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Review of Scientific Instruments

AC Zeeman effect in microfabricated surface traps

Megan Ivory, Christopher Nordquist, Kevin C Young, Craig Hogle, Susan Clark, Melissa Revelle

Published Sep 1, 2024• 1 citation

Abstract

Quantum processors and atomic clocks based on trapped ions often utilize an ion's hyperfine transition as the qubit state or frequency reference, respectively. These states are a good choice because they are insensitive in first order to magnetic field fluctuations, leading to long coherence times and stable frequency splittings. In trapped ions, however, these states are still subject to the second order AC Zeeman effect due to the necessary presence of an oscillating magnetic field used to confine the ions in a Paul trap configuration. Here, we measure the frequency shift of the 2S1/2 hyperfine transition of a 171Yb+ ion caused by the radio frequency (RF) electromagnetic field used to create confinement in several microfabricated surface trap designs. By comparing different trap designs, we show that two key design modifications significantly reduce the AC Zeeman effect experienced by the ion: (1) an RF ground layer routed directly below the entire RF electrode, and (2) a symmetric RF electrode. Both of these changes lead to better cancellation of the AC magnetic field and, thus, overall reduced frequency shifts due to the AC Zeeman effect and reduced variation across the device. These improvements enable a more homogeneous environment for quantum computing and can reduce errors for precision applications such as atomic clocks.

DOI: 10.1063/5.0204413

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Quantum processors and atomic clocks based on trapped ions often utilize an ion's hyperfine transition as the qubit state or frequency reference, respectively. These states are a good choice because they are insensitive in first order to magnetic field fluctuations, leading to long coherence times and stable frequency splittings. In trapped ions, however, these states are still subject to the second order AC Zeeman effect due to the necessary presence of an oscillating magnetic field used to confine the ions in a Paul trap configuration. Here, we measure the frequency shift of the 2S1/2 hyperfine transition of a 171Yb+ ion caused by the radio frequency (RF) electromagnetic field used to create confinement in several microfabricated surface trap designs. By comparing different trap designs, we show that two key design modifications significantly reduce the AC Zeeman effect experienced by the ion: (1) an RF ground layer routed directly below the entire RF electrode, and (2) a symmetric RF electrode. Both of these changes lead to better cancellation of the AC magnetic field and, thus, overall reduced frequency shifts due to the AC Zeeman effect and reduced variation across the device. These improvements enable a more homogeneous environment for quantum computing and can reduce errors for precision applications such as atomic clocks.

Microfabricated surface traps have enabled precise control over trapped ions in a compact device with lower power requirements than traditional traps, but have also presented unique challenges due to the small ion-surface distance.One such challenge is AC Zeeman effect which leads to a frequency shift due to the oscillating magnetic field associated with the RF drive.Here, we characterize the frequency shift of the ground state microwave transition of a 171 Yb + ion confined by microfabricated surface traps driven by an RF field.We compare the AC Zeeman effect due to the drive RF and induced RF current in the trap ground planes for various traps fabricated at Sandia National Laboratories.

We report an experimental determination of the ground-state hyperfine constant

A

of the

^{25}\mathrm{Mg}^{+}

ions by measuring the $|{S}_{1/2},F=2,m=0\ensuremath{\rangle}$ to $|{S}_{1/2},F=3,m=0\ensuremath{\rangle}$ transition (0-0 transition) frequency of the two ground-state hyperfine energy levels. The frequency is measured by rf resonant method in a Paul trap under a magnetic field of about 0.1 mT. The result is $A=\ensuremath{-}596.254$ 248 7(42) MHz. Different frequency shifts and uncertainties are evaluated. The main effect is quadratic Zeeman shift. Since the Paul trap is driven by rf on the electrodes, ac magnetic field can be induced by the rf at the site of the ion. The ac magnetic field causes quadratic Zeeman shift for ion frequency standards and also reduces the coherence time when the ion acts as a quantum bit. Precision measurement of this ac magnetic field can help evaluating the related uncertainty when a single-ion optical clock is established on the trap.

Many systems used for quantum computing possess additional states beyond those defining the qubit. Leakage out of the qubit subspace must be considered when designing quantum error correction codes. Here we consider trapped ion qubits manipulated by Raman transitions. Zeeman qubits do not suffer from leakage errors but are sensitive to magnetic fields to first order. Hyperfine qubits can be encoded in clock states that are insensitive to magnetic fields to first order, but spontaneous scattering during the Raman transition can lead to leakage. Here we compare a Zeeman qubit (

^{174}\mathrm{Yb}^{+}

) to a hyperfine qubit (

^{171}\mathrm{Yb}^{+}

) in the context of the surface code. We find that the number of physical qubits required to reach a specific logical qubit error can be reduced by using

^{174}\mathrm{Yb}^{+}

if the magnetic field can be stabilized with fluctuations smaller than $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{G}$.

Precision measurement of the ground-state hyperfine constant for

^9Be^+

in a linear Paul trap via magnetically insensitive hyperfine transitions

Direct measurements of the ground-state magnetically insensitive hyperfine transition |F=2,mF=0>->|F=1,mF=0> of

^9Be^+

ions have been performed using microwave-driven state transfer. The

^9Be^+

ions are confined and laser-cooled in a linear Paul trap, forming a Coulomb crystal. The transition frequencies have been measured over a magnetic field range of $ \pm 0.5 mT $ centered at zero magnetic field, and the acquired data were fitted accounting for the high-order Zeeman effect. The hyperfine constant A is determined to be -625.008840(35) MHz, achieving a relative precision of $ 5.6 \times 10^{-8}$.

We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on 40Caþ. By near-resonant magnetic coupling of the 2S1=2 and 2D5=2 Zeeman sublevels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2nd-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to 3ð2Þ mHz=μm2 and coherence times of 290(20) ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.

Direct measurements of the ground-state magnetically insensitive hyperfine transition | F = 2 , m F = 0 〉 → | F = 1 , m F = 0 〉 of Be + 9 ions have been performed using microwave-driven state transfer. The Be + 9 ions are confined and laser cooled in a linear Paul trap, forming a Coulomb crystal. The transition frequencies have been measured over a magnetic-field range of ± 0.5 mT centered at zero magnetic field and the acquired data were fitted accounting for the high-order Zeeman effect. The hyperfine constant A is determined to be − 625.008 840 ( 35 ) MHz, achieving a relative precision of 5.6 × 10 − 8 .