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arXiv:2312.16643 · Physical Review A

Optimal STIRAP shortcuts using the spin-to-spring mapping

Vasileios Evangelakos, Emmanuel Paspalakis, Dionisis Stefanatos

Published May 15, 2023• 14 citations
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Abstract

We derive STIRAP (stimulated Raman adiabatic passage) shortcuts to adiabaticity maximizing population transfer in a three-level $\mathrm{\ensuremath{\Lambda}}$ quantum system, using spin-to-spring mapping to formulate the corresponding optimal control problem on the simpler system of a classical driven dissipative harmonic oscillator. We solve the spring optimal control problem and obtain analytical expressions for the impulses, the durations of the zero control intervals, and the singular control, which are the elements composing the optimal pulse sequence. We also derive suboptimal solutions for the spring problem, one with less impulses than the optimal and others with smoother polynomial controls. We then apply the solutions derived for the spring system to the original system, and compare the population transfer efficiency with that obtained for the original system using numerical optimal control. For all dissipation rates used, the efficiency of the optimal spring control approaches that of the numerical optimal solution for longer durations, with the approach accomplished earlier for smaller decay rates. The efficiency achieved with the suboptimal spring control with less impulses is very close to that of the optimal spring control in all cases, while that obtained with polynomial controls lies below, and this is the price paid for not using impulses, which can quickly build a nonzero population in the intermediate state. The analysis of the optimal solution for the classical driven dissipative oscillator is not restricted to the system at hand but can also be applied in the transport of a coherent state trapped in a moving harmonic potential and the transport of a mesoscopic object in stochastic thermodynamics.

DOI
10.1103/physreva.107.052606

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We derive STIRAP (stimulated Raman adiabatic passage) shortcuts to adiabaticity maximizing population transfer in a three-level \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ quantum system, using spin-to-spring mapping to formulate the corresponding optimal control problem on the simpler system of a classical driven dissipative harmonic oscillator. We solve the spring optimal control problem and obtain analytical expressions for the impulses, the durations of the zero control intervals, and the singular control, which are the elements composing the optimal pulse sequence. We also derive suboptimal solutions for the spring problem, one with less impulses than the optimal and others with smoother polynomial controls. We then apply the solutions derived for the spring system to the original system, and compare the population transfer efficiency with that obtained for the original system using numerical optimal control. For all dissipation rates used, the efficiency of the optimal spring control approaches that of the numerical optimal solution for longer durations, with the approach accomplished earlier for smaller decay rates. The efficiency achieved with the suboptimal spring control with less impulses is very close to that of the optimal spring control in all cases, while that obtained with polynomial controls lies below, and this is the price paid for not using impulses, which can quickly build a nonzero population in the intermediate state. The analysis of the optimal solution for the classical driven dissipative oscillator is not restricted to the system at hand but can also be applied in the transport of a coherent state trapped in a moving harmonic potential and the transport of a mesoscopic object in stochastic thermodynamics.
We use optimal control theory to obtain shortcuts to adiabaticity which maximize population transfer in a three-level stimulated Raman adiabatic passage system, for a given finite duration of the process and a specified dissipation rate at the intermediate state. We fix the sum of the intensities of the pump and Stokes pulses and use the mixing angle of the fields as the sole control variable. We determine the optimal variation of this angle and reveal the role of the singular arc in the optimal trajectory, in order to minimize the effect of dissipation. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
The stimulated Raman adiabatic passage (STIRAP) shows an efficient technique that accurately transfers population between two discrete quantum states with the same parity, in three-level quantum systems based on adiabatic evolution. This technique has widely theoretical and experimental applications in many fields of physics, chemistry, and beyond. Here, we present a generally robust approach to speed up STIRAP with invariant-based shortcut to adiabaticity. By controlling the dynamical process, we inversely design a family of Hamiltonians that can realize fast and accurate population transfer from the first to the third level, while the systematic error is largely suppressed in general. Furthermore, a detailed trade-off relation between the population of the intermediate state and the amplitudes of Rabi frequencies in the transfer process is illustrated. These results provide an optimal route toward manipulating the evolution of three-level quantum systems in future quantum information processing.
STIRAP (stimulated Raman adiabatic passage) has proven to be an efficient and robust technique for transferring population in a three-level system without populating the intermediate state. Here we show that the counterintuitive pulse sequence in STIRAP, in which the Stokes pulse precedes the pump, emerges automatically from a variant of optimal control theory we have previously called ``local'' optimization. Since local optimization is a well-defined, automated computational procedure, this opens the door to automated computation of generalized STIRAP schemes in arbitrarily complicated NNN-level coupling situations. If the coupling is sequential, a simple qualitative extension of STIRAP emerges: the Stokes pulse precedes the pump as in the three-level system. But, in addition, spanning both the Stokes and pump pulses are pulses corresponding to the transitions between the $N\ensuremath{-}2$ intermediate states with intensities about an order of magnitude greater than those of the Stokes and pump pulses. This scheme is amazingly robust, leading to almost 100% population transfer with significantly less population transfer to the $N\ensuremath{-}2$ intermediate states than in previously proposed extensions of STIRAP.
We demonstrate that Optimal Control Theory (OCT) with a state-dependent constraint which depends on the state of the system at each instant can reproduce the famous counterintuitive mechanism of Stimulated Raman adiabatic passage (STIRAP). We examine this behavior in a Λ-type three-level system and we show that could be applied for sequentially coupled many-level systems. We study the robustness of the two methods with respect to pulse fluctuations and the decays. We show that new OCT formulation appears to be more robust than STIRAP when a perturbation is introduced in the pulses. Such method is of great use for systems involving coherence loss such as molecular systems with dissociation or ionization limits. It also may find potential applications in the control of chemical reactions, quantum optics, and quantum information processing.
The stimulated Raman adiabatic passage (STIRAP) allows selective, coherent population transfer in a three-level quantum system by the adiabatic control of two suitably chosen envelopes and delayed laser pulses. However, the long operation time involved with the adiabatic protocols makes them more susceptible to decay and decoherence. A shortcut-to-adiabaticity technique, namely, counterdiabatic driving (CD), suppresses the decoherence-induced loss by speeding up the STIRAP process, thereby enhancing the efficiency and fidelity of population transfer. The superadiabatic STIRAP (saSTIRAP) method requires the application of a shortcut drive or CD pulse, which couples the coherently trapped states in a three-level quantum system. Hence, the closed-loop $\mathrm{\ensuremath{\Lambda}}$ system consisting of all electric dipole-allowed transitions is an essential requirement for saSTIRAP, which is rarely admissible in a natural atom. This paper theoretically investigates an experimentally feasible model for implementing saSTIRAP using a closed-loop $\mathrm{\ensuremath{\Lambda}}$ system with doubly dressed polariton states in a driven circuit QED system. We show a population transfer with efficiencies close to 80.7580.75%80.75 and 98.1098.10%98.10 with fidelities of 89.8689.86%89.86 and 99.0499.04%99.04 for the resonant STIRAP and saSTIRAP protocols, respectively, with experimentally feasible parameters. The efficiency of the population transfer can be further increased by improving the coherence times of the cavity and the transmon qubit. This work may be useful in designing fast, efficient quantum gates for applications in quantum technologies.
We study different mechanisms of adiabatic population transfer in N-level systems by means of optimal control algorithms. Using two-dimensional topographic maps of the yield of population transfer as a function of time delay and intensity of the pulses we analyze the global properties of the schemes and the conditions that lead to optimization. For three-level systems it is shown that the optimal pulse sequence is the well-known STIRAP (stimulated Raman adiabatic passage) scheme. For five-level systems a family of solutions ranging from the alternating STIRAP scheme to the new straddling STIRAP (S-STIRAP) scheme is obtained and the behavior of the solutions is compared. For four-level systems we obtain as optimal a S-STIRAP type sequence that behaves as an effective two-level system. For both odd and even numbers of N-level systems, the crucial role of the straddling pulse in reducing the population of all intermediate levels is demonstrated.