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Physical Review A

Effect of spontaneous emission on the shortcut to adiabaticity in three-state systems

Xuan Shi, Hongquan Zhao

Published Nov 24, 2021• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.104.052221

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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⟩|2\ensuremath{\rangle}∣2\ensuremath⟩ in STA can be sufficiently ignored in the cases of the dark-state evolution and quantum overdamping, since the state ∣2\ensuremath⟩|2\ensuremath{\rangle}∣2\ensuremath⟩ is thoroughly separated from the three-state system. Moreover, the diabatic transitions induced by the spontaneous emission are also sufficiently suppressed in STA.
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.
Shortcuts to adiabaticity (STA) is a common protocol to realize high-fidelity and robust quantum control in various quantum systems. To date, STA has been widely applied in two- and three-level systems, whereas designing feasible strategies to achieve perfect quantum state engineering in multi-level systems still remains a challenging task. Here, we propose to use counterdiabatic (CD) driving and time-rescaling (TR) methods to construct multi-state stimulated Raman shortcut-to-adiabatic passage protocols for realizing robust and fast population transfer in chainwise-connected five-state systems. The first protocol is implemented by initially reducing the original five-state system to an equivalent two-state counterpart, and then designing the corresponding driving field by combining CD driving and unitary transformation. Further, we introduce the TR method to optimize the first protocol and thus offers an alternative solution. Numerical calculations show that both protocols can achieve complete population transfer and effectively suppress transient populations of all intermediate states. Compared with the first protocol, the optimized second exhibits better performance within a shorter evolution time.
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 The fractional shortcut to adiabaticity (f-STA) for the production of quantum superposition states is proposed firstly via a three-level system with a Λ-type linkage pattern and a four-level system with a tripod structure. The fast and robust production of the coherent superposition states is studied by comparing the populations for the f-STA and the fractional stimulated Raman adiabatic passage (f-STIRAP). The states with equal proportions can be produced by fixing the controllable parameters of the driving pulses at the final moment of the whole process. The effects of the pulse intensity and the time delay of the pulses on the production process are discussed by monitoring the populations on all of the quantum states. In particular, the spontaneous emission arising from the intermediate state is investigated by the quantum master equation. The result reveals that the f-STA exhibits superior advantages over the f-STIRAP in producing the superposition states.
We propose a method to improve the stimulated Raman adiabatic passage (STIRAP) via dissipative quantum dynamics, taking into account the dephasing effects. Fast and robust population transfer can be obtained with the scheme by the designed pulses and detuning, even though the initial state of the system is imperfect. With a concrete three-level system as an example, the influences of the imperfect initial state, variations in the control parameters, and various dissipation effects are discussed in detail. The numerical simulation shows that the scheme is insensitive to moderate fluctuations of experimental parameters and the relatively large dissipation effects of the excited state. Furthermore, the dominant dissipative factors, namely, the dephasing effects of the ground states and the imperfect initial state are no longer undesirable, in fact, they are the important resources to the scheme. Therefore, the scheme could provide more choices for the realization of the complete population transfer in the strong dissipative fields where the standard stimulated Raman adiabatic passage or shortcut schemes are invalid.
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.