arXiv subjects

Scott E. Parker

Publications and source records attributed to Scott E. Parker.

16 recordsLinked to original sources

arXiv2026

Optimizing Doppler laser cooling protocols for quantum sensing with 3D ion crystals in a Penning trap

Large, 3D trapped ion crystals offer improved sensitivity in quantum sensing protocols, and are expected to be implemented as platforms in near-future experiments. However, numerical techniques used to study the laser cooling of such crystals are inefficient as the number of ions, $N$, in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to $10^5$ ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated $\boldsymbol{E}\times\boldsymbol{B}$ modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.

quant-ph↗

arXiv2025

Adiabatic Cooling of Planar Motion in a Penning Trap Ion Crystal to Sub-Millikelvin Temperatures

Two-dimensional planar ion crystals in a Penning trap are a platform for quantum information science experiments. However, the low-frequency planar modes of these crystals are not efficiently cooled by laser cooling, which can limit the utility of the drumhead modes for quantum information processing. Recently, it has been shown that nonlinear mode coupling can enhance the cooling of the low-frequency planar modes. Here, we demonstrate in numerical simulations that this coupling can be dynamically tuned by adiabatically changing the rotation frequency of the ion crystal during experiments. Furthermore, we show that this technique can, in addition, produce lower temperatures for the low-frequency planar modes via an adiabatic cooling process. This result allows cooling of the planar modes to sub-millikelvin temperatures, resulting in improved spectral resolution of the drumhead modes at experimentally relevant rotation frequencies, which is crucial for quantum information processing applications.

quant-ph↗

arXiv2025

Saturation of the kinetic ballooning instability due to the electron parallel nonlinearity

The electron parallel nonlinearity (EPN) is implemented in the gyrokinetic Particle-in-Cell turbulence code GEM [Y. Chen and S. E. Parker, J. Comp. Phys. 220, 839 (2007)]. Application to the Cyclone Base Case reveals a strong effect of EPN on the saturated heat transport above the kinetic ballooning mode threshold. Evidence is provided to show that the strong effect is associated with the electron radial motion due to magnetic fluttering, which turns fine structures of the KBM eigenmode in radius into fine structures in velocity and increases the magnitude of the EPN term in the kinetic equation.

physics.plasm-ph↗

arXiv2024

Numerical Simulations of 3D Ion Crystal Dynamics in a Penning Trap using the Fast Multipole Method

We simulate the dynamics, including laser cooling, of 3D ion crystals confined in a Penning trap using a newly developed molecular dynamics-like code. The numerical integration of the ions' equations of motion is accelerated using the fast multipole method to calculate the Coulomb interaction between ions, which allows us to efficiently study large ion crystals with thousands of ions. In particular, we show that the simulation time scales linearly with ion number, rather than with the square of the ion number. By treating the ions' absorption of photons as a Poisson process, we simulate individual photon scattering events to study laser cooling of 3D ellipsoidal ion crystals. Initial simulations suggest that these crystals can be efficiently cooled to ultracold temperatures, aided by the mixing of the easily cooled axial motional modes with the low frequency planar modes. In our simulations of a spherical crystal of 1,000 ions, the planar kinetic energy is cooled to several millikelvin in a few milliseconds while the axial kinetic energy and total potential energy are cooled even further. This suggests that 3D ion crystals could be well-suited as platforms for future quantum science experiments.

quant-ph↗

arXiv2024

Rapid cooling of the in-plane motion of two-dimensional ion crystals in a Penning trap to millikelvin temperatures

We propose a highly feasible technique with no experimental overhead to rapidly cool the in-plane degrees of freedom of large two-dimensional ion crystals in Penning traps. Through simulations, we demonstrate that our approach enables the in-plane modes to cool down to a temperature of around 1 mK in less than 10 ms. Our technique relies on near-resonant coupling of the poorly cooled in-plane motions and the efficiently cooled out-of-plane motions, and is achieved without introducing additional potentials. The rapid cooling enabled by our approach is in contrast to typical operating conditions, where our simulations of the laser cooling dynamics suggest that the ion crystal's in-plane motion cools very slowly on a timescale of several hundreds of milliseconds, a rate likely slower than experimental heating rates. Our work sets the stage for sub-Doppler laser cooling of the planar motion, and more robust and versatile quantum simulation and quantum sensing experiments with two-dimensional crystals in Penning traps.

quant-ph↗

arXiv2023

Comparison of saturation rules used for gyrokinetic quasilinear transport modeling

Theory-based transport modeling has been widely successful and is built on the foundations of quasilinear theory. Specifically, the quasilinear expression of the flux can be used in combination with a saturation rule for the toroidal mode amplitude. Most transport models follow this approach. Saturation rules are heuristic and difficult to rigorously derive. We compare three common saturation rules using a fairly accurate quasilinear expression for the fluxes computed using local linear gyrokinetic simulation. We take plasma parameters from experimental H-mode profiles and magnetic equilibrium and include electrons, Deuterium, and Carbon species. We find that the various saturation rules give qualitatively similar behavior. This may help explain why the different theory-based transport models can all predict core tokamak profiles reasonably well. Comparisons with nonlinear local and global gyrokinetic simulations are also discussed.

physics.plasm-ph↗

arXiv2023

Correspondence between open bosonic systems and stochastic differential equations

Bosonic mean-field theories can approximate the dynamics of systems of $n$ bosons provided that $n \gg 1$. We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment and the mean-field theory is replaced by a stochastic differential equation. When the $n \to \infty$ limit is taken, the stochastic terms in this differential equation vanish, and a mean-field theory is recovered. Besides providing insight into the differences between the behavior of finite quantum systems and their classical limits given by $n \to \infty$, the developed mathematics can provide a basis for quantum algorithms that solve some stochastic nonlinear differential equations. We discuss conditions on the efficiency of these quantum algorithms, with a focus on the possibility for the complexity to be polynomial in the log of the stochastic system size. A particular system with the form of a stochastic discrete nonlinear Schrödinger equation is analyzed in more detail.

quant-ph↗

arXiv2021

Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously-studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.

physics.plasm-ph↗

arXiv2021

Equilibration of the planar modes of ultracold two dimensional ion crystals in a Penning trap

Planar thermal equilibration is studied using direct numerical simulations of ultracold two-dimensional (2D) ion crystals in a Penning trap with a rotating wall. The large magnetic field of the trap splits the modes that describe in-plane motion of the ions into two branches: High frequency cyclotron modes dominated by kinetic energy and low frequency $\mathbf{E \times B}$ modes dominated by potential energy associated with thermal position displacements. Using an eigenmode analysis we extract the equilibration rate between these two branches as a function of the ratio of the frequencies that characterize the two branches and observe this equilibration rate to be exponentially suppressed as the ratio increases. Under experimental conditions relevant for current work at NIST, the predicted equilibration time is orders of magnitude longer than any relevant experimental timescales. We also study the coupling rate dependence on the thermal temperature and the number of ions. Besides, we show how increasing the rotating wall strength improves crystal stability. These details of in-plane mode dynamics help set the stage for developing strategies to efficiently cool the in-plane modes and improve the performance of single-plane ion crystals for quantum information processing.

physics.plasm-ph↗

arXiv2020

Excitation of Zonal Flow by Intermediate-Scale Toroidal Electron Temperature Gradient Turbulence

We show that zonal flow can be preferentially excited by intermediate-scale toroidal electron temperature gradient (ETG) turbulence in tokamak plasmas. Previous theoretical studies that yielded an opposite conclusion assumed a fluid approximation for ETG modes. Here, we carry out a gyrokinetic analysis which ultimately yields a nonlinear Schrödinger equation for the ETG dynamics with a Navier-Stokes type nonlinearity. For typical tokamak parameters, it is found that zonal flow generation plays an important role in the intermediate-scale ETG turbulence. This finding offers an explanation for recent multi-scale gyrokinetic simulations.

physics.plasm-ph↗

arXiv2019

Quantum Algorithm for the Vlasov Equation

The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution function, we convert the Vlasov-Maxwell system into a Hamiltonian simulation problem. Then for the limiting case of electrostatic Landau damping, we design and verify a quantum algorithm, appropriate for a future error-corrected universal quantum computer. While the classical simulation has costs that scale as $\mathcal{O}(N_v t)$ for a velocity grid with $N_v$ grid points and simulation time $t$, our quantum algorithm scales as $\mathcal{O}(\text{polylog}(N_v) t/δ)$ where $δ$ is the measurement error, and weaker scalings have been dropped. Extensions, including electromagnetics and higher dimensions, are discussed. A quantum computer could efficiently handle a high-resolution, six-dimensional phase-space grid, but the $1/δ$ cost factor to extract an accurate result remains a difficulty. This paper provides insight into the possibility of someday achieving efficient plasma simulation on a quantum computer.

quant-ph↗

arXiv2019

Efficient Fourier Basis Particle Simulation

The standard particle-in-cell algorithm suffers from grid heating. There exists a gridless alternative which bypasses the deposition step and calculates each Fourier mode of the charge density directly from the particle positions. We show that a gridless method can be computed efficiently through the use of an Unequally Spaced Fast Fourier Transform (USFFT) algorithm. After a spectral field solve, the forces on the particles are calculated via the inverse USFFT (a rapid solution of an approximate linear system). We provide one and two dimensional implementations of this algorithm with an asymptotic runtime of $O(N_p + N_m^D \log N_m^D)$ for each iteration, identical to the standard PIC algorithm (where $N_p$ is the number of particles and $N_m$ is the number of Fourier modes, and $D$ is the spatial dimensionality of the problem) We demonstrate superior energy conservation and reduced noise, as well as convergence of the energy conservation at small time steps.

physics.plasm-ph↗

arXiv2019

First principle simulation of ultra-cold ion crystals in a Penning trap with Doppler cooling and a rotating wall potential

A direct numerical simulation of many interacting ions in a Penning trap with a rotating wall is presented. The ion dynamics is modelled classically. Both axial and planar Doppler laser cooling are modeled using stochastic momentum impulses based on two-level atomic scattering rates. The plasmas being modeled are ultra-cold two-dimensional crystals made up of 100's of ions. We compare Doppler cooled results directly to a previous linear eigenmodes analysis. Agreement in both frequency and mode structure are obtained. Additionally, when Doppler laser cooling is applied, the laser cooled steady state plasma axial temperature agrees with the Doppler cooling limit. Numerical simulations using the approach described and benchmarked here will provide insights into the dynamics of large trapped-ion crystals, improving their performance as a platform for quantum simulation and sensing.

physics.plasm-ph↗

arXiv2017

Verification of long wavelength electromagnetic modes with a gyrokinetic-fluid hybrid model in the XGC code

As an alternative option to kinetic electrons, the gyrokinetic total-f particle-in-cell (PIC) code XGC1 has been extended to the MHD/fluid type electromagnetic regime by combining gyrokinetic PIC ions with massless drift-fluid electrons analogous to Chen and Parker, Physics of Plasmas 8, 441 (2001). Two representative long wavelength modes, shear Alfvén waves and resistive tearing modes, are verified in cylindrical and toroidal magnetic field geometries.

physics.plasm-ph↗

arXiv2012

Global Gyrokinetic Simulation of Tokamak Edge Pedestal Instabilities

Global electromagnetic gyrokinetic simulations show the existence of near threshold conditions for both a high-$n$ kinetic ballooning mode (KBM) and an intermediate-$n$ kinetic version of peeling-ballooning mode (KPBM) in the edge pedestal of two DIII-D H-mode discharges. When the magnetic shear is reduced in a narrow region of steep pressure gradient, the KPBM is significantly stabilized, while the KBM is weakly destabilized and hence becomes the most-unstable mode. Collisions decrease the KBM's critical $β$ and increase the growth rate.

physics.plasm-ph↗

arXiv2009

Natural Fueling of a Tokamak Fusion Reactor

A natural fueling mechanism that helps to maintain the main core deuterium and tritium (DT) density profiles in a tokamak fusion reactor is discussed. In H-mode plasmas dominated by ion- temperature gradient (ITG) driven turbulence, cold DT ions near the edge will naturally pinch radially inward towards the core. This mechanism is due to the quasi-neutral heat flux dominated nature of ITG turbulence and still applies when trapped and passing kinetic electron effects are included. Fueling using shallow pellet injection or supersonic gas jets is augmented by an inward pinch of could DT fuel. The natural fueling mechanism is demonstrated using the three-dimensional toroidal electromagnetic gyrokinetic turbulence code GEM and is analyzed using quasilinear theory. Profiles similar to those used for conservative ITER transport modeling that have a completely flat density profile are examined and it is found that natural fueling actually reduces the linear growth rates and energy transport.

physics.plasm-ph↗