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arXiv:1305.6127 · Physical Review A

Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors

Xiao-Jing Lu, Xi Chen, A. Ruschhaupt, Daniel Alonso, S. Guérin, Juan Gonzalo Muga

Published Sep 5, 2013• 86 citations
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Abstract

We design, by invariant-based inverse engineering, driving fields that invert the population of a two-level atom in a given time, robustly with respect to dephasing noise and/or systematic frequency shifts. Without imposing constraints, optimal protocols are insensitive to the perturbations but need an infinite energy. For a constrained value of the Rabi frequency, a flat $\ensuremath{\pi}$ pulse is the least sensitive protocol to phase noise but not to systematic frequency shifts, for which we describe and optimize a family of protocols.

DOI
10.1103/physreva.88.033406

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We design, by invariant-based inverse engineering, driving fields that invert the population of a two-level atom in a given time, robustly with respect to dephasing noise and/or systematic frequency shifts. Without imposing constraints, optimal protocols are insensitive to the perturbations but need an infinite energy. For a constrained value of the Rabi frequency, a flat \ensuremathπ\ensuremath{\pi}\ensuremathπ pulse is the least sensitive protocol to phase noise but not to systematic frequency shifts, for which we describe and optimize a family of protocols.
We develop an effective scheme for implementing error-insensitive population transfer in a three-level system (qutrit) by invariant-based shortcuts with optimized drivings. Based on the method of inverse engineering, target population transfers can be performed in a shortcut manner. Taking into account the deviation errors and then optimizing the coherent drivings, we can improve the target population transfers to be insensitive to deviations of frequency detuning or Rabi coupling. Particularly, with an appropriate choice of coherent drivings, our scheme could be insensitive to these two kinds of errors simultaneously. As one of the potential applications, our scheme may remove the control errors of quantum operations on superconducting artificial atoms. By combining shortcuts to adiabaticity with optimal control, the protocol could offer a promising avenue to explore fast and robust quantum information processing experimentally.
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Shortening the operation time of implementing scheme and reducing the influence of harmful factors have always been the research objectives pursued by people. Based on invariant-based reverse engineering, we present a general scheme for implementing robust population transfer in a three-level system via optimal shortcut to adiabatic passage. The systematic error sensitivity is introduced to measure the robustness of the process. The smooth Rabi frequencies are expressed with some coefficients, which are also related to the systematic error sensitivity and the population of intermediate state. When the amplitude of control field is given, the transfer can be optimized within as small systematic error sensitivity as possible, i.e., the robustness against systematic errors is further improved by choosing suitable correlation coefficient. Additionally, we apply the technique to achieve robust excitation fluctuation transfer between two membranes in an optomechanical system. The relation between the fidelity of excitation fluctuation transfer and variation of effective optomechanical coupling strengths is analysed. Numerical result shows that the fidelity keeps over 0.95 even if the coupling strengths deviates from 20% of the theoretical value. Moreover, comparison with existing literature [Opt. Express29, 7998 (2021)10.1364/OE.417343], the proposed scheme possesses stronger robustness against variations of effective optomechanical coupling strengths and lower population of unwanted states. The idea may provide a promising approach for quantum information processing.
A systematic approach to design robust control protocols against the influence of different types of noise is introduced. We present control schemes which protect the decay of the populations avoiding dissipation in the adiabatic and nonadiabatic regimes and minimize the effect of dephasing. The effectiveness of the protocols is demonstrated in two different systems. Firstly, we present the case of population inversion of a two-level system in the presence of either one or two simultaneous noise sources. Secondly, we present an example of the expansion of coherent and thermal states in harmonic traps, subject to noise arising from monitoring and modulation of the control, respectively.