Optimal control of population transfer in multi-level systems by dynamical quantum geometric tensor

TL;DR

This paper introduces a quantum geometric tensor-based framework for optimizing population transfer in multi-level systems, significantly improving efficiency and speed over traditional methods, with detailed analysis and parameter influence studies.

Contribution

It develops a novel quantum geometric tensor approach for optimal control in multi-level systems, enhancing transfer efficiency and robustness compared to traditional STIRAP.

Findings

Optimal STIRAP achieves over 98% transfer efficiency.

Traditional STIRAP has about 72% efficiency.

Resonance window pulse parameters reduce infidelity below 10^-3.

Abstract

The optimal control of population transfer for multi-level systems is investigated from the perspective of quantum geometry. Firstly, the general theoretical framework of optimizing the stimulated Raman adiabatic passage (STIRAP) scheme based on the dynamical quantum geometric tensor is given, and then the dynamical quantum geometric tensor and the nonadiabatic transition rate are calculated by taking the detuned $\Lambda$-type three-level system and tripod-type four-level system for example. Secondly, the transfer dynamics of the particle population of the system are investigated in detail. For a three-level system, the optimal STIRAP scheme has an efficiency of over 98\% in transferring the population to the final state, while the transfer efficiency of traditional STIRAP is about 72\%. The superposition states with arbitrary proportions can be efficiently prepared for a four-level system due to the decoupling of the degenerate dark states. Finally, the influences of system parameters, such as the operation time of the Rabi pulses, the amplitude fluctuation and the single-photon detuning, on the transfer process are discussed. Especially, the phenomenon of the adiabatic resonance transfer is revealed. Choosing the pulse parameters in the resonance window can reduce the infidelity of the population transfer to below $10^{-3}$. It is found that the optimal STIRAP scheme by the dynamical quantum geometric tensor provides faster and more efficient transfer than the traditional STIRAP scheme.