Scalable Quantum Logic Spectroscopy

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Scalable Quantum Logic Spectroscopy

Kaifeng Cui, Jose Valencia, Kevin T. Boyce, Ethan R. Clements, David R. Leibrandt, and David B. Hume

Phys. Rev. Lett. 129, 193603 – Published 2 November 2022

Abstract

In quantum logic spectroscopy (QLS), one species of trapped ion is used as a sensor to detect the state of an otherwise inaccessible ion species. This extends precision measurements to a broader class of atomic and molecular systems for applications like atomic clocks and tests of fundamental physics. Here, we develop a new technique based on a Schrödinger cat interferometer to address the problem of scaling QLS to larger ion numbers. We demonstrate the basic features of this method using various combinations of ${}^{25}{Mg}^{+}$ logic ions and ${}^{27}{Al}^{+}$ spectroscopy ions. We observe higher detection efficiency by increasing the number of ${}^{25}{Mg}^{+}$ ions. Applied to multiple ${}^{27}{Al}^{+}$ , this method will improve the stability of high-accuracy optical clocks and could enable Heisenberg-limited QLS.

Received 17 April 2022
Revised 24 July 2022
Accepted 30 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.193603

Physics Subject Headings (PhySH)

Atomic, optical & lattice clocks Entanglement manipulation Laser spectroscopy Quantum sensing

Trapped ions

Fluorescence spectroscopy

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Kaifeng Cui ^1,2,3,*, Jose Valencia^1,4, Kevin T. Boyce^1,4, Ethan R. Clements^1,4, David R. Leibrandt^1,4, and David B. Hume ^1,†

¹National Institute of Standards and Technology, Boulder, Colorado 80305, USA
²HEP Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
³Key Laboratory of Atomic Frequency Standards, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
⁴Department of Physics, University of Colorado, Boulder, Colorado 80305, USA

^*cuikaifeng@apm.ac.cn
^†david.hume@nist.gov

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Issue

Vol. 129, Iss. 19 — 4 November 2022

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Images

Figure 1
(a) An ensemble of SIs (green dots) and LIs (yellow dots) confined within a linear ion trap. The arrows indicate SDDs provided by two bichromatic laser fields. (b) The energy levels involved in these experiments. (c)–(e) Schrödinger cat interferometry sequence in motional phase space.
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Figure 2
Quantum logic spectroscopy using a Schrödinger cat interferometer. (a) Using one ${}^{25}{Mg}^{+}$ as a LI and one ${}^{27}{Al}^{+}$ ion as a SI, the ground-state probability of the LI ( $P_{↓, L}$ ) is modulated by the geometric phase encoded in phase space when scanning the motional phase angle $ϕ_{M}$ . Experimental results (blue points) match the fit of Eq. (2) (solid line). (b) The duration of LI-SDD is scanned with ions cooled to the Doppler limit (orange points) and after sideband cooling (blue points). Lines are the results of numerical simulations without free parameters. (c) Spectroscopy of the ${{}^{1}S}_{0} \to {{}^{3}P}_{1}$ transition of one, two, and three ${}^{27}{Al}^{+}$ SIs using equal number of ${}^{25}{Mg}^{+}$ LIs. Insets on the top of each figure are fluorescence images of the ${}^{25}{Mg}^{+}$ ions (bright spots). ${}^{27}{Al}^{+}$ ion positions are marked in yellow circles based on theoretical calculations. The data (blue circles) are fit by numerical simulations (orange line). Error bars represent one standard deviation of the LI quantum projection noise. Note that, for the case of six ions, the ion chain has formed a zigzag geometry, but we still observe a resonant response in the interferometer, although with reduced contrast.
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Figure 3
Scaling the number of LIs to improve the detection efficiency of a single SI. (a) Transitions between $| ↓ ⟩_{S}$ and $| c ⟩_{S}$ control the output of the interferometer resulting in quantum jumps in the fluorescence of the LIs. Each of the data points is an average of 20 measurements, where a single measurement takes 1.8 ms. The histograms on the right show the full distribution of these data (1500 data points; Prob, probability density). (b) Observed error rate estimate comes from the comparison of two consecutive detection sequences during the detection. Error bars are symmetric, based on the standard variance of a Poisson distribution. The black solid line represents the lifetime-limited error probability due to the spontaneous decay of the $| c ⟩_{S}$ state.
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Figure 4
(a) ${}^{25}{Mg}^{+}$ fluorescence when scanning the duration of the SI-SDD pulse. The observed fluorescence for $N_{S} = 2$ is plotted along with the expected signal for $N_{S} = 1$ and 0. All lines come from numerical simulations using measured experimental parameters. (b) Three-level quantum jumps using two ${}^{25}{Mg}^{+}$ and two ${}^{27}{Al}^{+}$ ions. Each data point is an average of 100 measurements. (c) Quantum logic spectroscopy of the ${{}^{1}S}_{0} \leftrightarrow {{}^{3}P}_{0}$ transition of two ${}^{27}{Al}^{+}$ SIs. All experiments in this figure are done after 1.25 ms sideband cooling. Error bars represent one standard deviation of the mean.
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