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Journal of Modern Optics

Shortcuts to adiabaticity in two-level systems: control and optimization

A. Ruschhaupt, Juan Gonzalo Muga

Published Nov 11, 2013• 12 citations
Publisher

Abstract

We review the design and optimization for two-level systems of ‘shortcuts to adiabaticity’ which are stable with respect to noise or systematic deviations. Contrary to common wisdom, adiabatic approaches are not necessarily more stable than fixed-area pulses. ‘Robustness’ is a relative concept that depends on the type of perturbation. Different perturbations correspond to different optimal protocols.

DOI
10.1080/09500340.2013.846431

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We review the design and optimization for two-level systems of ‘shortcuts to adiabaticity’ which are stable with respect to noise or systematic deviations. Contrary to common wisdom, adiabatic approaches are not necessarily more stable than fixed-area pulses. ‘Robustness’ is a relative concept that depends on the type of perturbation. Different perturbations correspond to different optimal protocols.
Abstract Shortcuts to adiabaticity guide given systems to final destinations of adiabatic control via fast tracks. Various methods have been proposed as shortcuts to adiabaticity. The basic theory of shortcuts to adiabaticity was established in the 2010s, but it has still been developing and many fundamental findings have been reported. In this topical review, we give a pedagogical introduction to the theory of shortcuts to adiabaticity and revisit relations between different methods. Some versatile approximations in counterdiabatic driving, which is one of the methods of shortcuts to adiabaticity, will be explained in detail. We also summarize the recent progress in studies of shortcuts to adiabaticity.
Abstract We review methods to shuttle quantum particles fast and robustly. Ideal robustness amounts to the invariance of the desired transport results with respect to deviations, noisy or otherwise, from the nominal driving protocol for the control parameters; this can include environmental perturbations. “Fast” is defined with respect to adiabatic transport times. Special attention is paid to shortcut-to-adiabaticity protocols that achieve, in faster-than-adiabatic times, the same results of slow adiabatic driving.
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.