Robust population transfer by a detuning sign jump: from two-state quantum system to SU(2)-symmetric three-state quantum system
Peter Chernev, Andon A. Rangelov
TL;DR
The paper tackles robust population transfer in driven quantum systems by introducing a detuning-sign-jump protocol: a smooth coupling envelope paired with a fast sign flip of the detuning at the pulse maximum induces a single nonadiabatic event in an otherwise adiabatic evolution. The two-level dynamics are solved in an adiabatic–sudden framework, yielding a compact final-propagator result where the inversion fidelity depends only on the mixing-angle change $\delta\theta$, i.e., on the ratio $\Omega_0/\Delta_0$. The authors extend the approach to an SU(2)-symmetric three-state chain via the Majorana decomposition, obtaining closed-form three-state propagators from the two-level Cayley–Klein parameters and explicit transition probabilities for all initial states; in the strong-coupling limit this yields near-complete transfer between the outer states with minimal population in the middle state. Numerical simulations corroborate the analytic predictions and demonstrate robustness against parameter variations, while the proposed implementations span spin, optical, molecular, and multistate systems. Overall, the work provides a simple, analytically transparent, and robust route to controlled population transfer in both two- and three-state SU(2)-symmetric quantum systems, with practical relevance for quantum control and information processing.
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 Schrödinger 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.