Elementary laser-less quantum logic operations with (anti-)protons in Penning traps

TL;DR

This paper proposes a method to perform laser-less quantum logic operations on (anti-)protons in Penning traps using magnetic field gradients, enabling high-fidelity SWAP gates for quantum spectroscopy and fundamental tests.

Contribution

It introduces a novel approach for laser-less spin-motion coupling in Penning traps, facilitating quantum logic operations on (anti-)protons with potential applications in precision measurements.

Findings

High-fidelity SWAP gate achievable with proper initialization

Classical and quantum analysis of particle behavior in magnetic gradients

Feasibility of quantum logic spectroscopy in Penning traps

Abstract

Static magnetic field gradients superimposed on the electromagnetic trapping potential of a Penning trap can be used to implement laser-less spin-motion couplings that allow the realization of elementary quantum logic operations in the radio-frequency regime. An important scenario of practical interest is the application to $g$-factor measurements with single (anti-)protons to test the fundamental charge, parity, time reversal (CPT) invariance as pursued in the BASE collaboration [Smorra et al., Eur. Phys. J. Spec. Top. 224, 3055-3108 (2015), Smorra et al., Nature 550, 371-374 (2017), Schneider et al., Science 358, 1081-1084 (2017)]. We discuss the classical and quantum behavior of a charged particle in a Penning trap with a superimposed magnetic field gradient. Using analytic and numerical calculations, we find that it is possible to carry out a SWAP gate between the spin and the motional qubit of a single (anti-)proton with high fidelity, provided the particle has been initialized in the motional ground state. We discuss the implications of our findings for the realization of quantum logic spectroscopy in this system.