Counterdiabatic driving for random-gap Landau-Zener transitions

2026/01/15 by Georgios Theologou, Mikkel F. Andersen, Sandro Wimberger · 1 voice
Physics and Astronomy · #quant-ph #physics.atom-ph

paper · pdf · doi:10.1088/1751-8121/ae2c28

Abstract

The Landau--Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing. In the adiabatic limit, the transition probability vanishes. An auxiliary control field H_CD can be reverse-engineered so that the full Hamiltonian H₀ + H_CD reproduces adiabaticity for all parameter values. Our aim is to construct a single control field H₁ that drives an ensemble of LZ-type Hamiltonians with a distribution of energy gaps. H₁ works best statistically, minimizing the average transition probability. We restrict our attention to a special class of H₁ controls, motivated by H_CD. We found a systematic trade-off between instantaneous adiabaticity and the final transition probability. Certain limiting cases with a linear sweep can be treated analytically; one of them being the LZ system with Dirac δ(t) function. Comprehensive and systematic numerical simulations support and extend the analytic results.

Citations

• Geodesic Paths for Quantum Many-Body Systems
• Matrix exponential solution of the Landau-Zener problem
• Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)

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