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Laser Physics Letters

Optimal narrowband composite pulses in two-level systems

Shi-Peng Liang, Zhi‐Cheng Shi, Ye‐Hong Chen, Jie Song, Yan Xia

Published Mar 12, 2025• 2 citations
Publisher

Abstract

Abstract We propose a protocol to construct narrowband (NB) composite pulses using quantum optimal control in a full-parameter adjustable two-level system. The optimal NB composite pulses are highly sensitive to various types of parameter deviations. The optimal modulation parameters are obtained by minimizing the cost function composed of the weight factor and the expansion coefficients of transition probabilities. In this way, the problem of multi-parameter modulations and incomplete nullification of expansion coefficients can be effectively solved. Furthermore, the NB composite pulses with arbitrary population transfer can be flexibly achieved by only changing the constraint of the cost function, and the current protocol is easily extended to implement passband composite pulses.

DOI
10.1088/1612-202x/adbd1f

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Abstract We propose a protocol to construct narrowband (NB) composite pulses using quantum optimal control in a full-parameter adjustable two-level system. The optimal NB composite pulses are highly sensitive to various types of parameter deviations. The optimal modulation parameters are obtained by minimizing the cost function composed of the weight factor and the expansion coefficients of transition probabilities. In this way, the problem of multi-parameter modulations and incomplete nullification of expansion coefficients can be effectively solved. Furthermore, the NB composite pulses with arbitrary population transfer can be flexibly achieved by only changing the constraint of the cost function, and the current protocol is easily extended to implement passband composite pulses.
In this work, we put forward an approach of constructing the optimal composite pulse sequence for robust population transfer in two-level systems. This approach is quite universal and applicable to a variety of systems, because the modulation parameters of composite pulses are obtained by minimizing the homemade cost function rather than nullifying the error coefficients of the transition probability. Specifically, we design different forms of the cost function for implementing optimal robustness with respect to the single or multiple errors. When slightly adjusting the constraints of the cost function, this approach can be easily extended to achieve arbitrary population transfer. The numerical results demonstrate that the optimized sequences are immune from various systematic errors, allowing us to produce a broadening excitation range of the transition probability. Therefore, this work offers an optimal robust design for controlling quantum states in error-prone environments.
In this work, we propose a comprehensive design for narrowband and passband composite pulse sequences by involving the dynamics of all states in the three-state system. The design is quite universal as all pulse parameters can be freely employed to modify the coefficients of error terms. Two modulation techniques, the strength and phase modulations, are used to achieve arbitrary population transfer with a desired excitation profile, while the system keeps minimal leakage to the third state. Furthermore, the current sequences are capable of tolerating inaccurate waveforms, detuning errors, and work well when rotating wave approximation is not strictly justified. Therefore, this work provides versatile adaptability for shaping various excitation profiles in both narrowband and passband sequences.
We develop a systematic approach to derive narrowband (NB) and passband (PB) composite sequences which can produce any preselected transition probability with any desired accuracy. The NB composite pulses are derived by successive cancellation of derivative terms in the propagator. The PB pulses are built by combining two $\ensuremath{\pi}/2$ NB pulses. Both the NB and the PB pulses feature vanishing wings on both sides of the central region around the target transition probability, and the PB pulses offer also a flat (broadband) top around the target probability. The NB sequences are particularly suitable for sensing and metrology applications, whereas the PB sequences can be very useful for qubit control in the case of tightly spaced laser-driven qubits for they ensure both selectivity (suppressed cross talk to neighbors) and robustness (suppressed laser pointing instability). Other possible applications include selective (NB) or both selective and robust (PB) control of close transitions in frequency space.
This work presents a method for achieving complete, robust, and efficient population transfer between the two ground states in a three-level loop quantum system. The approach utilizes composite pulse sequences by effectively mapping the three-state system onto an equivalent two-level system. This transformation allows the use of broadband composite pulses designed initially for conventional two-state quantum systems. Unlike traditional implementations, the composite pulses in the three-level system are not controlled through phase adjustments; instead, they are realized via the amplitude ratio of the Rabi frequencies.
We perform comprehensive experimental tests of various composite pulse sequences using one of the open-access IBM quantum processors, based on superconducting transmon qubits. We implement explicit pulse control of the qubit by making use of the opportunity of low-level access to the backend, provided by IBM Quantum. We obtain the excitation profiles for a huge variety of broadband, narrowband, and passband composite pulses, producing any prechosen target probabilities, ranging from zero to one. We also test universal composite pulses that compensate errors in any experimental parameter. In all experiments, we find excellent agreement between theoretical and experimental excitation profiles. This proves both the composite pulses as a very efficient and flexible quantum control tool and the high quality of the IBM quantum processor. As an extreme example, we test and observe a pronounced narrowband excitation profile for a composite sequence of as many as 1001 pulses.
Abstract In this work, we propose a composite pulses (CPs) scheme by modulating phases to achieve high fidelity population transfer in three-level systems. To circumvent the obstacle that not enough variables are exploited to eliminate the systematic errors in the transition probability, we put forward a cost function to find the optimal value. The cost function is independently constructed either in ensuring an accurate population of the target state, or in suppressing the population of the leakage state, or both of them. The results demonstrate that population transfer is implemented with high fidelity even when existing the deviations in the coupling coefficients. Furthermore, our CPs scheme can be extensible to arbitrarily long pulse sequences. As an example, we employ the CPs sequence for achieving the three-atom singlet state in an atom-cavity system with ultrahigh fidelity. The final singlet state shows robustness against deviations and is not seriously affected by waveform distortions. Also, the singlet state maintains a high fidelity under the decoherence environment.