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

TL;DR

The paper addresses fast, high-fidelity population transfer in multi-level quantum systems by optimizing STIRAP via the dynamical quantum geometric tensor. It formulates a framework where the total nonadiabatic transition rate $\tilde{T}_n(s)$ is minimized and made approximately constant, yielding analytic pulse forms ${\widetilde{\Omega}}_P(s)$ and ${\widetilde{\Omega}}_S( s)$ with $\alpha=\frac{\pi}{2}$ for the three-level case and extending to a tripod four-level system. For the three-level system, the optimized STIRAP achieves $>98\%$ transfer efficiency, substantially exceeding traditional STIRAP, and exhibits adiabatic-resonance windows that enable high fidelity with shorter operation times and lower pulse amplitudes; for the four-level system, decoupling of degenerate dark states and a tunable parameter $\chi$ enable fast, robust preparation of arbitrary superpositions of the final states. The work provides a general, robust control framework for multi-level quantum state transfer and superposition-state engineering, with potential impact on quantum information processing and coherent control of complex atomic and molecular systems.

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 $Λ$-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.

Figures (14)

• Figure 1: Schematic diagram of the STIRAP scheme for a three-level system with single photon detuning
• Figure 2: Rabi pulse's structures and the evolution results of the populations for the three-level system: (a) Pulse structures for the optimal STIRAP; (b) Evolution of the populations for the optimal STIRAP; (c) Pulse structures for the traditional STIRAP; (d) Evolution of the populations for the traditional STIRAP (The pulse operating time $\tau=4\mu s$, the pulse peak $\Omega_0$=30.79MHz, and the detuning $\Delta=2\pi$MHz)
• Figure 3: Variation of the mixing angle with time (The red solid line indicates the mixing angle for the optimal STIRAP and the blue dashed line indicates the mixing angle for the traditional STIRAP)
• Figure 4: Change of the infidelity with time for the three-level system: (a) The case without detuning ($\Delta$=0); (b) The case with detuning ($\Delta$=2$\pi$MHz) (The red solid line corresponds to the optimal STIRAP scheme and the blue dashed line corresponds to the traditional STIRAP one; The pulse peak $\Omega_{0}$=35MHz)
• Figure 5: Variation of the infidelity with the fluctuation of the pulse peak for the three-level system: (a) The case without detuning ($\Delta$=0); (b) The case with detuning ($\Delta$=2$\pi$MHz) (The red solid line denotes the optimal STIRAP scheme and the blue dashed line denotes the traditional STIRAP one; The pulse peak $\Omega_{ 0 }$=35MHz and the operating time $\tau$=7.4$\mu s$)