluorescence spectrum, as well as the ratio of cascaded to original photon flux, giving insight into non-Markovian dynamics. Our results establish the longest-distance one-way cascaded atom-photon interface reported to date, providing a stepping stone towards a fiber-based platform for quantum networking.

quant-ph↗

arXiv2024

Multi-Mode Array Filtering of Resonance Fluorescence

We present a novel frequency-filtering method for measuring and calculating frequency-filtered photon-correlations. This novel method is a cavity-based system we call the multi-mode array filter, which consists of an array of tunable single-mode cavities that are equally spaced in frequency. By introducing a mode-dependent phase modulation, we produce a near rectangular frequency response, allowing us to increase the filter bandwidth -- and thus the temporal response -- without sacrificing frequency isolation. We model the frequency filtering using a cascaded quantum open systems approach which completely neglects any back-action of the filter onto the source system. This allows us to derive a closed set of operator moment equations for source and filter system operators, thus providing an extremely efficient method to calculate frequency-filtered first- and second-order correlation functions. We demonstrate this novel filtering method by applying it to a resonantly driven two-level atom. We present examples of frequency-filtered power spectra to demonstrate the improved frequency isolation of the multi-mode array filter over the single-mode filter. We then present results for the single-mode and multi-mode-array filtered second-order auto- and cross-correlation functions. These are compared against expressions derived in the secular approximation. The improved frequency isolation of the multi-mode array filter allows us to investigate new regimes of frequency-filtered photon correlations, such as two-photon leapfrog processes, and the effect of vanishing bandwidth on filtered auto-correlation functions.

quant-ph↗

arXiv2024

Wigner-negative states in the steady-state emission of a two-level system driven by squeezed light

Propagating modes of light with negative-valued Wigner distributions are of fundamental interest in quantum optics and represent a key resource in the pursuit of optics-based quantum information technologies. Most schemes proposed or implemented for the generation of such modes are probabilistic in nature and rely on heralding by detection of a photon or on conditional methods where photons are separated from the original field mode by a beam splitter. In this Letter we demonstrate theoretically, using a cascaded-quantum-systems model, the possibility of deterministic generation of Wigner-negativity in temporal modes of the steady-state emission of a two-level system driven by finite-bandwidth quadrature-squeezed light. Optimal negativity is obtained for a squeezing bandwidth similar to the linewidth of the transition of the two-level system. While the Wigner distribution associated with the incident squeezed light is Gaussian and everywhere positive, the Wigner functions of the outgoing temporal modes show distinct similarities and overlap with a superposition of displaced squeezed states.

quant-ph↗

arXiv2024

Dynamics of a Generalized Dicke Model for Spin-1 Atoms

The Dicke model is a staple of theoretical cavity Quantum Electrodynamics (cavity QED), describing the interaction between an ensemble of atoms and a single radiation mode of an optical cavity. It has been studied both quantum mechanically and semiclassically for two-level atoms, and demonstrates a rich variety of dynamics such as phase transitions, phase multistability, and chaos. In this work we explore an open, spin-1 Dicke model with independent co- and counter-rotating coupling terms as well as a quadratic Zeeman shift enabling control over the atomic energy-level structure. We investigate the stability of operator and moment equations under two approximations and show the system undergoes phase transitions. To compliment these results, we relax the aforementioned approximations and investigate the system semiclassically. We show evidence of phase transitions to steady-state and oscillatory superradiance in this semiclassical model, as well as the emergence of chaotic dynamics. The varied and complex behaviours admitted by the model highlights the need to more rigorously map its dynamics.

quant-ph↗

arXiv2024

Cavity QED systems for steady-state sources of Wigner-negative light

We present a theoretical investigation of optical cavity QED systems, as described by the driven, open Jaynes-Cummings model and some of its variants, as potential sources of steady-state Wigner-negative light. We consider temporal modes in the continuous output field from the cavity and demonstrate pronounced negativity in their Wigner distributions for experimentally-relevant parameter regimes. We consider models of both single and collective atomic spin systems, and find a rich structure of Wigner-distribution negativity as the spin size is varied. We also demonstrate an effective realization of all of the models considered using just a single 87Rb atom and based upon combinations of laser- and laser-plus-cavity-driven Raman transitions between magnetic sublevels in a single ground hyperfine state.

quant-ph↗

arXiv2023

Quantum Fluctuation Dynamics of Dispersive Superradiant Pulses in a Hybrid Light-Matter System

We consider theoretically a driven-dissipative quantum many-body system consisting of an atomic ensemble in a single-mode optical cavity as described by the open Tavis-Cummings model. In this hybrid light-matter system the interplay between coherent and dissipative processes leads to superradiant pulses with a build-up of strong correlations, even for systems comprising hundreds to thousands of particles. A central feature of the mean-field dynamics is a self-reversal of two spin degrees of freedom due to an underlying time-reversal symmetry, which is broken by quantum fluctuations. We demonstrate a quench protocol that can maintain highly non-Gaussian states over long time scales. This general mechanism offers interesting possibilities for the generation and control of complex fluctuation patterns, as suggested for the improvement of quantum sensing protocols for dissipative spin-amplification.

quant-ph↗

arXiv2022

Lasing and counter-lasing phase transitions in a cavity QED system

We study the effect of spontaneous emission and incoherent atomic pumping on the nonlinear semiclassical dynamics of the unbalanced Dicke model -- a generalization of the Dicke model that features independent coupling strengths for the co- and counter-rotating interaction terms. As well as the ubiquitous superradiant behavior the Dicke model is well-known for, the addition of spontaneous emission combined with the presence of strong counter-rotating terms creates laser-like behavior termed counter-lasing. These states appear in the semiclassical model as stable periodic orbits. We perform a comprehensive dynamical analysis of the appearance of counter-lasing in the unbalanced Dicke model subject to strong cavity dissipation, such that the cavity field can be adiabatically eliminated to yield an effective Lipkin-Meshkov-Glick (LMG) model. If the coupling strength of the co-rotating interactions is small, then the counter-lasing phase appears via a Hopf bifurcation of the de-excited state. We find that if the rate of spontaneous emission is small, this can lead to resurgent superradiant pulses. However, if the co-rotating coupling is larger, then the counter-lasing phase must emerge via the steady-state superradiant phase. Such a transition is the result of the competition of the coherent and incoherent processes that drive superradiance and counter-lasing, respectively. We observe a surprisingly complex transition between the two, associated with the formation of a chaotic attractor over a thin transitional parameter region.

quant-ph↗

arXiv2021

Interference-induced directional emission from an unpolarized two level emitter into a circulating cavity

Chiral coupling between quantum emitters and evanescent fields allows directional emission into nanophotonic devices and is now considered to be a vital ingredient for the realization of quantum networks. However, such coupling requires a well defined circular dipole moment for the emitter -- something difficult to achieve for solid state emitters at room temperature due to thermal population of available spin states. Here, we demonstrate that a two level emitter with a randomly polarized dipole moment can be made to emit directionally into a circulating cavity if a separate emitter is chirally coupled to the same cavity, for the case when both emitter-cavity couplings are strong but in the bad-cavity regime. Our analysis of this system first considers a transient scenario, which highlights the physical mechanism giving rise to the directional emission of the two level emitter into the cavity. An alternative setup involving a weak laser field continuously driving the system is also considered, where the directionality (our proposed figure of merit for this scheme) is shown to be significantly more robust against noise processes. The results presented here take the form of approximate analytical expressions backed by complete numerical simulations of the system.

quant-ph↗

arXiv2021

Generation of Spin Cat States in an Engineered Dicke Model

We study trajectories of collective spin states of an ensemble of spinors. The spinors considered here are either trapped ions in free space or atoms confined in a cavity, both systems of which are engineered through their interactions with light fields to obey an effective Dicke model. In an appropriate limit of the Dicke model, one obtains one-axis twisting dynamics of the collective spin and evolution after a finite time to a spin cat state, or, in the long-time limit, the Dicke state $|S,0\rangle_x$, conditioned upon there being no photon emissions from the system (i.e., no quantum jumps). If there is a jump, however, the system evolves probabilistically into one of a finite number of entangled-state cycles, where the system then undergoes a persistent sequence of jumps between two Dicke state superpositions in a rotated basis. The different cycles can be distinguished by the frequency at which jumps occur.

quant-ph↗