Robust state preparation in quantum simulations of Dirac dynamics

Abstract

A non-relativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between momentum and internal levels poses some difficulties to manipulate the internal states accurately in wave packets. We use invariants of motion to inverse engineer robust population inversion processes with a homogeneous, time-dependent simulated electric field. This exemplifies the usefulness of inverse-engineering techniques to improve the performance of quantum simulation protocols.

8 pages, 7 figures

References in corpus (7)

• Dirac materials
• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Zitterbewegung of electronic wave packets in semiconductor nanostructures
• Quantum simulation of the Klein paradox with trapped ions
• Klein tunneling and Dirac potentials in trapped ions
• Relativistic quantum effects of Dirac particles simulated by ultracold atoms

Cited by in corpus (4)

• Shortcuts to adiabaticity using flow fields
• Optimal shortcut approach based on an easily obtained intermediate Hamiltonian
• Time-rescaling of Dirac dynamics: shortcuts to adiabaticity in ion traps and Weyl semimetals
• Shortcut Scheme for One-Step Implementation of a Three-Qubit Nonadiabatic Holonomic Gate