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arXiv:1904.09452 · Physical Review Research

Second order phase dispersion by optimized rotation pulses

David L. Goodwin, Martin R. M. Koos, Burkhard Luy

Published Jul 28, 2020• 12 citations
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Abstract

This work presents a new class of pulse to perform a broadband universal rotation on two-level systems, independent of the system preparation, using a phase dispersion function. The authors present a method of optimal control to avoid traps on the control manifold, and find pulses of half the duration compared to the previous best universal rotation pulses.

DOI
10.1103/physrevresearch.2.033157

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This work presents a new class of pulse to perform a broadband universal rotation on two-level systems, independent of the system preparation, using a phase dispersion function. The authors present a method of optimal control to avoid traps on the control manifold, and find pulses of half the duration compared to the previous best universal rotation pulses.
The coherent control of a small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator due to the noncommutation of the pulse and the bath Hamiltonian. The conditions are computed that make the leading corrections vanish. The pulse shapes optimized in this way are given for $\ensuremath{\pi}$ and $\frac{\ensuremath{\pi}}{2}$ pulses.
In the previous paper on this topic it was shown how, for a pulse of arbitrary shape and duration, the drive frequency can be analytically optimized to maximize the amplitude of the population oscillations between the selected two levels in a general many level quantum system. It was shown how the standard Rabi theory can be extended beyond the simple two-level systems. Now, in order to achieve the quickest and as complete as possible population transfer between two pre-selected levels, driving pulse should be tailored so that it produces only a single half-oscillation of the population. In this paper, this second (and final) step towards the controlled population transfer using modified (i.e. many level system) Rabi oscillations is discussed. The results presented herein can be regarded as an extension of the standard πππ-pulse theory - also strictly valid only in the two level systems - to the coherently driven population oscillations in general many level systems.
We study the interplay between rotating-wave approximation and optimal control. In particular, we show that for a wide class of optimal control problems one can choose the control field such that the Hamiltonian becomes time independent under the rotating-wave approximation. Thus, we show how to recast the functional minimization defined by the optimal control problem into a simpler multivariable function minimization. We provide the analytic solution to the state-to-state transfer of the paradigmatic two-level system and to the more general star configuration of an NNN-level system. We demonstrate numerically the usefulness of this approach in the more general class of connected acyclic NNN-level systems with random spectra. Finally, we use it to design a protocol to entangle Rydberg via constant laser pulse atoms in an experimentally relevant range of parameters.