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Physical Review A

Precision measurement of the Mg+25 ground-state hyperfine constant

Zhilin Xu, Ke Deng, H. Che, W. H. Yuan, Jie Zhang, Z. H. Lu

Published Nov 21, 2017• 15 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.96.052507

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We report an experimental determination of the ground-state hyperfine constant AAA of the 25Mg+^{25}\mathrm{Mg}^{+}25Mg+ ions by measuring the ∣S1/2,F=2,m=0\ensuremath⟩|{S}_{1/2},F=2,m=0\ensuremath{\rangle}∣S1/2​,F=2,m=0\ensuremath⟩ to ∣S1/2,F=3,m=0\ensuremath⟩|{S}_{1/2},F=3,m=0\ensuremath{\rangle}∣S1/2​,F=3,m=0\ensuremath⟩ 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−596.254A=\ensuremath{-}596.254A=\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.
Precision measurement of the ground-state hyperfine constant for 9Be+^9Be^+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+^9Be^+9Be+ ions have been performed using microwave-driven state transfer. The 9Be+^9Be^+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}$.
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 .
We calculate the polarizabilities of the Zeeman sublevels of 25Mg+^{25}\mathrm{Mg}^{+}25Mg+ ion hyperfine ground states. To verify the calculation result, a single 25Mg+^{25}\mathrm{Mg}^{+}25Mg+ ion is trapped in a Paul trap and a microwave resonance measurement is carried out on the ground states with and without the light shift. A good agreement between the experimental result and the calculation result is obtained.
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.
The hyperfine structure of the $4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\text{\ensuremath{-}}3d\phantom{\rule{0.2em}{0ex}}^{2}S_{5∕2}$ quadrupole transition at 729nm729\phantom{\rule{0.3em}{0ex}}\mathrm{nm}729nm in 43Ca+^{43}\mathrm{Ca}^{+}43Ca+ has been investigated by laser spectroscopy using a single trapped 43Ca+^{43}\mathrm{Ca}^{+}43Ca+ ion. We determine the hyperfine structure constants of the metastable level as AD5∕2=3.8931(2)MHz{A}_{{D}_{5∕2}}=3.8931(2)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}AD5∕2​​=3.8931(2)MHz and BD5∕2=4.241(4)MHz{B}_{{D}_{5∕2}}=4.241(4)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}BD5∕2​​=4.241(4)MHz. The isotope shift of the transition with respect to 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ was measured to be ${\ensuremath{\Delta}}_{\mathrm{iso}}^{43,40}=4134.713(5)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at nonzero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known ``clock transitions'' between m=0m=0m=0 levels at zero magnetic field.
The Ramsey fringes on the ground-state hyperfine transition of 199 Hg + (ΔF = 1, Δm F = 0) ions trapped in a hyperbolic Paul trap are firstly observed with the method of time-separated oscillatory fields. The full width at half maximum of central Ramsey fringes is about 25 mHz and the corresponding quality factor Q of the line is greater than 10 12 for the trapped 199 Hg + microwave frequency standard. The hyperfine transition frequency shifted by magnetic field is also measured by the high-resolution Ramsey fringes. The final result is Δν h f s = 40507347997.3(0.5) Hz, which is corrected to zero magnetic field.