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arXiv:2003.09939 · Physical Review Research

Majorana representation of adiabatic and superadiabatic processes in three-level systems

Shruti Dogra, Antti P. Vepsäläinen, Gheorghe Sorin Paraoanu

Published Oct 15, 2020• 16 citations
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Abstract

This work explores the two-star Majorana representation of adiabatic and superadiabatic stimulated Raman passage in a three-level system. The authors derive the counteradiabatic Hamiltonian and provide a generalization of this geometrical picture to mixed states.
DOI
10.1103/physrevresearch.2.043079

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The superadiabatic quantum driving, producing a perfect adiabatic transfer on a given Hamitonian by introducing an additional Hamiltonian, is theoretically analysed for transfers within a three-level system. Our starting point is the stimulated Raman adiabatic passage, realized through different schemes of laser pulses. We determine the superadiabatic correction for each scheme. The fidelity, robustness and transfer time of all the superadiabatic transfer schemes are discussed. We derive that all superadiabatic corrections are based on a πππ- (or near-πππ)-area pulse coupling between the initial and final states. The benefits in the protocol robustness overcome the difficulties associated to the actual implementation of the three-level superadiabatic transfer.
Quantum control methods for three-level systems have become recently an important direction of research in quantum information science and technology. Here we present numerical simulations using realistic experimental parameters for quantum process tomography in STIRAP (stimulated Raman adiabatic passage) and saSTIRAP (superadiabatic STIRAP). Specifically, we identify a suitable basis in the operator space as the identity operator together with the 8 Gell-Mann operators, and we calculate the corresponding process matrices, which have 9 × 9=81 elements. We discuss these results for the ideal decoherence-free case, as well as for the experimentally-relevant case with decoherence included.
We propose a scheme which can produce desired nonadiabatic passages for the stimulated Raman transition in three-level systems. The state transfer in the protocol is realized by following the evolution of the dynamical basis itself and no additional coupling field is required. We also investigate the interplay between the present nonadiabatic passages and the shortcut to adiabaticity. By incorporating the latter technology, we show that alternative passages with less occupancy of the intermediate level could be designed.
The Hamiltonian encoding is a means for revealing the mechanism of controlled quantum dynamics. In this context, the mechanism is defined by the dominant quantum pathways starting from the initial state and proceeding through a set of intermediate states to end at the final state. The nature and interpretation of the mechanism depends on the choice of the states to represent the dynamics. Alternative representations may provide distinct insights into the system mechanism, and representations producing fewer pathways are especially interesting. In addition, a suitable choice of representation may highlight the role of certain couplings in a system that would normally be masked by other, higher magnitude couplings. A simple three-level system is chosen for illustration, where different values for the Rabi frequencies lead to mechanistic analyses that are best described in terms of particular representations. As an examlple, the role of the nonadiabatic terms in stimulated Raman adiabatic passage dynamics is analyzed through the Hamiltonian encoding.