Robust population transfer by a detuning sign jump: from two-state quantum system to SU(2)-symmetric three-state quantum system

TL;DR

This paper introduces a robust population transfer method using a sudden detuning sign change in two- and three-state quantum systems, achieving high fidelity and robustness through a simple analytic approach and extension to SU(2) symmetry.

Contribution

It presents a novel population transfer protocol based on a detuning sign jump, extending it from two-level to SU(2)-symmetric three-state systems with explicit transition probabilities.

Findings

High-fidelity inversion depends only on the ratio of Rabi frequency to detuning.

Numerical simulations confirm robustness over broad parameters.

Almost complete population transfer between outer states with minimal middle state occupation.

Abstract

We propose and analyze a robust population-transfer protocol in a driven two-level system based on a sudden sign change of the detuning at the maximum of a smooth coupling pulse. Away from the jump the dynamics is adiabatic, while the sign flip produces a single nonadiabatic kick in the adiabatic basis. Within a simple stepwise adiabatic-sudden approximation we obtain a compact analytic expression for the final transition probability, identify the parameter regimes that yield high-fidelity inversion, and show that the result depends only on the change of the mixing angle across the detuning jump, i.e., solely on the ratio of the peak Rabi frequency to the detuning. Numerical simulations of the full time-dependent Schr\"odinger equation confirm the validity and robustness of this description over a broad parameter range. We then use the Majorana decomposition to extend the scheme to an SU(2)-symmetric three-state chain driven by the same coupling and detuning functions. In this setting the three-state propagator is expressed in closed form through the two-level Cayley-Klein parameters, which allows us to derive explicit transition probabilities for all three initial states. In particular, we show that for strong coupling the protocol yields almost complete population transfer between the two outer states, with only small transient population of the middle state, while retaining the same intrinsic robustness as in the underlying two-level model.