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Chinese Physics B

Robust excitation of 229 Th via generalized composite pulses: Compensating generic errors across arbitrary pulse shapes

Rui Zhao, Yingdan Wang

Published Mar 7, 2026• 0 citations
Publisher

Abstract

Abstract High-fidelity coherent control is a universal challenge due to complex errors and imperfect pulse shapes. Here, we propose a generalized composite pulses scheme independent of pulse profile to correct generic errors. This approach could simultaneously compensate for pulse area errors, detuning, and phase imperfections. We demonstrate its application in the direct laser excitation of the 229 Th nucleus isomer state, and show a significant improvement in the robustness against various operation errors, such as detuning, phase error, and pulse area error.

DOI
10.1088/1674-1056/ae4e8d

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Abstract High-fidelity coherent control is a universal challenge due to complex errors and imperfect pulse shapes. Here, we propose a generalized composite pulses scheme independent of pulse profile to correct generic errors. This approach could simultaneously compensate for pulse area errors, detuning, and phase imperfections. We demonstrate its application in the direct laser excitation of the 229 Th nucleus isomer state, and show a significant improvement in the robustness against various operation errors, such as detuning, phase error, and pulse area error.
Composite pulses---sequences of pulses with well-defined relative phases---are an efficient, robust, and flexible technique for coherent control of quantum systems. Composite sequences can compensate for a variety of experimental errors in the driving field (e.g., in the pulse amplitude, duration, detuning, chirp, etc.) or in the quantum system and its environment (e.g., inhomogeneous broadening, stray electric or magnetic fields, unwanted couplings, etc.). The control parameters are the relative phases between the constituent pulses in the composite sequence, an accurate control over which is required in all composite sequences reported hitherto. In this paper, we introduce two types of composite pulse sequences which, in addition to error compensation in the basic experimental parameters, compensate for systematic errors in the composite phases. In the first type of such composite sequences, which compensate for pulse area errors, relative phase errors of over 10% can be tolerated with reasonably short sequences while maintaining the fidelity above the 99.99% quantum computing benchmark. In the second type of composite sequences, which compensate for simultaneous pulse area and detuning errors, relative phase errors of over 5% can be compensated.
We present a method to construct high-fidelity quantum phase gates, which are insensitive to errors in various experimental parameters. The phase gates consist of a pair of two sequential broadband composite pulses, with a phase difference $\ensuremath{\pi}+\ensuremath{\alpha}/2$ between them, where $\ensuremath{\alpha}$ is the desired gate phase. By using composite pulses which compensate systematic errors in the pulse area, the frequency detuning, or both the area and the detuning, we thereby construct composite phase gates which compensate errors in the same parameters. Particularly interesting are phase gates which use the recently discovered universal composite pulses, which compensate systematic errors in any parameter of the driving field, which keep the evolution Hermitian (e.g., pulse amplitude and duration, pulse shape, frequency detuning, Stark shifts, residual frequency chirps, etc.).
We introduce a method to rotate arbitrarily the excitation profile of universal broadband composite pulse sequences for robust high-fidelity population inversion. These pulses compensate deviations in any experimental parameter (e.g., pulse amplitude, pulse duration, detuning from resonance, Stark shifts, unwanted frequency chirp, etc.) and are applicable with any pulse shape. The rotation allows one to achieve higher-order robustness to any combination of pulse area and detuning errors at no additional cost. The latter can be particularly useful, e.g., when detuning errors are due to Stark shifts that are correlated with the power of the applied field. We demonstrate the efficiency and universality of these composite pulses by experimental implementation for rephasing of atomic coherences in a Pr3+:Y2SiO5{\text{Pr}}^{3+}\text{:}{\text{Y}}_{2}{\text{SiO}}_{5}Pr3+:Y2​SiO5​ crystal.
We present a systematic method for constructing universal composite phase gates with a continuously tunable target phase. Using a general Cayley--Klein parametrization of the single-pulse propagator, we design gates from an even number of nominal πππ pulses and derive analytic phase families by canceling, order by order in a small deviation parameter, the leading contributions to the undesired off-diagonal element of the composite propagator, independently of the dynamical phase. The resulting sequences provide intrinsic robustness against generic control imperfections and parameter fluctuations and remain valid for arbitrary pulse shapes. Numerical simulations in a standard two-level model confirm high-order error suppression and demonstrate broad, flat high-fidelity plateaus over wide ranges of simultaneous pulse-area and detuning errors, highlighting the efficiency of the proposed universal composite phase gates for resilient phase control in quantum information processing.
We present a systematic SU(2) approach for construction of composite sequences of pulses with smooth temporal shapes that produce high-fidelity two-state excitation profiles. This makes possible the application of composite pulses to quantum control and quantum information processing with short and ultrashort laser pulses. We present an exact analytic formula for the composite phases for arbitrarily accurate broadband pulses and examples of narrowband, passband, and fractional-$\ensuremath{\pi}$ pulses as well as composite pulses with detuning compensation.
Probing an atomic resonance without disturbing it is an ubiquitous issue in physics. This problem is critical in high-accuracy spectroscopy or for the next generation of atomic optical clocks. Ultra-high resolution frequency metrology requires sophisticated interrogation schemes and robust protocols handling pulse length errors and residual frequency detuning offsets. This review reports recent progress and perspective in such schemes, using sequences of composite laser-pulses tailored in pulse duration, frequency and phase, inspired by NMR techniques and quantum information processing. After a short presentation of Rabi technique and NMR-like composite pulses allowing efficient compensation of electromagnetic field perturbations to achieve robust population transfers, composite laser-pulses are investigated within Ramsey's method of separated oscillating fields in order to generate non-linear compensation of probe-induced frequency shifts. Laser-pulses protocols such as hyper-Ramsey, modified hyper-Ramsey, generalized hyper-Ramsey and hybrid schemes as auto-balanced Ramsey spectroscopy are reviewed. These techniques provide excellent protection against both probe induced light-shift perturbations and laser intensity variations. More sophisticated schemes generating synthetic frequency-shifts are presented. They allow to reduce or completely eliminate imperfect correction of probe-induced frequency-shifts even in presence of decoherence due to the laser line-width. Finally, two universal protocols are presented which provide complete elimination of probe-induced frequency shifts in the general case where both decoherence and relaxation dissipation effects are present by using exact analytic expressions for phase-shifts and the clock frequency detuning. These techniques might be applied to atomic, molecular and nuclear frequency metrology, Ramsey-type mass spectrometry as well as precision spectroscopy.