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

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 non-adiabatic 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 non-adiabatic transitions. Finally, we provide an extension of these results to mixed states and processes with decoherence.

Comments are welcome

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Cited by in corpus (8)

• The shape of higher-dimensional state space: Bloch-ball analog for a qutrit
• Majorana's approach to nonadiabatic transitions validates the adiabatic-impulse approximation
• Entangling power of symmetric two-qubit quantum gates
• Quantum Polarimetry
• Experimental realization of phase-controlled dynamics with hybrid digital-analog approach
• Coherent interaction-free detection of microwave pulses with a superconducting circuit
• Experimental demonstration of robustness under scaling errors for superadiabatic population transfer in a superconducting circuit
• Quantum process tomography of adiabatic and superadiabatic stimulated Raman passage