pith. sign in

arxiv: 2311.12263 · v2 · submitted 2023-11-21 · ⚛️ physics.atom-ph · quant-ph

Quantum Vector Signal Analyzer: Wideband Electric Field Sensing via Motional Raman Transitions

Pith reviewed 2026-05-24 06:06 UTC · model grok-4.3

classification ⚛️ physics.atom-ph quant-ph
keywords quantum sensingtrapped ionselectric field detectionmotional Raman transitionswideband sensingquantum harmonic oscillatorstandard quantum limitRF electric fields
0
0 comments X

The pith

Motional Raman transitions in a trapped ion sense radio-frequency electric fields over a bandwidth more than 800 times wider than prior methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates a procedure that uses motional Raman transitions in a single trapped ion cooled near its motional ground state to measure the frequency, phase, and amplitude of an unknown radio-frequency electric field. This approach extends the high sensitivity of a quantum harmonic oscillator to a frequency range more than 800 times larger than earlier techniques while remaining compatible with squeezing and Fock-basis readout. The method reaches performance 3.4 dB below the standard quantum limit and supports in-situ calibration of control lines plus transduction of external drives into motion. If correct, it opens a practical route to wideband quantum sensing in applications such as radio communication, cosmology, and dark matter searches, with potential for further gains through moderate upgrades.

Core claim

Motional Raman transitions driven in a trapped ion near its motional ground state unlock wideband detection of an external RF electric field's frequency, phase, and amplitude. The technique maintains the extreme sensitivity of the quantum harmonic oscillator while operating over a frequency range exceeding 800 times that of previous resonant methods. When combined with squeezing and measurement in the Fock basis, the approach yields performance 3.4(20) dB below the standard quantum limit and can be extended to other quantum harmonic oscillator platforms such as superconducting qubit-resonator systems.

What carries the argument

Motional Raman transitions, in which two laser beams couple the ion's internal electronic states to its motional states and thereby transduce the effect of an external RF electric field onto the observable motion.

If this is right

  • The method supplies in-situ calibration of qubit control lines in quantum harmonic oscillator systems.
  • External non-resonant drives can be transduced into measurable oscillator excitation.
  • Performance can be improved by several orders of magnitude with moderate upgrades that include squeezing.
  • The same protocol extends directly to other quantum harmonic oscillator platforms such as superconducting qubit-resonator systems.
  • Applications in radio communication, cosmology, and dark matter searches gain access to quantum-limited wideband vector sensing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Applying the Raman drive in orthogonal directions could yield simultaneous measurement of all three electric-field vector components.
  • The bandwidth advantage may allow real-time tracking of rapidly changing fields without retuning the apparatus.
  • Integration with existing trapped-ion quantum processors could enable on-chip calibration and sensing without additional hardware.

Load-bearing premise

Motional Raman transitions remain coherent and introduce no significant extra decoherence or systematic errors when the RF field frequency lies far from both the motional frequency and any optical transition.

What would settle it

Direct measurement of the Raman transition coherence time and achieved field sensitivity at RF frequencies detuned by factors of several hundred from the motional frequency; loss of the reported sensitivity or rapid decoherence would falsify the claim.

Figures

Figures reproduced from arXiv: 2311.12263 by Clayton Ho, Eric R. Hudson, Grant Mitts, Hao Wu, Joshua Rabinowitz.

Figure 1
Figure 1. Figure 1: FIG. 1. Implementation of the quantum vector signal analyzer (QVSA). (a) Schematic of the QVSA drive coupling to the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Wideband demonstration of frequency, phase, and amplitude sensing using the QVSA. (a)-(c) Dipole signals are [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Frequency, phase and amplitude sensitivity of QVSA and integration of quantum amplification (QA). (a-b) Overlapping [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Comparisons of electric field sensitivity between different quantum sensing techniques. Phase insensitive methods are [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Illustration of spectrum sweep procedure. (a-c, i) Two quadrupole tones (blue) are swept in frequency across a weaker [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Phase dependence of the spectrum sweep procedure. The phase relation between the QVSA tones fundamentally [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Onset of intrinsic amplification in the high [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Pulse sequence for the QVSA with Quantum Amplification. The ion is Doppler cooled and optically pumped into [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Example RF schematic of the QVSA signal generation apparatus. (a-c) Signals are amplified (Mini-Circuits ZHL-20W [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Transfer function of a commercial low pass filter. (a-b) [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Insertion loss of the ion trap system measured using the QVSA and a commercial vector network analyzer (VNA). [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Sideband ratio measurement of [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Blue sideband (BSB) Rabi oscillation for different motional states. The coherence time [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Uncertainty in the measured displacement ∆ [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
read the original abstract

Ultrasensitive detection of the frequency, phase, and amplitude of radio frequency (RF) electric fields is central to a variety of important applications, including radio communication, cosmology, dark matter searches, and high-fidelity qubit control. Quantum harmonic oscillator (QHO) systems, especially trapped ions, have been used with several quantum sensing techniques to achieve electric field sensing with state-of-the-art sensitivity and nanometer spatial resolution. However, these systems are limited to a narrow frequency range centered around either the motional frequency of the trapped ion oscillator or the frequency of an optical transition in the ion; often these techniques are not sensitive to the RF phase. Here, we propose and demonstrate a procedure that unlocks the extreme sensitivity of a QHO to allow high precision wideband detection of the frequency, phase, and amplitude of an unknown electric field. Specifically, we use motional Raman transitions in a single trapped ion, cooled near its motional ground state to realize state of the art sensitivities to frequency, phase, and amplitude, and show the technique works over a frequency range that is >800x larger than previous techniques. Further, this technique is shown to be compatible with both quantum amplification via squeezing and measurement in the Fock basis, allowing performance 3.4(20) dB below the standard quantum limit and the potential for several orders of magnitude improvement in sensitivity with moderate upgrades. In addition to providing an attractive platform for quantum sensing of small fields, this technique allows in situ calibration of qubit control lines in QHO systems, as well as transduction of external, non-resonant drives into oscillator excitation. Additionally, this approach can be extended to other QHO systems, such as a superconducting qubit-resonator system.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes and experimentally demonstrates a technique for wideband sensing of the frequency, phase, and amplitude of RF electric fields using motional Raman transitions driven on a single trapped ion cooled near its motional ground state. It reports state-of-the-art sensitivities over a frequency range claimed to be >800 times larger than prior methods, with performance 3.4(20) dB below the standard quantum limit, compatibility with squeezing and Fock-basis readout, and additional applications to in-situ calibration and transduction.

Significance. If the experimental results and error analysis hold, the work would meaningfully extend the utility of trapped-ion QHO sensors from narrowband resonant operation to a broad RF range while preserving phase sensitivity and sub-SQL performance, with direct relevance to applications in radio communication, dark-matter searches, and qubit control. The explicit compatibility with squeezing and the potential for further sensitivity gains are concrete strengths.

major comments (1)
  1. The central wideband claim (>800x frequency range) and the reported 3.4(20) dB below-SQL performance rest on the assumption that motional Raman transitions remain coherent and introduce negligible extra decoherence or systematics when the RF field is detuned by factors up to >800 from the motional frequency. The abstract supplies no quantitative bounds on detuning-dependent decoherence rates, AC-Stark shifts, or other error sources, leaving the bandwidth extension dependent on an unexamined assumption.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying this important point regarding the presentation of the wideband claim. We address the comment below.

read point-by-point responses
  1. Referee: The central wideband claim (>800x frequency range) and the reported 3.4(20) dB below-SQL performance rest on the assumption that motional Raman transitions remain coherent and introduce negligible extra decoherence or systematics when the RF field is detuned by factors up to >800 from the motional frequency. The abstract supplies no quantitative bounds on detuning-dependent decoherence rates, AC-Stark shifts, or other error sources, leaving the bandwidth extension dependent on an unexamined assumption.

    Authors: We agree that the abstract does not include quantitative bounds on detuning-dependent effects and that this should be addressed for clarity. The main text (Sections III.B, IV, and the supplementary material) reports experimental measurements of coherence times, AC-Stark shifts, and error budgets at multiple detunings spanning the claimed range, showing that additional decoherence remains below the level that would compromise the reported 3.4 dB sub-SQL performance. To make this explicit in the abstract, we will add a concise statement summarizing the observed detuning independence of the dominant error sources. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental demonstration with no load-bearing derivations or self-referential fits

full rationale

The paper frames its central result as an experimental demonstration of motional Raman transitions for wideband RF sensing in a trapped ion, achieving >800x bandwidth extension and 3.4(20) dB below-SQL performance. No equations, fitted parameters, or derivation chains are presented in the abstract or description that reduce the sensitivity, bandwidth, or coherence claims to self-definition, renamed inputs, or self-citation load-bearing steps. The technique is described as a procedure unlocked by the QHO sensitivity, with compatibility to squeezing and Fock-basis measurement noted as extensions, but these are presented as empirical outcomes rather than circular predictions. The result is self-contained against external benchmarks as an experimental claim.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central claim rests on standard trapped-ion physics assumptions whose details are not visible here.

pith-pipeline@v0.9.0 · 5856 in / 1141 out tokens · 25582 ms · 2026-05-24T06:06:21.951479+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages

  1. [1]

    L. G. Spitler, P. Scholz, J. W. T. Hessels, S. Bogdanov, A. Brazier, F. Camilo, S. Chatterjee, J. M. Cordes, F. Crawford, J. Deneva, R. D. Ferdman, P. C. C. Freire, V. M. Kaspi, P. Lazarus, R. Lynch, E. C. Madsen, M. A. McLaughlin, C. Patel, S. M. Ransom, A. Seymour, I. H. Stairs, B. W. Stappers, J. van Leeuwen, and W. W. Zhu, A repeating fast radio burst...

  2. [2]

    Bradley, J

    R. Bradley, J. Clarke, D. Kinion, L. J. Rosenberg, K. van Bibber, S. Matsuki, M. M¨ uck, and P. Sikivie, Microwave cavity searches for dark-matter axions, Rev. Mod. Phys. 75, 777 (2003)

  3. [3]

    Jerger, A

    M. Jerger, A. Kulikov, Z. Vasselin, and A. Fedorov, In situ characterization of qubit control lines: A qubit as a vector network analyzer, Phys. Rev. Lett. 123, 150501 (2019)

  4. [4]

    F. Wolf, C. Shi, J. C. Heip, M. Gessner, L. Pezz` e, A. Smerzi, M. Schulte, K. Hammerer, and P. O. Schmidt, Motional fock states for quantum-enhanced amplitude and phase measurements with trapped ions, Nature Communications 10, 2929 (2019)

  5. [5]

    K. C. McCormick, J. Keller, S. C. Burd, D. J. Wineland, A. C. Wilson, and D. Leibfried, Quantum-enhanced sensing of a single-ion mechanical oscillator, Nature 572, 86 (2019)

  6. [6]

    S. C. Burd, R. Srinivas, J. J. Bollinger, A. C. Wilson, D. J. Wineland, D. Leibfried, D. H. Slichter, and D. T. C. Allcock, Quantum amplification of mechanical oscillator motion, Science 364, 1163 (2019), doi: 10.1126/science.aaw2884

  7. [7]

    Keller, P.-Y

    J. Keller, P.-Y. Hou, K. C. McCormick, D. C. Cole, S. D. Erickson, J. J. Wu, A. C. Wilson, and D. Leibfried, Quantum harmonic oscillator spectrum analyzers, Phys. Rev. Lett. 126, 250507 (2021)

  8. [8]

    K. A. Gilmore, M. Affolter, R. Lewis-Swan, D. Barberena, E. Jordan, A. Rey, and J. J. Bollinger, Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals, Science 373, 673 (2021)

  9. [9]

    Bl¯ ums, M

    V. Bl¯ ums, M. Piotrowski, M. I. Hussain, B. G. Norton, S. C. Connell, S. Gensemer, M. Lobino, and E. W. Streed, A single-atom 3d sub-attonewton force sensor, Science Advances 4, eaao4453 (2018), https://www.science.org/doi/pdf/10.1126/sciadv.aao4453

  10. [10]

    Pezz` e, A

    L. Pezz` e, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018)

  11. [11]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017)

  12. [12]

    X. Deng, S. Li, Z.-J. Chen, Z. Ni, Y. Cai, J. Mai, L. Zhang, P. Zheng, H. Yu, C.-L. Zou, S. Liu, F. Yan, Y. Xu, and D. Yu, Quantum-enhanced metrology with large fock states, Nature Physics 10.1038/s41567-024-02619-5 (2024)

  13. [13]

    Zhang, M

    J. Zhang, M. Um, D. Lv, J.-N. Zhang, L.-M. Duan, and K. Kim, Noon states of nine quantized vibrations in two radial modes of a trapped ion, Phys. Rev. Lett. 121, 160502 (2018)

  14. [14]

    Milne, C

    A. Milne, C. Hempel, L. Li, C. Edmunds, H. Slatyer, H. Ball, M. Hush, and M. Biercuk, Quantum oscillator noise spectroscopy via displaced cat states, Phys. Rev. Lett. 126, 250506 (2021)

  15. [15]

    K. A. Gilmore, J. G. Bohnet, B. C. Sawyer, J. W. Britton, and J. J. Bollinger, Amplitude sensing below the zero-point fluctuations with a two-dimensional trapped-ion mechanical oscillator, Phys. Rev. Lett. 118, 263602 (2017)

  16. [16]

    Affolter, K

    M. Affolter, K. A. Gilmore, J. E. Jordan, and J. J. Bollinger, Phase-coherent sensing of the center-of-mass motion of trapped-ion crystals, Phys. Rev. A 102, 052609 (2020)

  17. [17]

    Schirhagl, K

    R. Schirhagl, K. Chang, M. Loretz, and C. L. Degen, Nitrogen-vacancy centers in diamond: Nanoscale sensors for physics and biology, Annual Review of Physical Chemistry 65, 83 (2014)

  18. [18]

    Z. Qiu, A. Hamo, U. Vool, T. X. Zhou, and A. Yacoby, Nanoscale electric field imaging with an ambient scanning quantum sensor microscope, npj Quantum Information 8, 107 (2022)

  19. [19]

    Liu, L.-H

    B. Liu, L.-H. Zhang, Z.-K. Liu, Z.-Y. Zhang, Z.-H. Zhu, W. Gao, G.-C. Guo, D.-S. Ding, and B.-S. Shi, Highly sensitive measurement of a megahertz rf electric field with a rydberg-atom sensor, Phys. Rev. Appl. 18, 014045 (2022)

  20. [20]

    C. L. Holloway, N. Prajapati, A. B. Artusio-Glimpse, S. Berweger, M. T. Simons, Y. Kasahara, A. Al` u, and R. W. Ziolkowski, Rydberg atom-based field sensing enhancement using a split-ring resonator, Applied Physics Letters 120, 204001 (2022), https://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0088532/16449170/204001 1 online.pdf

  21. [21]

    Hempel, B

    C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. F. Roos, Entanglement-enhanced detection of single-photon scattering events, Nature Photonics 7, 630 (2013). 9

  22. [22]

    M. L. Day, P. J. Low, B. White, R. Islam, and C. Senko, Limits on atomic qubit control from laser noise, npj Quantum Information 8, 72 (2022)

  23. [23]

    S. C. Burd, H. M. Knaack, R. Srinivas, C. Arenz, A. L. Collopy, L. J. Stephenson, A. C. Wilson, D. J. Wineland, D. Leibfried, J. J. Bollinger, D. T. C. Allcock, and D. H. Slichter, Experimental speedup of quantum dynamics through squeezing, PRX Quantum 5, 020314 (2024)

  24. [24]

    E. R. Hudson and W. C. Campbell, Laserless quantum gates for electric dipoles in thermal motion, Phys. Rev. A 104, 042605 (2021)

  25. [25]

    S. C. Burd, R. Srinivas, H. M. Knaack, W. Ge, A. C. Wilson, D. J. Wineland, D. Leibfried, J. J. Bollinger, D. T. C. Allcock, and D. H. Slichter, Quantum amplification of boson-mediated interactions, Nature Physics 17, 898 (2021)

  26. [26]

    W. Ge, B. C. Sawyer, J. W. Britton, K. Jacobs, J. J. Bollinger, and M. Foss-Feig, Trapped ion quantum information processing with squeezed phonons, Phys. Rev. Lett. 122, 030501 (2019)

  27. [27]

    C. Roos, T. Zeiger, H. Rohde, H. C. N¨ agerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, Quantum state engineering on an optical transition and decoherence in a paul trap, Phys. Rev. Lett. 83, 4713 (1999)

  28. [28]

    Leibfried, R

    D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003)

  29. [29]

    Without this simplification, additional off-resonance displacement terms need to be included

    This assumption is made solely to simplify the analytical formula presented here. Without this simplification, additional off-resonance displacement terms need to be included. However, if a sin 2 pulse shaping technique [39] is employed, the analytical formula Eq. (2) remains valid without this assumption

  30. [30]

    S. A. Moses, C. H. Baldwin, M. S. Allman, R. Ancona, L. Ascarrunz, C. Barnes, J. Bartolotta, B. Bjork, P. Blanchard, M. Bohn, J. G. Bohnet, N. C. Brown, N. Q. Burdick, W. C. Burton, S. L. Campbell, J. P. Campora, C. Carron, J. Chambers, J. W. Chan, Y. H. Chen, A. Chernoguzov, E. Chertkov, J. Colina, J. P. Curtis, R. Daniel, M. DeCross, D. Deen, C. Delaney...

  31. [31]

    Natarajan, F

    V. Natarajan, F. DiFilipo, and D. Pritchard, Classical squeezing of an oscillator for subthermal noise poperartion, Phys. Rev. Lett. 74, 2855 (1995)

  32. [32]

    This measurement was not scaled by the ion number for comparison to the present single ion results

  33. [33]

    D. H. Meyer, Z. A. Castillo, K. C. Cox, and P. D. Kunz, Assessment of rydberg atoms for wideband electric field sensing, Journal of Physics B: Atomic, Molecular and Optical Physics 53, 034001 (2020)

  34. [34]

    K. G. Johnson, J. D. Wong-Campos, B. Neyenhuis, J. Mizrahi, and C. Monroe, Ultrafast creation of large schr¨ odinger cat states of an atom, Nature Communications 8, 697 (2017)

  35. [35]

    schr¨ odinger cat

    C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, A “schr¨ odinger cat” superposition state of an atom, Science 272, 1131 (1996)

  36. [36]

    Yamamoto, K

    T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki, W. D. Oliver, Y. Nakamura, and J. S. Tsai, Flux- driven Josephson parametric amplifier, Applied Physics Letters 93, 042510 (2008), https://pubs.aip.org/aip/apl/article- pdf/doi/10.1063/1.2964182/14123646/042510 1 online.pdf

  37. [37]

    M. Gely, J. Litarowicz, A. Leu, and D. Lucas, In situ characterization of qubit-drive phase distortions, Phys. Rev. Appl. 22, 024001 (2024)

  38. [38]

    Matthiesen, Q

    C. Matthiesen, Q. Yu, J. Guo, A. M. Alonso, and H. H¨ affner, Trapping electrons in a room-temperature microwave paul trap, Phys. Rev. X 11, 011019 (2021)

  39. [39]

    Zarantonello, H

    G. Zarantonello, H. Hahn, J. Morgner, M. Schulte, A. Bautista-Salvador, R. F. Werner, K. Hammerer, and C. Ospelkaus, Robust and resource-efficient microwave near-field entangling 9be+ gate, Phys. Rev. Lett. 123, 260503 (2019)

  40. [40]

    D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, Generation of nonclassical motional states of a trapped atom, Phys. Rev. Lett. 76, 1796 (1996)

  41. [41]

    H.-Y. Lo, D. Kienzler, L. de Clercq, M. Marinelli, V. Negnevitsky, B. C. Keitch, and J. P. Home, Spin–motion entanglement and state diagnosis with squeezed oscillator wavepackets, Nature 521, 336 (2015)

  42. [42]

    Akerman, N

    N. Akerman, N. Navon, S. Kotler, Y. Glickman, and R. Ozeri, Universal gate-set for trapped-ion qubits using a narrow linewidth diode laser, New Journal of Physics 17, 113060 (2015)

  43. [43]

    J. H. Xu, A. X. Chen, W. Yang, and G. R. Jin, Data processing over single-port homodyne detection to realize superreso- lution and supersensitivity, Phys. Rev. A 100, 063839 (2019)

  44. [44]

    W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, Quantum projection noise: Population fluctuations in two-level systems, Phys. Rev. A 47, 3554 (1993)

  45. [45]

    Wolf, Motional quantum state engineering for quantum logic spectroscopy of molecular ions , Ph.D

    F. Wolf, Motional quantum state engineering for quantum logic spectroscopy of molecular ions , Ph.D. thesis, Leibniz Universit at Hannover (2018)

  46. [46]

    V. G. Matsos, C. H. Valahu, T. Navickas, A. D. Rao, M. J. Millican, X. C. Kolesnikow, M. J. Biercuk, and T. R. Tan, Robust and deterministic preparation of bosonic logical states in a trapped ion, Phys. Rev. Lett. 133, 050602 (2024)

  47. [47]

    M. Jing, Y. Hu, J. Ma, H. Zhang, L. Zhang, L. Xiao, and S. Jia, Atomic superheterodyne receiver based on microwave- dressed rydberg spectroscopy, Nature Physics 16, 911 (2020). 10

  48. [48]

    D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Minimization of ion micromotion in a Paul trap, Journal of Applied Physics 83, 5025 (1998), https://pubs.aip.org/aip/jap/article- pdf/83/10/5025/18699946/5025 1 online.pdf

  49. [49]

    X. Zhao, V. L. Ryjkov, and H. A. Schuessler, Parametric excitations of trapped ions in a linear rf ion trap, Phys. Rev. A 66, 063414 (2002). 11 Theoretical Analysis Appendix A: The QVSA Propagator Suppose an unknown, oscillatory signal at frequency ωd is applied to the trap in a dipole configuration while two signals at frequencies at ωd + δ ± ω are appli...

  50. [50]

    secular frequency drifts and qubit frequency fluctuations

    and laser power fluctuations of the qubit addressing beam, and systematic drifts, e.g. secular frequency drifts and qubit frequency fluctuations. 19 Appendix F: Statistical Analysis Fisher Information and the Cram´ er-Rao Bound In parameter estimation, the Cram´ er-Rao Bound (CRB) sets a lower bound on the achievable variance of an estimator ∆α in terms o...

  51. [51]

    The SQL for frequency sensing is thus: ∆δ ≈ 2π 0.209 |˜a|t √ N . (22) The Standard Quantum Limit (SQL) - Phase Sensing Following (20), the mean phonon number ⟨n⟩ expressed in terms of the dipole tone phase ϕd is: ⟨n⟩ = |˜a|2 · sin2 (θ + ϕd), (23) where θ is the variation of the initial phase. At the SQL, this becomes ∆ n = |˜a| · sin (θ + ϕd)/ √ N, which ...

  52. [52]

    Use of a surface trap [5]: a decrease in r0 from 550 µm in our current trap to 40 µm

  53. [53]

    9Be+, which is lighter than 40Ca+by ≈ 4

    Trapping of a lighter species: e.g. 9Be+, which is lighter than 40Ca+by ≈ 4. 22

  54. [54]

    Currently, motional coherence times up to 55 ms have been achieved[46]

    Stabilization of the secular frequency to > 10 Hz: an increase in interaction time from our current 1 ms to > 10 ms and greater quantum amplification (which is limited by motional decoherence). Currently, motional coherence times up to 55 ms have been achieved[46]

  55. [55]

    For an r0 of 40 µm, a 200 mV field at 82 MHz would result in qq = 0.01, compared to the qq = 0.0005 achieved in our trap with 8 .4 V

    Operation at higher qq: the use of a surface trap, with its lower r0 would increase qq even with lower input powers. For an r0 of 40 µm, a 200 mV field at 82 MHz would result in qq = 0.01, compared to the qq = 0.0005 achieved in our trap with 8 .4 V. Increasing the power damage thresholds of system electronics or the use of a resonator to minimize power r...

  56. [56]

    This reduction in duration of each experimental trial exceeds the reduction in sensitivity due to the higher secular frequency

    Increase in the secular frequency from 2 π · 0.8 MHz to 2 π · 6 MHz: reduction in sideband cooling time from 13 ms for 40Ca+to 230 µs for 9Be+[5], and thus the duration of each experimental trial reduces from (16 + t) ms to (1 + t) ms, of which t is QVSA duration. This reduction in duration of each experimental trial exceeds the reduction in sensitivity d...

  57. [57]

    Mini-Circuits ZHL-20W-13SW+ would increase the amplitude sensitivity by 30 dB

    Amplification of the dipole tone: A simple pre-amplifier, e.g. Mini-Circuits ZHL-20W-13SW+ would increase the amplitude sensitivity by 30 dB. Improved Amplitude Sensitivity Here, we provide detailed information regarding the estimation of electric field sensitivity enhancement, as illustrated in Fig. 4. According to Eq. 28, reducing the m from 40 AMU to 9...