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

Shruti Dogra*, Antti Vepsalainen, G. S. Paraoanu

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

We show that stimulated Raman adiabatic passage (STIRAP) and its superadiabatic version (saSTIRAP) have a natural geometric two-star representation on the Majorana sphere. In the case of STIRAP, we find that the evolution is confined to a vertical plane. A faster evolution can be achieved in the saSTIRAP protocol, which employs a counterdiabatic Hamiltonian to nullify the nonadiabatic excitations. We derive this Hamiltonian in the Majorana picture, and we observe how, under realistic experimental parameters, the counterdiabatic term corrects the trajectory of the Majorana stars toward the dark state. We also introduce a spin-1 average vector and present its evolution during the two processes, demonstrating that it provides a measure of nonadiabaticity. We show that the Majorana representation can be used as a sensitive tool for the detection of process errors due to ac Stark shifts and nonadiabatic transitions. Finally, we provide an extension of these results to mixed states and processes with decoherence.

Original languageEnglish
Article number043079
Number of pages12
JournalPHYSICAL REVIEW RESEARCH
Volume2
Issue number4
DOIs
Publication statusPublished - 15 Oct 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • COHERENT POPULATION TRANSFER
  • QUANTUM
  • GEOMETRY
  • ATOMS
  • PHASE
  • GAS

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