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Simulations of dynamics of ultra-cold quantum plasma

Andrej Rendek

Published Jan 1, 2022• 0 citations
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Abstract

Title: Simulations of dynamics of ultra-cold quantum plasma Author: Andrej Rendek Department: Department of Surface and Plasma Science Supervisor: Mgr. Michal Hejduk, Ph.D., Department of Surface and Plasma Science Abstract: We investigate the confinement of charged particles in an oscillating electromagnetic field, intending to trap electrons and calcium ions simultaneously. The theoretical part of this thesis focuses on the derivation of exact and effective potentials in a single frequency quadrupole trap. We show a general treatment of stability in such a field. Passing attained knowledge onto two-frequency trapping, which is much more suitable for confining two species with widely different charge-to-mass ratios. We follow up by studying the stability of electrons, employing computer simulations in the ideal two- frequency Paul trap. Our ambition is to identify a stable configuration minimizing electrons' temperature. We create multiple ion Coulomb crystals and examine the effect of their presence on electrons' stability. These efforts support the development of an experiment with the ambition to create and study quantum plasma. The composition of this experiment is outlined here as well. Keywords: Ion trapping, Coulomb crystal, Two frequency Paul trap

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We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for ${\mathit{q}}_{\mathit{z}}$\ensuremath{\lesssim}0.6, whereas rapid heating is seen for ${\mathit{q}}_{\mathit{z}}$=0.8.

Physical Review Letters•Jun 10, 1991•65 citations
Title: Simulations of dynamics of ultra-cold quantum plasma Author: Andrej Rendek Department: Department of Surface and Plasma Science Supervisor: Mgr. Michal Hejduk, Ph.D., Department of Surface and Plasma Science Abstract: We investigate the confinement of charged particles in an oscillating electromagnetic field, intending to trap electrons and calcium ions simultaneously. The theoretical part of this thesis focuses on the derivation of exact and effective potentials in a single frequency quadrupole trap. We show a general treatment of stability in such a field. Passing attained knowledge onto two-frequency trapping, which is much more suitable for confining two species with widely different charge-to-mass ratios. We follow up by studying the stability of electrons, employing computer simulations in the ideal two- frequency Paul trap. Our ambition is to identify a stable configuration minimizing electrons' temperature. We create multiple ion Coulomb crystals and examine the effect of their presence on electrons' stability. These efforts support the development of an experiment with the ambition to create and study quantum plasma. The composition of this experiment is outlined here as well. Keywords: Ion trapping, Coulomb crystal, Two frequency Paul trap
Molecular dynamics simulations of ion Coulomb crystals in linear Paul traps allow for the extraction of properties such as ion temperature and ion counts enabling the investigation of ion chemistry in the ultra-cold regime. These simulations reproduce experimental CCD images using density plots of simulated ions allowing for comparisons to be drawn between simulated and experimental results and providing information inaccessible to the researcher, such as the locations of clouds of non- uorescing species. In this thesis, a method for creating these simulated CCD images is presented, as well as the demonstration of a fourth order integrator for producing more accurate calculations of the ion energy. The simulation of a single frequency Paul trap is presented and the ability to match simulations with experimental parameters as inputs to experimental results is demonstrated in order to show that the simulations that have been constructed can be used to analyze experimental data and work as a predictive lab tool for future explorations of ultra-cold chemistry.
The quadrupole linear Paul trap is one of the key instruments in building highly stable atomic clocks. However, a frequency reference based on a single trapped ion is limited in stability due to the time needed for the interrogation cycle which cannot be further shortened. A promising strategy is the utilization of multiple trapped ions. The ions of the same kind then repulse each other with the Coulomb force, which is countered by the ponderomotive force of the time depended field in the trap. A few ions form a chain along the axis of a linear Paul trap. Adding more ions (a few tens or hundreds) gives rise to Coulomb crystals. We created an efficient simulation code which calculates the motion of such collections of ions in quasi-static radiofrequency fields of real linear quadrupole traps (including the micromotion). We include a model for laser cooling of the ions. The simulation tool can be used to study the formation and the dynamics of Coulomb crystals under conditions corresponding to various experimental setups.
We present a theoretical study of trapping an electron in a two-frequency Paul trap, motivated by future hybrid architecture consisting of a doubly charged calcium ion (Ca2+^{2+}2+) and an electron. By isolating the electron from ionic-electron interactions, we formulate the equations of motion for the electron in the time-dependent trap potentials and cast them in the Hill form. Stability and dynamics are then analysed in terms of the dimensionless q-parameters, which encode the applied voltages, drive frequencies, trap geometry, and the particle's charge-to-mass ratio. Under the combined action of the two radio-frequency fields, the trapped electron's classical motion is shown to be approximated well by a slow secular oscillation modulated by two distinct motion sidebands originating from the low- and high-frequency RF drives. The approximation method presented here enables a quick evaluation of the relation between the device-design q-parameters and the electron motion. It offers a crucial foundation for developing physical models of electron-ion interactions in electron-ion traps.
Ultracold neutral plasmas represent a regime of plasmas that is not entirely described by theory, but is critical to our understanding of many phenomena. Though their low temperature makes observing them more manageable, even "confined" ultracold plasmas do not remain contained for more than a few hundred microseconds. No steady state or long-term confinement of an ultracold plasma created by pulse ionization has ever been demonstrated. In this thesis, the construction of a Penning trap for calcium ultracold neutral plasma is presented. The trap consists of a uniform magnetic field to trap the electrons radially and a quadrupole electric field to trap them in the axial direction, under the hypothesis that the space charge of the electrons will trap the ions. To the best of the author's knowledge, no ion trap of this configuration has been used to confine ultracold neutral plasmas. In addition to the Penning trap, this thesis also presents work done on other projects. This includes data acquisition and analysis on freely expanding ultracold neutral plasmas with varying density gradients, research on dielectric discharge barrier plasmas, and presentations given on these subjects. Finally, a short list of skills developed over the course of this program is given.
We have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V.S. Melezhik et. al., Phys. Rev. A100, 063406 (2019)). The important element of the hybrid atom-ion systems is the electromagnetic Paul trap confining the charged ion. The oscillating motion of the confined ion is defined by two frequencies of the Paul trap. It is the frequency of the order of 100 kHz due to the constant electric field and the radio-frequency of about 1-2 MHz defined by the alternating electromagnetic field of the ion trap. The necessity to accurately treat the ion motion in the combined field with two time scales defined by these two very different frequencies has demanded to develop the stable computational scheme for integration of the classical Hamilton equations for the ion motion. Moreover, the scheme must be stable on rather long time-interval of the ion collision with the cold atom ∼ 10 × 2/ defined by the atomic trap frequency ∼ 10 kHz and in the moment of the atom-ion collision when the Hamilton equations are strongly coupled. The developed numerical method takes into account all these features of the problem and makes it possible to integrate the system of coupled quantum-semiclassical equations with the necessary accuracy and quantitatively describes the processes of atomic-ion collisions in hybrid traps, including resonance effects.
We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for qz{\mathit{q}}_{\mathit{z}}qz​\ensuremath{\lesssim}0.6, whereas rapid heating is seen for qz{\mathit{q}}_{\mathit{z}}qz​=0.8.