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Optics Express

Robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control

Xue‐Ke Song, Fei Meng, Bao-Jie Liu, Dong Wang, Liu Ye, Man‐Hong Yung

Published Feb 22, 2021• 27 citations
Publisher

Abstract

The stimulated Raman adiabatic passage 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 general approach to robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control. By controlling the dynamical process, we inversely design a family of Hamiltonians with non-divergent Rabi frequencies that can realize fast and accurate population transfer from the first to the third level, while the systematic errors are 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.

DOI
10.1364/oe.417343

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The stimulated Raman adiabatic passage 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 general approach to robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control. By controlling the dynamical process, we inversely design a family of Hamiltonians with non-divergent Rabi frequencies that can realize fast and accurate population transfer from the first to the third level, while the systematic errors are 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.
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.
Abstract One of the challenging tasks in quantum control is to manipulate quantum systems with high fidelity and as fast as possible. Simulated Raman shortcuts to adiabatic passage with invariant-based optimal control is an efficient technique accurately used to transfer population between two quantum states in three-level systems. This technique requires tuning parameters continuously which results in analog quantum control. However, a digital quantum controller design is of great importance in the era of digital quantum computing. Here, we use deep reinforcement learning to obtain digital Stokes and pump fields that can realize fast and accurate population transfer between states with the same parity in the three-level Λ configuration. We find that deep reinforcement learning follows exactly theshortcuts to adiabaticity (STA) based on dynamical invariant and leads to a robust population transfer against systematic errors and dephasing. This is a promising enhancement in digital quantum information processing.
Stimulated Raman adiabatic passage is a prominent and widely applied technique that transfers population between quantum states in three-level quantum systems. In this paper, we propose an optimized version of stimulated Raman adiabatic passage, which can be implemented faster than the conventional version. In order to achieve quantum adiabaticity in shorter times, we use the geometric optimization method based on the dynamical quantum geometric tensor to regularize nonadiabatic transitions and to eliminate nonadiabatic effects during the evolution process. Optimal stimulated Raman adiabatic passage can shorten the operation time required for adiabatic population transfer appreciably, thereby avoiding decoherence resulting from long-time evolution. Moreover, optimal stimulated Raman adiabatic passage is robust against systematic and random errors. Our results provide an optimal route for the realization of fast and accurate population transfer in three-level quantum systems.
Abstract The multistate stimulated Raman adiabatic passage (STIRAP) is an efficient technique to achieve a selective and accurate population transfer in a chainwise-linked system. However, their efficiency is imperfect due to the nonadiabatic losses from the long runtime of the adiabatic evolution. Here, we focus on realizing a perfect and robust coherent control of the quantum states with optimal shortcut to adiabaticity in a realistic five-state hybrid quantum system. In particular, the optimal shortcut field requires minimal additional coupling (only one coupling strength) to accelerate the adiabatic evolution in this five-state system. Compared to the original STIRAP, the optimal shortcut shows the ultra-high fidelity of quantum state manipulations even though the control parameters of the Hamiltonians are changed in different ways. Furthermore, we study the efficiency of the optimal shortcut field technique in the presence of various experimental errors, such as systematic error, Rabi frequency error, and coupling strength error, and it features a broad range of high efficiencies above 99.9%, showing its robustness against the above errors. The results might shed insight on the further applications of shortcuts to adiabaticity on robust quantum information processing in multi-level quantum systems.
Shortening the operation time of implementing scheme and reducing the influence of harmful factors have always been the research objectives pursued by people. Based on invariant-based reverse engineering, we present a general scheme for implementing robust population transfer in a three-level system via optimal shortcut to adiabatic passage. The systematic error sensitivity is introduced to measure the robustness of the process. The smooth Rabi frequencies are expressed with some coefficients, which are also related to the systematic error sensitivity and the population of intermediate state. When the amplitude of control field is given, the transfer can be optimized within as small systematic error sensitivity as possible, i.e., the robustness against systematic errors is further improved by choosing suitable correlation coefficient. Additionally, we apply the technique to achieve robust excitation fluctuation transfer between two membranes in an optomechanical system. The relation between the fidelity of excitation fluctuation transfer and variation of effective optomechanical coupling strengths is analysed. Numerical result shows that the fidelity keeps over 0.95 even if the coupling strengths deviates from 20% of the theoretical value. Moreover, comparison with existing literature [Opt. Express29, 7998 (2021)10.1364/OE.417343], the proposed scheme possesses stronger robustness against variations of effective optomechanical coupling strengths and lower population of unwanted states. The idea may provide a promising approach for quantum information processing.
The shortcut to adiabaticity (STA) is a powerful technique to speed up population transfer via quantum coherent control. This paper demonstrates that STA provides a fast, robust, and efficient population transfer compared to the stimulated Raman adiabatic passage. In the ideal situation of a closed system, STA is insensitive to the detunings and Rabi frequencies, and the undesired diabatic transitions could be eliminated by the auxiliary pulses, so the complete population transfer from the initial state to the target state in the designed adiabatic passage can be rapidly achieved against the inevitable amplitude noises of the interactions and systematic errors. When we consider the situation including the environment noises, spontaneous emission from the intermediate state $|2\ensuremath{\rangle}$ in STA can be sufficiently ignored in the cases of the dark-state evolution and quantum overdamping, since the state $|2\ensuremath{\rangle}$ is thoroughly separated from the three-state system. Moreover, the diabatic transitions induced by the spontaneous emission are also sufficiently suppressed in STA.