Abstract

We study qubit manipulations by a train of pulses in a systematic approach based on the Magnus expansion and Furry representation in quantum electrodynamics. Furry–Magnus expansion gives approximate exponential representation of a time-evolution operator without the Dyson time-ordering procedure for interactions with external fields of arbitrary intensity and allows us to obtain general expression for single-qubit populations as a function of time-dependent Rabi frequency. The concrete calculations are performed for tunneling quantum dynamics, for multiphoton resonance interactions of qubits, as well as for off-resonance excitations of qubits driven by Gaussian pulses beyond rotating wave approximation. In this way, the populations of qubit states are investigated for various operational regimes, including single-pulse excitation and two-pulse excitation with a phase shift between pulse envelopes being the controlling parameter, and for excitation with sequential pulses. In the last case, we demonstrate the formation of quasi-energetic states and quasi-energies of qubits driven by a train of identical pulses. In this case the transition probability of the qubit generally exhibiting aperiodic oscillations becomes periodically regular for definite values of the quasi-energy.

© 2016 Optical Society of America

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