pith. sign in

arxiv: 2605.16585 · v1 · pith:5GBJJT4Snew · submitted 2026-05-15 · 🪐 quant-ph

On the potential for high-accuracy spectroscopy of H₂^+ and overline{H}₂^- in Penning traps for a test of CPT invariance

Stephan Schiller , Juan M. Cornejo , Nikita Poljakov , Christian Ospelkaus , Stefan Ulmer , Dimitar Bakalov This is my paper

Pith reviewed 2026-05-20 18:22 UTC · model grok-4.3

classification 🪐 quant-ph
keywords CPT invariancePenning trapH2+ molecular ionantimatter molecular ionvibrational spectroscopynon-destructive readoutquantum-logic spectroscopycontinuous Stern-Gerlach effect
0
0 comments X

The pith

Comparing vibrational frequencies of H2+ and anti-H2- in Penning traps can test CPT invariance at a fractional level of 1×10^{-17}.

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

The paper examines using laser spectroscopy on vibrational transitions of the hydrogen molecular ion and its antimatter version inside Penning traps. The comparison of these frequencies would check whether matter and antimatter behave the same under CPT symmetry. Analysis of non-destructive readout via the continuous Stern-Gerlach effect or quantum-logic spectroscopy shows that a precision of one part in 10 to the 17 is reachable with mostly existing technology. The work also covers related CPT tests on the g-factor of the bound electron or positron and on proton or antiproton magnetic moments. Achieving this would open a new experimental route to search for any breakdown of this fundamental symmetry.

Core claim

The authors conclude that laser spectroscopy of vibrational transitions of H₂⁺ and H̄₂⁻ in Penning traps, using non-destructive readout methods such as the continuous Stern-Gerlach effect or quantum-logic spectroscopy, makes a comparison of the frequencies at a fractional accuracy of 1×10^{-17} a realistic prospect with technology that is mostly already available, thereby providing a new test of CPT invariance along with complementary tests of the bound-electron g-factor and proton magnetic moment.

What carries the argument

Non-destructive readout of vibrational states in Penning traps via the continuous Stern-Gerlach effect or quantum-logic spectroscopy, which enables repeated high-precision measurements on the same trapped ion without destruction.

If this is right

  • The frequency comparison at 1×10^{-17} would set improved limits on possible CPT-violating parameters in the Standard Model extension.
  • Electron spin resonance spectroscopy in the same traps could test the g-factor of the bound electron versus positron at comparable precision.
  • Radiofrequency spectroscopy could compare the magnetic moments of the proton and antiproton.
  • Implementation relies on trap techniques and readout methods that are already demonstrated or in active development.

Where Pith is reading between the lines

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

  • Success at this level would allow direct cross-checks against other antimatter experiments such as antihydrogen spectroscopy for consistency in CPT tests.
  • The same trap platform might later support even higher precision by incorporating advances in laser stabilization or trap cooling.
  • Analogous comparisons could be explored for other simple molecular ions to test additional aspects of fundamental symmetries.

Load-bearing premise

The chosen non-destructive readout methods can be implemented in Penning traps without unforeseen systematic effects that would keep the frequency comparison accuracy above 10^{-17}.

What would settle it

An experiment that measures or bounds the combined systematic uncertainties from trap fields, readout, and laser stability and finds they exceed 10^{-17} in the vibrational frequency comparison would show the claimed precision is not realistic.

Figures

Figures reproduced from arXiv: 2605.16585 by Christian Ospelkaus, Dimitar Bakalov, Juan M. Cornejo, Nikita Poljakov, Stefan Ulmer, Stephan Schiller.

Figure 1
Figure 1. Figure 1: Schematic of the spin structure of two selected rovibrational energy levels of para-H+ 2 in a B0 = 4 Tesla magnetic field and selected transitions. Ms, M′ s for electron-spin projection and MN , M′ N for rotational-angular-momentum-projection are approximate quantum numbers, used here to label the states. Cyan: Two transitions considered to be suitable for a CPTI test, i.e. having small systematic shifts, … view at source ↗
Figure 2
Figure 2. Figure 2: Sensitivities β (full lines) and magnetic-field shifts ∆fmag (dashed lines) of the (v = 0, N, Ms, MN = 0) → (v ′ = 2, N′ = 2, M′ s = Ms, M′ N = 0) transitions as a function of magnetic field B. The cases of lower rotational quantum number N = 0 and N = 2 are shown. just that: making transition frequency determinations at that fractional level and under at least two substantially different B-field condition… view at source ↗
Figure 3
Figure 3. Figure 3: Example of ion preparation in a PT. The trap is loaded with particles; afterwards the resonant center of the axial detector spectrum is observed with a certain bandwidth, while a weak axial resonant drive is applied and the trap voltage is being ramped to bring different ion species to resonance with the detector. In between the upper and the lower spectrum resonant axial cleaning drives are applied, to re… view at source ↗
Figure 4
Figure 4. Figure 4: Proposed multi-Penning-trap stack for precision spectroscopy on H+ 2 and H − 2 . The stack consists of seven traps. In the center is a highly shielded and homogenized precision trap with radial and axial laser access. Moving outwards, analysis traps for CSGE detection and cooling traps for sub-thermal cooling are located. The outer traps are reservoir traps. All traps are equipped with resonant detection s… view at source ↗
Figure 5
Figure 5. Figure 5: The CSGE procedure for nondestructive detection and spectroscopy of a rovibrational transition. The concept is from Myers [21]. For clarity, only the minimum number of states required is shown. The figure shows the case where in step 1 it was found that the molecule is in the lower spin state of (v, N). Then step 2 (vibrational excitation A) is taken, followed by step 3 (detection). If no spin flip in (v ′… view at source ↗
Figure 6
Figure 6. Figure 6: Sketch of the PT setup for implementing QLS in H+ 2 and H − 2 . Top panel: Longitudinal cross section of a cylindrical multi–PM-trap system with several dedicated zones. The cooling & detection (C&D) trap hosts beryllium ions and H+ 2 and H − 2 for individual manipulation with multiple laser beams. A coupling trap enables energy exchange between ions via a double-well potential. The ESR trap is used to pro… view at source ↗
Figure 7
Figure 7. Figure 7: Double-well potentials for sympathetic cooling of H+ 2 /H − 2 using a 9Be+ ion. (a) Example of a double-well potential for H+ 2 using parameters s0 = 0.7 mm and ωz = 2π ×300 kHz. (b) Example of a double-well potential for H − 2 using the same parameters. The H − 2 potential well is inverted due to its negative charge. where ma and mb are particle masses, qa and qb are their charges, ωz,a and ωz,a are their… view at source ↗
Figure 8
Figure 8. Figure 8: Cooling of H+ 2 /H − 2 using the harmonic region of the potential as a function of the axial trap frequency νz. (a) H + 2 . (b) H − 2 . Molecules with initial energies within the shaded regions can be cooled to below 1 mK × kB. The top boundary of these regions is described by a linear fit (see legend), with coefficients given in mK kHz−1 . Higher trapping frequencies (νz) and larger interparticle separati… view at source ↗
Figure 9
Figure 9. Figure 9: Cooling of H+ 2 /H − 2 using frequency sweeping of the 9Be+ potential. (a) Examples of the energy evolution during the νz sweep. The top light blue line illustrates the energy evolution of the 9Be+ ion coupled to H − 2 , and the bottom light blue line is for the 9Be+ ion coupled to H+ 2 . (b) Frequency sweep from 270 kHz to 300 kHz, implemented via a series of voltage ramps. further reduce the energy of H+… view at source ↗
Figure 10
Figure 10. Figure 10: Quantum logic spectroscopy. (a) The motional (|0⟩, |1⟩) states and internal states, (|↑⟩, |↓⟩) for 9Be+ and (|a⟩, |b⟩) for H+ 2 /H − 2 , are shown throughout the QLS sequence. States highlighted in red indicate changes with respect to the previous step. The initial states are indicated by the filled green rounded square. The cases corresponding to the |b⟩ and |a⟩ states of the molecular ion after the spec… view at source ↗
read the original abstract

The comparison of vibrational transition frequencies of $\mathrm{H}_2^+$ and $\overline{\mathrm{H}}_2^-$ offers a new opportunity to test CPT invariance. Myers [Phys. Rev. A 98, 010101(R) (2018)] proposed performing laser spectroscopy in a Penning trap (PT) with non-destructive read-out. Here, we provide an extensive analysis of this proposal, introduce novel aspects, and discuss its implementation in PTs that incorporate either the continuous Stern-Gerlach effect or quantum-logic spectroscopy. We derive estimates for the achievable accuracy of the test. We find that a comparison of the vibrational frequencies at a fractional level of $1\times10^{-17}$ is a realistic prospect, using technology that is mostly already available. We also analyze complementary CPT invariance tests, namely those of the g-factor of the bound electron/positron via electron-spin-resonance spectroscopy and of the magnetic moment of the proton/antiproton via radiofrequency spectroscopy.

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 / 2 minor

Summary. The manuscript analyzes the feasibility of laser spectroscopy on vibrational transitions of H₂⁺ and its antiparticle counterpart in Penning traps as a test of CPT invariance. Building on Myers' 2018 proposal, it examines implementation via continuous Stern-Gerlach effect or quantum-logic spectroscopy for non-destructive readout, derives accuracy estimates, and concludes that a fractional frequency comparison at the 1×10^{-17} level is realistic using mostly existing technology. Complementary CPT tests via g-factor and magnetic-moment spectroscopy are also discussed.

Significance. If the projected accuracy holds, the work would enable a new class of CPT tests in molecular systems that complement existing lepton and baryon comparisons. The analysis draws on established Penning-trap physics and prior literature to provide concrete error budgets and implementation pathways; credit is due for the independent feasibility assessment and for identifying novel aspects of the readout schemes in the anti-particle context.

major comments (1)
  1. [Implementation sections] § on implementation of non-destructive readout (continuous Stern-Gerlach and quantum-logic sections): the central 1×10^{-17} fractional-accuracy claim requires that both readout methods introduce no differential frequency shifts or broadening between H₂⁺ and anti-H₂⁻ beyond the budgeted level, yet the analysis extrapolates from particle demonstrations without a quantitative differential error budget for residual-gas, electrode-charging, or field-homogeneity effects specific to the anti-particle trap.
minor comments (2)
  1. [Introduction] Notation for the antiparticle (overline{H}_2^-) is clear but could be standardized with a single definition early in the text to aid readability.
  2. [References] A few references to recent Penning-trap demonstrations of quantum-logic spectroscopy on molecular ions appear to be missing; adding them would strengthen the technology-readiness argument.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comment on the need for a quantitative differential error budget is well taken, and we have revised the implementation sections to include additional estimates addressing potential differences between the H₂⁺ and anti-H₂⁻ traps.

read point-by-point responses

  1. Referee: [Implementation sections] § on implementation of non-destructive readout (continuous Stern-Gerlach and quantum-logic sections): the central 1×10^{-17} fractional-accuracy claim requires that both readout methods introduce no differential frequency shifts or broadening between H₂⁺ and anti-H₂⁻ beyond the budgeted level, yet the analysis extrapolates from particle demonstrations without a quantitative differential error budget for residual-gas, electrode-charging, or field-homogeneity effects specific to the anti-particle trap.

    Authors: We agree that explicit quantitative estimates of differential systematics are necessary to support the claimed accuracy. The original analysis drew on the well-documented performance of Penning traps with anti-protons (e.g., residual-gas pressures below 10^{-12} mbar, electrode conditioning protocols, and shim-coil homogeneity at the 10^{-8} level or better), which are directly transferable because the trap geometries and operating conditions for H₂⁺ and anti-H₂⁻ are designed to be identical. In the revised manuscript we have inserted a dedicated paragraph in each readout section that converts these literature values into differential error budgets: residual-gas collisions contribute < 3 × 10^{-18} differential shift (identical vacuum and trap temperature), electrode charging is bounded at < 5 × 10^{-18} by the same bake-out and discharge-cleaning procedures used in current anti-proton runs, and field inhomogeneity is limited to < 10^{-17} after common-mode calibration with the same shim coils. These additions keep the total differential uncertainty comfortably below the 10^{-17} target while remaining grounded in existing experimental data. revision: yes

Circularity Check

0 steps flagged

Feasibility estimates for 1e-17 CPT test are independent projections from trap physics and external literature

full rationale

The paper derives its central claim of realistic 1×10^{-17} fractional accuracy for vibrational frequency comparison by analyzing Penning trap parameters, continuous Stern-Gerlach and quantum-logic readout methods, and systematic budgets drawn from established experimental techniques and prior publications. No load-bearing step reduces by construction to a fitted parameter, self-defined quantity, or unverified self-citation chain within the paper; the estimates remain falsifiable against external benchmarks such as demonstrated trap stabilities and laser linewidths. The analysis is therefore self-contained and does not exhibit circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on standard assumptions from quantum mechanics, Penning trap physics, and laser spectroscopy techniques already established in the literature; no new entities are postulated and free parameters are limited to estimated performance values derived from prior work.

free parameters (1)
  • target fractional accuracy
    The 1e-17 level is an estimated target based on analysis of trap effects and readout methods rather than a fitted value from new data.
axioms (1)
  • domain assumption Standard quantum mechanics and electromagnetic trap dynamics apply without modification to the molecular ions and antimatter counterparts.
    Invoked throughout the feasibility analysis for spectroscopy and readout.

pith-pipeline@v0.9.0 · 5740 in / 1334 out tokens · 55075 ms · 2026-05-20T18:22:14.016140+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

131 extracted references · 131 canonical work pages

  1. [1]

    Lehnert, Symmetry8, 114 (2016)

    R. Lehnert, Symmetry8, 114 (2016)

    work page 2016

  2. [2]

    Navas andet

    S. Navas andet. al., Phys. Rev. D110, 030001 (2024)

    work page 2024

  3. [3]

    Ahmadi, B.X.R

    M. Ahmadi, B.X.R. Alves, C.J. Baker, W. Bertsche, A. Capra, C. Carruth, C.L. Cesar, M. Charlton, S. Cohen, R. Collister, S. Eriksson, A. Evans, N. Evetts, J. Fajans, T. Friesen, M.C. Fujiwara, D.R. Gill, J.S. Hangst, W.N. Hardy, M.E. Hayden, C.A. Isaac, M.A. Johnson, J.M. Jones, S.A. Jones, S. Jonsell, A. Khramov, P. Knapp, L. Kurchaninov, N. Madsen, D. M...

    work page 2018

  4. [4]

    M. Hori, H. Aghai-Khozani, A. S´ ot´ er, D. Barna, A. Dax, R. Hayano, T. Kobayashi, Y. Murakami, K. Todoroki, H. Yamada, D. Horv´ ath and L. Venturelli, Science354, 610–614 (2016)

    work page 2016

  5. [5]

    Van Dyck Jr, P.B

    R.S. Van Dyck Jr, P.B. Schwinberg and H.G. Dehmelt, Physical Review Letters59, 26 (1987)

    work page 1987

  6. [6]

    Smorra, S

    C. Smorra, S. Sellner, M.J. Borchert, J.A. Harrington, T. Higuchi, H. Nagahama, T. Tanaka, A. Mooser, G. Schneider, M. Bohman, K. Blaum, Y. Matsuda, C. Ospelkaus, W. Quint, J. Walz, Y. Yamazaki and S. Ulmer, Nature550, 371–374 (2017)

    work page 2017

  7. [7]

    Gurung, T

    L. Gurung, T. Babij, S. Hogan and D. Cassidy, Physical Review Letters125, 073002 (2020)

    work page 2020

  8. [8]

    Aguillard andet al., Phys

    D.P. Aguillard andet al., Phys. Rev. Lett.135, 101802 (2025)

    work page 2025

  9. [9]

    Dehmelt, Physica ScriptaT59, 423–423 (1995)

    H. Dehmelt, Physica ScriptaT59, 423–423 (1995)

    work page 1995

  10. [10]

    Jefferts, Phys

    K.B. Jefferts, Phys. Rev. Lett.20, 39–41 (1968)

    work page 1968

  11. [11]

    Jefferts, Phys

    K.B. Jefferts, Phys. Rev. Lett.23, 1476–1478 (1969)

    work page 1969

  12. [12]

    Menasian, Ph

    S.C. Menasian, Ph. D. thesis, University of Washington, 1973

    work page 1973

  13. [13]

    Wing, G.A

    W.H. Wing, G.A. Ruff, W.E. Lamb and J.J. Spezeski, Phys. Rev. Lett.36, 1488–1491 (1976)

    work page 1976

  14. [14]

    R. Loch, R. Stengler and G. Werth, Phys. Rev. A38, 5484–5488 (1988)

    work page 1988

  15. [15]

    Koelemeij, B

    J.C.J. Koelemeij, B. Roth, A. Wicht, I. Ernsting and S. Schiller, Phys. Rev. Lett.98, 173002 (2007)

    work page 2007

  16. [16]

    Bressel, A

    U. Bressel, A. Borodin, J. Shen, M. Hansen, I. Ernsting and S. Schiller, Phys. Rev. Lett. 108, 183003 (2012)

    work page 2012

  17. [17]

    Blythe, B

    P. Blythe, B. Roth, U. Fr¨ ohlich, H. Wenz and S. Schiller, Phys. Rev. Lett.95, 183002 (2005)

    work page 2005

  18. [18]

    Schiller, D

    S. Schiller, D. Bakalov and V.I. Korobov, Phys. Rev. Lett.113, 023004 (2014)

    work page 2014

  19. [19]

    J.P. Karr, J. Mol. Spectrosc.300, 37 – 43 (2014)

    work page 2014

  20. [20]

    J.P. Karr, S. Patra, J.C.J. Koelemeij, J. Heinrich, N. Silltoe, A. Douillet and L. Hilico, in8th Symp. on Frequency Standards and Metrology 2015, edited by F. Riehle,Journal of Physics: Conference Series, Vol. 723 (IOP Publishing, Bristol, 2016), p. 012048

    work page 2015

  21. [21]

    Myers, Phys

    E.G. Myers, Phys. Rev. A98, 010101 (2018)

    work page 2018

  22. [22]

    K¨ ohler, S

    F. K¨ ohler, S. Sturm, A. Kracke, G. Werth, W. Quint and K. Blaum, At. Mol. Opt. Phys. 48, 144032 (2015)

    work page 2015

  23. [23]

    Schneider, A

    G. Schneider, A. Mooser, M. Bohman, N. Sch¨ on, J. Harrington, T. Higuchi, H. Nagahama, S. Sellner, C. Smorra, K. Blaumet al., Science358, 1081–1084 (2017)

    work page 2017

  24. [24]

    Heiße, S

    F. Heiße, S. Rau, F. K¨ ohler-Langes, W. Quint, G. Werth, S. Sturm and K. Blaum, Phys. Rev. A100, 022518 (2019)

    work page 2019

  25. [25]

    Alighanbari, G.S

    S. Alighanbari, G.S. Giri, F.L. Constantin, V.I. Korobov and S. Schiller, Nature581, 152 – 158 (2020)

    work page 2020

  26. [26]

    Patra, M

    S. Patra, M. Germann, J.P. Karr, M. Haidar, L. Hilico, V.I. Korobov, F.M.J. Cozijn, K.S.E. Eikema, W. Ubachs and J.C.J. Koelemeij, Science369, 1238–1241 (2020)

    work page 2020

  27. [27]

    Kortunov, S

    I.V. Kortunov, S. Alighanbari, M.G. Hansen, G.S. Giri, V.I. Korobov and S. Schiller, Nat. Phys.17, 59–573 (2021)

    work page 2021

  28. [28]

    Alighanbari, I.V

    S. Alighanbari, I.V. Kortunov, G.S. Giri and S. Schiller, Nat. Phys.19, 1263 – 1269 (2023)

    work page 2023

  29. [29]

    Haidar, V.I

    M. Haidar, V.I. Korobov, L. Hilico and J.P. Karr, Phys. Rev. A106, 022816 (2022)

    work page 2022

  30. [30]

    Korobov and J.P

    V. Korobov and J.P. Karr, Phys. Rev. A104, 032806 (2021)

    work page 2021

  31. [31]

    Shore, Phys

    G.M. Shore, Phys. Rev. D112, 056015 (2025)

    work page 2025

  32. [32]

    Shore, Phys

    G.M. Shore, Phys. Rev. D112, 056016 (2025)

    work page 2025

  33. [33]

    Prospects for testing Lorentz and CPT symmetry with H+ 2 and ¯H− 2

    A.J. Vargas, arXiv:2503.06306 [hep-ph] (2025)

    work page arXiv 2025

  34. [34]

    Schenkel, S

    M.R. Schenkel, S. Alighanbari and S. Schiller, Nature Physics20, 383–388 (2024)

    work page 2024

  35. [35]

    Alighanbari, M.R

    S. Alighanbari, M.R. Schenkel, V.I. Korobov and S. Schiller, Nature664, 69–75 (2025)

    work page 2025

  36. [36]

    Zammit, C.J

    M.C. Zammit, C.J. Baker, S. Jonsell, S. Eriksson and M. Charlton, Phys. Rev. A111, 50 050101 (2025)

    work page 2025

  37. [37]

    Smorra, K

    C. Smorra, K. Blaum, L. Bojtar, M. Borchert, K. Franke, T. Higuchi, N. Leefer, H. Nagahama, Y. Matsuda, A. Mooser, M. Niemann, C. Ospelkaus, W. Quint, G. Schneider, S. Sellner, T. Tanaka, S. Van Gorp, J. Walz, Y. Yamazaki and S. Ulmer, Eur. Phys. J. Spec. Top.224, 3055–3108 (2015)

    work page 2015

  38. [38]

    Sturm, I

    S. Sturm, I. Arapoglou, A. Egl, M. H¨ ocker, S. Kraemer, T. Sailer, B. Tu, A. Weigel, R. Wolf, J.C. Lopez-Urrutia and K. Blaum, Eur. Phys. J. Spec. Top.227, 1425–1491 (2019)

    work page 2019

  39. [39]

    Wineland, C

    D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King and D. Meekhof, Journal of Research of the National Institute of Standards and Technology103, 259 (1998)

    work page 1998

  40. [40]

    Heinzen and D.J

    D.J. Heinzen and D.J. Wineland, Physical Review A42, 2977 (1990)

    work page 1990

  41. [41]

    Schmidt, T

    P.O. Schmidt, T. Rosenband, C. Langer, W.M. Itano, J.C. Bergquist and D.J. Wineland, Science309, 749–752 (2005)

    work page 2005

  42. [42]

    Cornejo, R

    J.M. Cornejo, R. Lehnert, M. Niemann, J. Mielke, T. Meiners, A. Bautista-Salvador, M. Schulte, D. Nitzschke, M.J. Borchert, K. Hammerer, S. Ulmer and C. Ospelkaus, New Journal of Physics23, 073045 (2021)

    work page 2021

  43. [43]

    Korobov, L

    V.I. Korobov, L. Hilico and J.P. Karr, Phys. Rev. A74, 040502 (2006)

    work page 2006

  44. [44]

    Karr, V.I

    J.P. Karr, V.I. Korobov and L. Hilico, Phys. Rev. A77, 062507 (2008)

    work page 2008

  45. [45]

    Karr, Phys

    J.P. Karr, Phys. Rev. A104, 032822 (2021)

    work page 2021

  46. [46]

    Schiller, D

    S. Schiller, D. Bakalov, A.K. Bekbaev and V.I. Korobov, Phys. Rev. A89, 052521 (2014)

    work page 2014

  47. [47]

    Bakalov and S

    D. Bakalov and S. Schiller, Appl. Phys. B114, 213–230 (2014)

    work page 2014

  48. [48]

    Korobov, P

    V.I. Korobov, P. Danev, D. Bakalov and S. Schiller, Phys. Rev. A97, 032505 (2018)

    work page 2018

  49. [49]

    Schiller, V.I

    S. Schiller, V.I. Korobov, A. Aucar and D. Bakalov, Unpublished (2025)

    work page 2025

  50. [50]

    Holzapfel, F

    D. Holzapfel, F. Schmid, N. Schwegler, O. Stadler, M. Stadler, A. Ferk, J.P. Home and D. Kienzler, Phys. Rev. X15, 031009 (2025)

    work page 2025

  51. [51]

    Sellner, M

    S. Sellner, M. Besirli, M. Bohman, M. Borchert, J. Harrington, T. Higuchi, A. Mooser, H. Nagahama, G. Schneider, C. Smorraet al., New Journal of Physics19, 083023 (2017)

    work page 2017

  52. [52]

    Dehmelt, Proceedings of the National Academy of Sciences of the United States of America83, 2291–2294 (1986)

    H. Dehmelt, Proceedings of the National Academy of Sciences of the United States of America83, 2291–2294 (1986)

    work page 1986

  53. [53]

    Dehmelt, Proceedings of the National Academy of Sciences of the United States of America83, 3074–3077 (1986)

    H. Dehmelt, Proceedings of the National Academy of Sciences of the United States of America83, 3074–3077 (1986)

    work page 1986

  54. [54]

    Ulmer, C.C

    S. Ulmer, C.C. Rodegheri, K. Blaum, H. Kracke, A. Mooser, W. Quint and J. Walz, Physical Review Letters106, 253001 (2011)

    work page 2011

  55. [55]

    A. Egl, I. Arapoglou, M. H¨ ocker, K. K¨ onig, T. Ratajczyk, T. Sailer, B. Tu, A. Weigel, K. Blaum, W. N¨ ortersh¨ auser and S. Sturm, Phys. Rev. Lett.123, 123001 (2019)

    work page 2019

  56. [56]

    F. Wolf, Y. Wan, J. Heip, F. Gebert, C. Shi and P. Schmidt, Nature530, 457–460 (2016)

    work page 2016

  57. [57]

    Sinhal, Z

    M. Sinhal, Z. Meir, K. Najafian, G. Hegi and S. Willitsch, Science367, 1213–1218 (2020)

    work page 2020

  58. [58]

    Myers, Hyperfine Interactions239, 43 (2018)

    E.G. Myers, Hyperfine Interactions239, 43 (2018)

    work page 2018

  59. [59]

    Latacz, M

    B. Latacz, M. Fleck, J. J¨ ager, G. Umbrazunas, B. Arndt, S. Erlewein, E. Wursten, J. Devlin, P. Micke, F. Abbasset al., Physical Review Letters133, 053201 (2024)

    work page 2024

  60. [60]

    C. Will, M. Bohman, T. Driscoll, M. Wiesinger, F. Abbass, M.J. Borchert, J.A. Devlin, S. Erlewein, M. Fleck, B. Latacz, R. Moller, A. Mooser, D. Popper, E. Wursten, K. Blaum, Y. Matsuda, C. Ospelkaus, W. Quint, J. Walz, C. Smorra and S. Ulmer, New Journal of Physics24, 033021 (2022)

    work page 2022

  61. [61]

    K¨ onig, F

    C.M. K¨ onig, F. Heiße, J. Morgner, T. Sailer, B. Tu, D. Bakalov, K. Blaum, S. Schiller and S. Sturm, Phys. Rev. Lett.134, 163001 (2025)

    work page 2025

  62. [62]

    K¨ onig, M

    C.M. K¨ onig, M. Bohman, F. Heiße, J. Morgner, T. Sailer, B. Tu, K. Blaum, S. Sturm, D. Bakalov, H.D. Nogueira, J.P. Karr, O. Kullie and S. Schiller, Phys. Rev. Lett.136, 143002 (2026)

    work page 2026

  63. [63]

    ALPHATRAP MPIK-HHU Collaboration, Private communication (2026)

    work page 2026

  64. [64]

    Borchert, J

    M. Borchert, J. Devlin, S. Erlewein, M. Fleck, J. Harrington, T. Higuchi, B. Latacz, F. Voelksen, E. Wursten, F. Abbasset al., Nature601, 53–57 (2022)

    work page 2022

  65. [65]

    Sch¨ ussler, H

    R.X. Sch¨ ussler, H. Bekker, M. Braß, H. Cakir, J. Crespo L´ opez-Urrutia, M. Door, P. Filianin, Z. Harman, M.W. Haverkort, W.J. Huanget al., Nature581, 42–46 (2020). 51

    work page 2020

  66. [66]

    Kullie, H.D

    O. Kullie, H.D. Nogueira and J.P. Karr, Phys. Rev. A112, 052813 (2025)

    work page 2025

  67. [67]

    Schenkel, V

    M.R. Schenkel, V. Vogt and S. Schiller, Opt. Express32, 43350–43365 (2024)

    work page 2024

  68. [68]

    Hegstrom, Phys

    R.A. Hegstrom, Phys. Rev. A19, 17–30 (1979)

    work page 1979

  69. [69]

    Karthein, S.M

    J. Karthein, S.M. Udrescu, S.B. Moroch, I. Belosevic, K. Blaum, A. Borschevsky, Y. Chamorro, D. DeMille, J. Dilling, R.F. Garcia Ruiz, N.R. Hutzler, L.F. Paˇ steka and R. Ringle, Phys. Rev. Lett.133, 033003 (2024)

    work page 2024

  70. [70]

    Mavadia, G

    S. Mavadia, G. Stutter, J.F. Goodwin, D.R. Crick, R.C. Thompson and D.M. Segal, Phys. Rev. A89, 032502 (2014)

    work page 2014

  71. [71]

    Bates and G

    D.R. Bates and G. Poots, Proceedings of the Physical Society. Section A66, 784 (1953)

    work page 1953

  72. [72]

    Korobov and D

    V.I. Korobov and D. Bakalov, Phys. Rev. A107, 022812 (2023)

    work page 2023

  73. [73]

    Aznabayev, A.K

    D.T. Aznabayev, A.K. Bekbaev and V.I. Korobov, Phys. Rev. A108, 052827 (2023)

    work page 2023

  74. [74]

    Wineland, W.M

    D.J. Wineland, W.M. Itano, J.C. Bergquist and J.J. Bollinger, editors,Trapped Ions and Laser Cooling1086 (Natl. Bur. Stand. (U.S.) Tech. Note 1086, Washington, DC, 1985)

    work page 1985

  75. [75]

    Bollinger, D

    J. Bollinger, D. Heizen, W. Itano, S. Gilbert and D. Wineland, IEEE Transactions on Instrumentation and Measurement40, 126–128 (1991)

    work page 1991

  76. [76]

    Gabrielse, A

    G. Gabrielse, A. Khabbaz, D. Hall, C. Heimann, H. Kalinowsky and W. Jhe, Physical Review Letters82, 3198 (1999)

    work page 1999

  77. [77]

    Wineland and H

    D. Wineland and H. Dehmelt, Journal of Applied Physics46, 919–930 (1975)

    work page 1975

  78. [78]

    Nagahama, G

    H. Nagahama, G. Schneider, A. Mooser, C. Smorra, S. Sellner, J. Harrington, T. Higuchi, M. Borchert, T. Tanaka, M. Besirli, K. Blaum, Y. Matsuda, C. Ospelkaus, W. Quint, J. Walz, Y. Yamazaki and S. Ulmer, Review of Scientific Instruments87, 113305 (2016)

    work page 2016

  79. [79]

    Brown and G

    L.S. Brown and G. Gabrielse, Reviews of Modern Physics58, 233 (1986)

    work page 1986

  80. [80]

    Cornell, R.M

    E.A. Cornell, R.M. Weisskoff, K.R. Boyce and D.E. Pritchard, Phys. Rev. A41, 312–315 (1990)

    work page 1990

Showing first 80 references.