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Journal of Physics B Atomic Molecular and Optical Physics

Measurement and suppression of magnetic field noise of trapped ion qubit

Wenzhe Wei, P. Hao, Zhiyu Ma, Huixing Zhang, Liren Pang, Fang-Fei Wu, Ke Deng, Jie Zhang, Z. H. Lu

Published Mar 16, 2022• 13 citations
Publisher

Abstract

Abstract Magnetic field noise is an important factor causing quantum decoherence in quantum systems. In order to suppress the decoherence effect, magnetic field noise needs to be properly measured and controlled. Magnetic field noise power spectrum measurement using a single trapped ion based quantum spectrum analyzer is a very effective way. In this paper, the magnetic field noise measurement based on dynamic decoupling technique is analyzed theoretically. Furthermore, we use magnetically insensitive transition to measure the magnetic field noise, which has the potential to measure stronger magnetic field noise and speed up the measurement process. In our experiment, we suppress the magnetic field noise by using active feedback control and passive compensation, where the required passive compensation amplitude is obtained by measuring the magnetic field noise spectrum of a single 25Mg+ ion. With the magnetic field noise suppressed, the expected contribution of the magnetic field noise to the stability of the 25Mg+–27Al+ ion optical clock can be decreased from 2.8 × 1 0 − 15 / τ to 7.2 × 1 0 − 16 / τ .

DOI
10.1088/1361-6455/ac5e7d

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Abstract Magnetic field noise is an important factor causing quantum decoherence in quantum systems. In order to suppress the decoherence effect, magnetic field noise needs to be properly measured and controlled. Magnetic field noise power spectrum measurement using a single trapped ion based quantum spectrum analyzer is a very effective way. In this paper, the magnetic field noise measurement based on dynamic decoupling technique is analyzed theoretically. Furthermore, we use magnetically insensitive transition to measure the magnetic field noise, which has the potential to measure stronger magnetic field noise and speed up the measurement process. In our experiment, we suppress the magnetic field noise by using active feedback control and passive compensation, where the required passive compensation amplitude is obtained by measuring the magnetic field noise spectrum of a single 25Mg+ ion. With the magnetic field noise suppressed, the expected contribution of the magnetic field noise to the stability of the 25Mg+–27Al+ ion optical clock can be decreased from 2.8 × 1 0 − 15 / τ to 7.2 × 1 0 − 16 / τ .
Magnetic field fluctuations are a dominant source of dephasing in Zeeman-encoded trapped-ion qubits, limiting coherence time and the fidelity of quantum operations, particularly in modular quantum networks where phase stability must be maintained across spatially separated nodes. In this work, we design and characterize an active magnetic field stabilization system based on real-time feedback using a high-resolution magnetometer, a digitally controlled Red Pitaya platform, and a coil actuator with a measured gain of ∼ −5.37 G/V. Spectral measurements of the laboratory environment reveal dominant 60 Hz magnetic noise with amplitudes on the order of 400 µG and significant harmonic content. The system operates at a sampling rate of ∼ 605 Hz with an actuator bandwidth of ∼ 85 Hz, enabling targeted suppression of these low-frequency components. Given a Zeeman sensitivity of ∼ 2.8 MHz/G, such fluctuations correspond to kilohertz-scale frequency noise, which rapidly dephases qubit superpositions. Suppression of these fluctuations is therefore expected to reduce phase noise and extend coherence times, with first-order estimates suggesting improvement from the submillisecond regime into the few-millisecond regime for Zeeman-sensitive qubits. These results demonstrate that active magnetic-field stabilization is a practical approach to reducing environmental dephasing and improving the performance of trapped-ion quantum network experiments.
We propose a method to dynamically decouple every magnetically sensitive hyperfine sublevel of a trapped ion from magnetic field noise, simultaneously using integrated circuits to adiabatically rotate its local quantization field. These integrated circuits allow passive adjustment of the effective polarization of any external (control or noise) field. By rotating the ion's quantization direction relative to this field's polarization, we can perform ``passive'' dynamical decoupling (PDD), inverting the linear Zeeman sensitivity of every hyperfine sublevel. This dynamically decouples the entire ion, rather than just a qubit subspace. Fundamentally, PDD drives the transition ${m}_{F}\ensuremath{\rightarrow}\ensuremath{-}{m}_{F}$ for every magnetic quantum number mF{m}_{F}mF​ in the system---with only one operation---indicating it applies to qudits with constant overhead in the dimensionality of the qudit. We show how to perform pulsed and continuous PDD, weighing each technique's insensitivity to external magnetic fields versus their sensitivity to diabaticity and control errors. Finally, we show that we can tune the sinusoidal oscillation of the quantization axis to a motional mode of the crystal in order to perform a laser-free two-qubit gate that is insensitive to magnetic field noise.
We present a study of dynamical decoupling schemes for the suppression of phase errors from various noise environments using ions in a Penning trap as a model ensemble of qubits. By injecting frequency noise we demonstrate that in an ohmic noise spectrum with a sharp, high-frequency cutoff the recently proposed UDD decoupling sequence gives noise suppression superior to the traditional CPMG technique. Under only the influence of ambient magnetic field fluctuations with a 1/ω4 power spectrum, we find little benefit from using the UDD sequence, consistent with theoretical predictions for dynamical decoupling performance in the presence of noise spectra with soft cutoffs. Finally, we implement an optimization algorithm using measurement feedback, demonstrating that local optimization of dynamical decoupling can further lead to significant gains in error suppression over known sequences.
Decoherence induced by laser frequency noise is one of the most important obstacles in quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In particular, the noise spectrum measurement based on the coherence characteristics of qubits would be a meaningful and still challenging method. Here, we theoretically analyze and experimentally obtain the spectrum of laser frequency noise based on the continuous dynamical decoupling technique. We first estimate the mixture-noise (including laser and magnetic noises) spectrum up to $(2\ensuremath{\pi})530$ kHz by monitoring the transverse relaxation from an initial state +X+X+X, followed by a gradient descent data process protocol. Then the contribution from the laser noise is extracted by encoding the qubits on different Zeeman sublevels. We also investigate two sufficiently strong noise components by making an analogy between these noises and driving lasers whose linewidth is assumed to be negligible. This method is verified experimentally and finally helps to characterize the noise.
Abstract The low-frequency magnetic field noise resulting from the lab[1]oratory power supply is one of the main decoherence sources of trapped-ion qubits. Synchronizing the experimental sequence to the phase of the power line is widely used to mitigate this problem, but it will greatly reduce the ex[1]perimental efficiency. In this paper, we experimentally demonstrate a simple active compensation method to reduce the observed 50 Hz and 150 Hz strong magnetic noise in an ion trap induced by the power line. In our method, a single 40Ca+ ion is used as the noise probe and an reverse compensation sig[1]nal is generated by a programmable arbitrary waveform generator (AWG).After compensation, an 86% reduction of the periodic magnetic field fluc[1]tuation and over 35-fold extension of the coherence time from 70 µs to 2500 µs were observed. This method can also be applied to compensate other spectral components of the magnetic field noise related to the power line, and it is also useful for other atomic systems such as neutral atoms.
Quantum magnetometry represents a fundamental component of quantum metrology, where trapped-ion systems have achieved pT/Hz\rm{pT}/\sqrt{\rm{Hz}}pT/Hz​ sensitivity in single-ion radio-frequency magnetic field measurements via dressed states based dynamical decoupling. Here we propose a scalable trapped-ion magnetometer utilizing the mixed dynamical decoupling method, combining dressed states with periodic sequences to suppress decoherence and spatial magnetic field inhomogeneity. With numerical simulations for a 10410^4104 ion system with realistic experimental parameters, we demonstrate that a sensitivity of 13 fT/Hz\rm{fT}/\sqrt{\rm{Hz}}fT/Hz​ for the radio-frequency field could be reached. Such a sensitivity could be obtained via robust resilience to magnetic field drift noise and inhomogeneity, where coherence time could be extended to the order of several minutes on average. This method enables scalable trapped-ion magnetometry, demonstrating its potential as a robust and practical solution for advancing quantum sensing applications.