Numerical Investigations of Electron Dynamics in a Linear Paul Trap

Trapped electrons have emerged as an interesting platform for quantum information processing due to their light mass, two-level spin states, and potential for fully electronic manipulation. Previous experiments have demonstrated electron trapping in Penning traps, Paul traps, on solid neon, and superfluid films. In this work, we consider electrons confined in Paul traps, with their spin states as the qubits. For this approach, if the two electrons are trapped in the same potential well, they must form Wigner crystals and remain stable under a static magnetic field to enable two-qubit gates, achievable only within certain trapping parameters. To identify feasible operating conditions, we performed numerical simulations of electron dynamics in linear Paul traps, finding the threshold temperatures required to form two-electron Wigner crystals and studying how the thresholds scale with trap frequencies. In addition, we numerically verified the cooling methods required to reach the crystallization thresholds. Lastly, we examined the stability of electrons under various magnetic field strengths and identified stable regions of trap operation.