Pith. sign in

REVIEW 3 major objections 4 minor 52 references

Multipassage Landau-Zener tunneling oscillations in transverse/longitudinal dual dressing of atomic qubits

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The measured coherence of a dressed atomic qubit oscillates at the time-dependent Larmor frequency of the effective field, matching theory with no adjustable parameters.

desk verdict A solid experimental and theoretical study of XZ dual-dressing, but the central zero-crossing analysis needs an explicit test against the paper's own numerics before the parameter-free claim is fully convincing. read the letter →

arxiv 2506.03398 v1 pith:CWNUD4XS submitted 2025-06-03 quant-ph physics.atom-ph

Alessandro Fregosi , Carmela Marinelli , Carlo Gabbanini , Valerio Biancalana , Maria Allegrini , Ennio Arimondo , Francesco Petiziol , Sandro Wimberger
show 2 more authors
Andrea Fioretti Giuseppe Bevilacqua
This is my paper
classification quant-phphysics.atom-ph
keywords multipassageLandau-ZenerinterferometrydualdressingdressedLarmorfrequencyqubitcoherenceatomicmagnetometernonadiabaticdynamicsFloquetperturbationtheoryBesselfunctions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports an experimental and theoretical study of an atomic qubit driven by two off-resonant radio-frequency fields, one transverse and one longitudinal to the static magnetic field. The authors claim that the qubit coherence evolves at the time-dependent dressed Larmor frequency $\Omega_{Ld}(t)$ of Eq. (3), and that this frequency can be read directly from zero-crossing times of the polarimeter signal. They show that the measured $f_{Ld}(t)$ matches the theoretical curve with no adjustable parameters for rubidium and cesium magnetometers. The work matters because it extends Landau-Zener multipassage interferometry to a regime where standard high-frequency Floquet engineering does not apply, and it gives experimental access to the phase of the qubit wavefunction.

What carries the argument

The load-bearing object is the time-dependent dressed Larmor frequency $\Omega_{Ld}(t)=\sqrt{\Omega_x^2\cos^2(\omega t)+(\omega_{0z}+\Omega_z\cos(\omega t+\Phi_{0z}))^2}$, the instantaneous energy gap of the effective Hamiltonian. The experiment extracts it through Eq. (8), which converts successive zero-crossings of the polarimeter signal into $f_{Ld}(j)$ values assumed to follow the adiabatic phase $\varphi(t)=\int \Omega_{Ld}\,d\tau$. The supporting theory is a perturbative Floquet expansion in a rotating frame where the Hamiltonian's Fourier components are proportional to Bessel functions $J_n(\Omega_z/\omega)$; because these are small for large $\Omega_z/\omega$, the effective Hamiltonian and kick operator can be computed to second order.

What would settle it

Simulate numerically the exact Schrödinger evolution for nonadiabatic parameters (e.g., $\omega\sqrt{\Omega_x^2+\Omega_z^2}>\omega_{0z}^2$), extract zero-crossing times from the simulated coherence, and compare the resulting $f_{Ld}(t)$ with the time derivative of the numerically computed phase; any systematic disagreement would show the zero-crossing method fails outside the adiabatic regime.

Watch

Extended reading notes

Core claim

The central discovery is that in the XZ dual-dressing configuration the qubit's transverse coherence oscillates at the instantaneous dressed Larmor frequency $\Omega_{Ld}(t)=\sqrt{\Omega_x^2\cos^2(\omega t)+[\omega_{0z}+\Omega_z\cos(\omega t+\Phi_{0z})]^2}$, rather than at a constant effective frequency. Zero-crossings of the $\langle\sigma_y\rangle$ or $\langle\sigma_x\rangle$ signal, converted to a time-dependent $f_{Ld}$ via Eq. (8), follow the prediction of Eq. (3) over a range of dressing amplitudes and phases, including cases with two avoided crossings per period. The paper further claims that a modified Floquet treatment built on a rotating frame with Bessel-function Fourier coefficients captures the nonadiabatic dynamics where both the adiabatic approximation and the standard high-frequency expansion fail.

Load-bearing premise

The method assumes the monitored spin component follows $\sin\varphi(t)$ from the adiabatic solution, even for nonadiabatic parameters where the adiabatic theorem is not formally valid; a systematic phase error at those points could masquerade as a frequency shift.

Editorial extensions

If this is right

  • Coherence readout turns LZSM interferometry into a phase-resolved measurement, not just a transition-probability measurement.
  • The $f_{Ld}$ extraction provides a parameter-free way to verify the effective field produced by strong dual dressing in situ.
  • Rabi-like interference appears in the coherence as amplitude modulation of the $\Omega_{Ld}$ oscillations, with a measured oscillation period of 4.13(2) in reduced time for the Fig. 2(c) parameters.
  • The Bessel-function Floquet expansion extends quantitative description into the low-frequency strong-z-dressing regime where the standard high-frequency expansion is invalid.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The zero-crossing readout could be reused as an in-situ calibration tool for strong radio-frequency field amplitudes in atomic magnetometers, since $f_{Ld}(t)$ contains both amplitude and phase information.
  • The sensitivity to $\Phi_{0z}$ suggests the relative phase between the two dressing fields could serve as a coherent control knob for shaping the interference pattern, an avenue the paper does not pursue.
  • Because the paper compares $f_{Ld}$ to $\Omega_{Ld}$ visually, a quantitative residual analysis on the nonadiabatic points would test how far the adiabatic zero-crossing interpretation can be pushed.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reports an experimental and theoretical study of a two-level atomic qubit driven by two off-resonant radio-frequency fields, one transverse (x) and one longitudinal (z) to the static field. The Hamiltonian is given in Eqs. (1)-(2), and the central object is the instantaneous dressed Larmor frequency Ω_Ld(t) of Eq. (3). The authors measure the transverse spin component in Rb and Cs magnetometers, extract an experimental frequency f_Ld from zero crossings of the polarimeter signal via Eq. (8), and compare it with Ω_Ld(t) computed from independently set field parameters with no adjustable parameters (Fig. 4). They also develop a Floquet-type perturbative treatment based on a Bessel-function expansion in a rotating frame (Appendix "Model for the low-frequency nonadiabatic regime") and show that it reproduces exact numerical dynamics in a nonadiabatic regime (Fig. 3(c)-(d)).

Significance. If the parameter-free agreement in Fig. 4 is robust, the paper provides a valuable way to continuously monitor the qubit coherence phase in multipassage Landau-Zener-Stückelberg-Majorana interferometry, in a regime beyond standard high-frequency Floquet engineering. The experiment, with Rabi frequencies several times the Larmor frequency and with direct coherence readout rather than transition-probability readout, is a meaningful addition to the LZSM literature. The numerical simulations and the analytical Floquet-Bessel treatment are generally careful, and the absence of fitted parameters in the main comparison is a strength. The main reservation is that the zero-crossing estimator is used in regimes where its underlying adiabatic assumption is not justified, and the paper does not validate the estimator against its own exact simulations; this issue must be addressed before the central claim is fully supported.

major comments (3)
  1. [LZSM data analysis, Eq. (8)] Equation (8) defines f_Ld(j)=2π/[t_P(j+1)-t_P(j)], with t_P(j) the j-th zero of the polarimeter signal. For a signal proportional to sin φ(t) (Eq. (5)), adjacent zeros differ in phase by π, not 2π; the angular frequency over that interval is π/Δt. As written, Eq. (8) therefore overestimates the instantaneous Larmor frequency by a factor of two unless t_P(j) is intended to denote every second zero. The text states that the time separation between 'neighbouring zero values' represents the period of a single Larmor precession, which selects adjacent zeros. Please correct Eq. (8) or explicitly define the zero indexing, because the apparent agreement in Fig. 4 depends directly on this factor.
  2. [LZSM data analysis, Eq. (8)] The conversion of zero-crossing times into f_Ld rests on the adiabatic relation ⟨σ_y⟩ ∝ sin φ(t) of Eq. (5). However, the parameters of Fig. 4(a) satisfy ω sqrt(Ω_x^2+Ω_z^2) ≈ 21.9 kHz^2 > ω_0z^2 ≈ 19.5 kHz^2, which by the paper's own criterion Eq. (7) is the nonadiabatic regime. In that regime the spin signal is not a single sin φ component, and the zeros of the full signal do not in general occur at φ = nπ. Since the authors already have exact numerical Schrödinger solutions, they should apply the same zero-crossing estimator to the simulated ⟨σ_y(t)⟩ and show that it recovers Ω_Ld(t) for each Fig. 4 parameter set; without this benchmark, the parameter-free agreement may reflect the estimator's built-in assumption rather than the physical dressed frequency.
  3. [Fig. 4] The agreement between the measured f_Ld and the predicted Ω_Ld is assessed only visually. Error bars are shown for only one or two points per panel, and no residuals, root-mean-square deviation, or goodness-of-fit statistic is reported. Given that the extracted f_Ld values are sparse in regions of rapid oscillation (e.g., Fig. 4(d)) and that the sampling-rate-limited errors grow at short time intervals, a quantitative measure of the discrepancy is needed to support the claim of remarkable agreement, especially for the nonadiabatic case of Fig. 4(a).
minor comments (4)
  1. [Appendix, Eq. (39)] In Eq. (39), the second term in parentheses should read e^{-i4ωt} σ_- (or be expressed with an explicit Hermitian conjugate), not e^{-i4ωt} σ_+ as written; this appears to be a typographical error but should be corrected for clarity.
  2. [Units and notation, Eqs. (3) and (8)] Equation (3) defines an angular frequency, while Eq. (8) as written gives 2π/Δt, which is an angular frequency only if Δt is measured in seconds and the result is reported in rad/s. The text labels both as kHz without distinguishing cyclic from angular frequencies. Please state the convention explicitly so that the factor of 2π in Eq. (8) is unambiguous.
  3. [Experimental data, Fig. 4] The caption states that error bars are determined by the sampling rate, but no uncertainty propagation formula is given. A brief description of how Δt uncertainties translate into f_Ld uncertainties would help the reader judge the significance of the deviations from the red curves.
  4. [Rabi-like oscillations, Fig. 5 and Fig. 4(d)] The fitted Rabi-like oscillation period in Fig. 5 is 4.61τ, while the text quotes an experimental period of 4.13(2)τ for the parameters of Fig. 2(c)/Fig. 4(d). The possible origin of this discrepancy should be discussed, especially because the Rabi-like oscillations are invoked to explain missing f_Ld data points.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted dressed-Larmor frequency is computed from independently set Hamiltonian parameters, and the zero-crossing estimator is a physical measurement protocol rather than a fitted restatement of the prediction.

full rationale

The central comparison in Fig. 4 is between the measured zero-crossing-derived frequency f_Ld (Eq. 8) and the theoretically computed dressed Larmor frequency Ω_Ld (Eq. 3). Eq. (3) is evaluated from the independently chosen experimental parameters (ω, ω0z, Ωx, Ωz, Φ0z); the paper states explicitly that "no adjustable parameters are introduced in the calculation" (Fig. 4 caption). The zero-crossing estimator assumes the adiabatic relation ⟨σ_y⟩ ∝ sin φ with φ = ∫ Ω_Ld dt (Eqs. 4–5, 35a), but this is a physical modeling assumption about the spin evolution, not a definition of Ω_Ld in terms of the measured times; if the adiabatic assumption failed, the extracted f_Ld would disagree with Eq. (3), so the comparison is falsifiable rather than forced. The concern that the estimator may be unreliable in the nonadiabatic regime is a validity/error issue, not a construction-level circularity. The modified Floquet treatment is tested against exact Schrödinger-equation numerics within the paper and does not import a uniqueness or ansatz result from self-citations. Self-citations (Refs. 20, 21, 22, 23, 37, 38) are used for experimental setup and motivation, not as load-bearing evidence for the central frequency prediction. Limitations flagged in the text, such as parameter sensitivity and sampling-rate errors, are acknowledged experimental uncertainties, not circular reductions.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central comparison is parameter-free (Eq. 3 uses only experimentally controlled fields), so no fitted constants enter the main claim. The main axioms are the two-level spin description of the atoms, the neglect of decoherence, the linear relation between the polarimeter signal and the spin component, and the use of the adiabatic phase relation for zero-crossing extraction. No new entities are introduced.

free parameters (1)
  • Rabi-like oscillation period (simulation fit) = 4.61τ (Ω_Rl ≈ 0.213 kHz)
    Fitted to the numerical simulation in Fig. 5 to illustrate Rabi-like oscillations; not used in the central f_Ld vs Ω_Ld comparison.
assumptions (5)
  • domain assumption Atoms can be described as an assembly of independent one-half spins
    Section 'The qubit system and its detection': 'the atomic structure of rubidium/caesium atoms can be described by a collection of degenerate two-level systems, representing the qubits.' This neglects higher multipole moments and possible multi-level effects in F=3 and F=4 hyperfine manifolds.
  • domain assumption Decoherence is negligible on the evolution timescale
    Section 'The qubit system and its detection': 'Owing to negligible decoherence processes this Hamiltonian is complete.'
  • domain assumption The polarimeter signal is proportional to the monitored spin component and can be renormalized linearly
    Section 'Experimental setup': 'the measured Faraday rotation signal is renormalized to compensate for the signal decay.' This is standard for magnetometry but not demonstrated here.
  • ad hoc to paper The zero-crossing extraction of f_Ld assumes the adiabatic relation ⟨σ_y⟩ ∝ sin φ(t)
    Eq. (8) converts zero-crossing times into frequencies using the adiabatic phase solution of Eq. (5), even in nonadiabatic parameter regimes.
  • ad hoc to paper The Fourier coefficients of H'' are small enough for a second-order Floquet expansion
    Appendix 'Model for the low-frequency nonadiabatic regime': 'Since the Bessel functions have small value for large argument Ωz/ω' and 'Provided Ωx/Ωz ≪ 1 and δ/Ωz ≪ 1'. The Bessel smallness assertion is not generally true for orders near the argument.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Multipassage Landau-Zener tunneling oscillations in transverse/longitudinal dual dressing of atomic qubits." pith.science (2026). https://pith.science/paper/CWNUD4XS

@misc{pith2026250603398,
  author       = {Pith},
  title        = {Pith review of: Multipassage Landau-Zener tunneling oscillations in transverse/longitudinal dual dressing of atomic qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CWNUD4XS}},
  note         = {Machine review of arXiv:2506.03398}
}
abstract

We investigate the time evolution of a non-resonant dressed-atom qubit in an XZ original configuration. It is composed of two electromagnetic fields, one oscillating parallel and the other orthogonal to the quantisation magnetic static field. The experiments are performed in rubidium and caesium atomic magnetometers, confined in a magneto-optical trap and in a vapour cell, respectively. Static fields in the $\mu$T range and kHz oscillating fields with large Rabi frequencies are applied. This dual-dressing configuration is an extension of the Landau-Zener multipassage interferometry in the presence of an additional dressing field controlling the tunneling process by its amplitude and phase. Our measurement of the qubit coherence introduces additional features to the transition probability readout of standard interferometry. The coherence time evolution is characterized by oscillations at several frequencies, each of them produced by a different quantum contribution. Such frequency description introduces a new picture of the qubit multipassage evolution. Because the present low-frequency dressing operation does not fall within the standard Floquet engineering paradigm based on the high-frequency expansion, we develop an ad-hoc dressing perturbation treatment. Numerical simulations support the adiabatic and non-adiabatic qubit evolution.

Figures

Figures reproduced from arXiv: 2506.03398 by the authors.

Figure 1
Figure 1. Schematic of a qubit dressed by the Bx and Bz oscillating fields, generated by the radiofrequency coils and in the presence of a B0z static field. In this figure the ⟨σy(t)⟩ expectation value is monitored by the polarization rotation of a probe beam propagating along the y axis. with the effective⃗h(t) field given by ⃗h(t) =   Ωx cos(ωt) 0 ω0z +Ωz cos(ωt +Φ0z)  . (2) Owing to negligible decoherence processes thi… view at source ↗
Figure 2
Figure 2. (Color online) Time evolution of the atomic spin. Black lines (left axis) report experimental polarimeter signals, red lines (right axis) the theoretical ΩLd of Eq. (3) derived from the applied static and oscillating field values. On the horizontal axis the τ reduced time. Parameters (ω,ω0z ,Ωx,Ωz) all in kHz and Φ0z . In (a) Rb atoms, (3.0, 77.645, 2.06, 2.0) and Φ0z = 0, a linearly polarized oscillating field; in … view at source ↗
Figure 3
Figure 3. (Color online) Left column: in (a) black line experimental polarimeter signal and in (b) P+ probability occupation of the |+⟩ eigenstate derived from numerical solution of the Schrödinger equation as function of the τ = ωt/(2π) reduced time. Red lines: in the time dependence of the ΩLd Larmor dressed frequency. Right column: comparison between the exact numerical time evolution and the analytical estimate [see the m… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: (Color online) Measured fLd and predicted ΩLd values for time dependent adiabatic frequency versus time. Frequencies in kHz and times τ in reduced units. fLd frequencies (black squares) are derived from the polarimeter zero values as in Eq. (8). The typical error bars,…
Figure 5
Figure 5. Figure 5: (Color online) Theoretical simulation of the Rabi-like oscillations with initial ⟨σx(0)⟩ = 1. In a) P+(τ) occupation probability and in b) ⟨σx(τ)⟩. Blue dashed lines are fits of the Rabi-like oscillations with 4.61τ oscillation period and the ΩRl = 0.213 kHz frequency.…
Figure 6
Figure 6. Figure 6: (a) Absolute value of the Bessel functions Jn(Ωz/ω) entering the Fourier coefficients of H ′′(t) of Eq. (41). (b) Fourier coefficients of f(t) of Eq. (42). Model for the low-frequency nonadiabatic regime In this Appendix, an analytical approximation for the dynamics in…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

52 extracted references · 36 canonical work pages

  1. [1]

    Shirley, J. H. Solution of the Schrödinger equation with a Hamiltonian periodic in time.Phys. Rev.138, B979–B987, DOI: 10.1103/PhysRev.138.B979 (1965)

    doi:10.1103/physrev.138.b979 1965

  2. [2]

    Steady states and quasienergies of a quantum-mechanical system in an oscillating field.Phys

    Sambe, H. Steady states and quasienergies of a quantum-mechanical system in an oscillating field.Phys. Rev. A7, 2203–2213, DOI: 10.1103/PhysRevA.7.2203 (1973)

    doi:10.1103/physreva.7.2203 1973

  3. [3]

    & Dalibard, J

    Goldman, N. & Dalibard, J. Periodically driven quantum systems: Effective Hamiltonians and engineered gauge fields. Phys. Rev. X4, 031027, DOI: 10.1103/PhysRevX.4.031027 (2014)

    doi:10.1103/physrevx.4.031027 2014

  4. [4]

    & Polkovnikov, A

    Bukov, M., D’Alessio, L. & Polkovnikov, A. Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering.Adv. Phys.64, 139–226 (2015)

    work page 2015

  5. [5]

    Colloquium: Atomic quantum gases in periodically driven optical lattices.Rev

    Eckardt, A. Colloquium: Atomic quantum gases in periodically driven optical lattices.Rev. Mod. Phys.89, 011004, DOI: 10.1103/RevModPhys.89.011004 (2017)

    doi:10.1103/revmodphys.89.011004 2017

  6. [6]

    Aidelsburger, M.et al.Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices.Phys. Rev. Lett. 111, 185301, DOI: 10.1103/PhysRevLett.111.185301 (2013)

    doi:10.1103/physrevlett.111.185301 2013

  7. [7]

    J., Lauber, K., Daley, A

    Meinert, F., Mark, M. J., Lauber, K., Daley, A. J. & Nägerl, H.-C. Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms.Phys. Rev. Lett.116, 205301, DOI: 10.1103/PhysRevLett.116.205301 (2016)

    doi:10.1103/physrevlett.116.205301 2016

  8. [8]

    Geier, S.et al.Floquet Hamiltonian engineering of an isolated many-body spin system.Science374, 1149–1152, DOI: 10.1126/science.abd9547 (2021)

    doi:10.1126/science.abd9547 2021

Show all 52 references
  1. [9]

    & Simonet, J

    Weitenberg, C. & Simonet, J. Tailoring quantum gases by Floquet engineering.Nat. Phys.17, 1342–1348, DOI: 10.1038/s41567-021-01316-x (2021). 12/15

    2021 doi

  2. [10]

    Scholl, P.et al.Microwave engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms.PRX Quantum3, 020303, DOI: 10.1103/PRXQuantum.3.020303 (2022)

    2022 doi

  3. [11]

    Yin, M.-J.et al.Floquet engineering Hz-level Rabi spectra in shallow optical lattice clock.Phys. Rev. Lett.128, 073603, DOI: 10.1103/PhysRevLett.128.073603 (2022)

    2022 doi

  4. [12]

    Zhang, J.-Y .et al.Tuning anomalous Floquet topological bands with ultracold atoms.Phys. Rev. Lett.130, 043201, DOI: 10.1103/PhysRevLett.130.043201 (2023)

    2023 doi

  5. [13]

    Salathé, Y .et al.Digital quantum simulation of spin models with circuit quantum electrodynamics.Phys. Rev. X5, 021027, DOI: 10.1103/PhysRevX.5.021027 (2015)

    2015 doi

  6. [14]

    Phys.12, 306, DOI: 10.1038/nphys3609 (2016)

    Mahmood, F.et al.Selective scattering between Floquet-Bloch and Volkov states in a topological insulator.Nat. Phys.12, 306, DOI: 10.1038/nphys3609 (2016)

    2016 doi

  7. [15]

    & Cappellaro, P

    Peng, P., Yin, C., Huang, X., Ramanathan, C. & Cappellaro, P. Floquet prethermalization in dipolar spin chains.Nat. Phys. 17, 444–447, DOI: 10.1038/s41567-020-01120-z (2021)

    2021 doi

  8. [16]

    & Arimondo, E

    Allegrini, M. & Arimondo, E. Atoms dressed by virtual and real photons.Physics6, 60–74, DOI: 10.3390/physics6010005 (2024)

    2024 doi

  9. [17]

    & Rizzuto, L

    Passante, R. & Rizzuto, L. Vacuum self-dressing of an atom and its physical effects.doi: 10.20944/preprints202503.1700.v1 (2025)

    2025

  10. [18]

    & Schermann, J

    Haroche, S., Cohen-Tannoudji, C., Audoin, C. & Schermann, J. P. Modified Zeeman hyperfine spectra observed in H1 and Rb87 ground states interacting with a nonresonant rf field.Phys. Rev. Lett.24, 861, DOI: 10.1103/PhysRevLett.24.861 (1970)

    1970 doi

  11. [19]

    & Cohen-Tannoudji, C

    Haroche, S. & Cohen-Tannoudji, C. Resonant transfer of coherence in nonzero magnetic field between atomic levels of differentgfactors.Phys. Rev. Lett.24, 974–978, DOI: 10.1103/PhysRevLett.24.974 (1970)

    1970 doi

  12. [20]

    & Arimondo, E

    Bevilacqua, G., Biancalana, V ., Vigilante, A., Zanon-Willette, T. & Arimondo, E. Harmonic fine tuning and triaxial spatial anisotropy of dressed atomic spins.Phys. Rev. Lett.125, 093203, DOI: 10.1103/PhysRevLett.125.093203 (2020)

    2020 doi

  13. [21]

    & Arimondo, E

    Bevilacqua, G., Biancalana, V ., Zanon-Willette, T. & Arimondo, E. Harmonic dual dressing of spin-1/2 systems.Phys. Rev. A105, 022619, DOI: 10.1103/PhysRevA.105.022619 (2022)

    2022 doi

  14. [22]

    & Wimberger, S

    Petiziol, F., Dive, B., Mintert, F. & Wimberger, S. Fast adiabatic evolution by oscillating initial hamiltonians.Phys. Rev. A 98, 043436, DOI: 10.1103/PhysRevA.98.043436 (2018)

    2018 doi

  15. [23]

    & Wimberger, S

    Petiziol, F., Mintert, F. & Wimberger, S. Quantum control by effective counterdiabatic driving.Europhys. Lett.145, 15001, DOI: 10.1209/0295-5075/ad19e3 (2024)

    2024 doi

  16. [24]

    & Nori, F

    Shevchenko, S., Ashhab, S. & Nori, F. Landau–Zener–Stückelberg interferometry.Phys. Reports492, 1–30, DOI: https://doi.org/10.1016/j.physrep.2010.03.002 (2010)

    2010 doi

  17. [25]

    V ., Shevchenko, S

    Ivakhnenko, O. V ., Shevchenko, S. N. & Nori, F. Nonadiabatic Landau–Zener–Stückelberg–Majorana transitions, dynamics, and interference.Phys. Reports995, 1–89, DOI: https://doi.org/10.1016/j.physrep.2022.10.002 (2023)

    2023 doi

  18. [26]

    D.et al.Mach-Zehnder interferometry in a strongly driven superconducting qubit.Science310, 1653–1657, DOI: 10.1126/science.1119678 (2005)

    Oliver, W. D.et al.Mach-Zehnder interferometry in a strongly driven superconducting qubit.Science310, 1653–1657, DOI: 10.1126/science.1119678 (2005)

    2005 doi

  19. [27]

    & Hakonen, P

    Sillanpää, M., Lehtinen, T., Paila, A., Makhlin, Y . & Hakonen, P. Continuous-time monitoring of Landau-Zener interference in a Cooper-pair box.Phys. Rev. Lett.96, 187002, DOI: 10.1103/PhysRevLett.96.187002 (2006)

    2006 doi

  20. [28]

    Zhou, J.et al.Observation of time-domain Rabi oscillations in the Landau-Zener regime with a single electronic spin. Phys. Rev. Lett.112, 010503, DOI: 10.1103/PhysRevLett.112.010503 (2014)

    2014 doi

  21. [29]

    & Li, W.-D

    Liu, W.-X., Wang, T., Zhang, X.-F. & Li, W.-D. Time-domain Landau-Zener-Stückelberg-Majorana interference in an optical lattice clock.Phys. Rev. A104, 053318, DOI: 10.1103/PhysRevA.104.053318 (2021)

    2021 doi

  22. [30]

    O., Ivakhnenko, O

    Kofman, P. O., Ivakhnenko, O. V ., Shevchenko, S. N. & Nori, F. Majorana’s approach to nonadiabatic transitions validates the adiabatic-impulse approximation.Sci. Reports13, 5033, DOI: 10.1038/s41598-023-31084-y (2023)

    2023 doi

  23. [31]

    D., Dobrovitski, V

    Fuchs, G. D., Dobrovitski, V . V ., Toyli, D. M., Heremans, F. J. & Awschalom, D. D. Gigahertz dynamics of a strongly driven single quantum spin.Science326, 1520–1522, DOI: 10.1126/science.1181193 (2009)

    2009 doi

  24. [32]

    Tuorila, J.et al.Stark effect and generalized Bloch-Siegert shift in a strongly driven two-level system.Phys. Rev. Lett.105, 257003, DOI: 10.1103/PhysRevLett.105.257003 (2010). 13/15

    2010 doi

  25. [33]

    Phys.16, 093022, DOI: 10.1088/1367-2630/16/9/093022 (2014)

    Scheuer, J.et al.Precise qubit control beyond the rotating wave approximation.New J. Phys.16, 093022, DOI: 10.1088/1367-2630/16/9/093022 (2014)

    2014 doi

  26. [34]

    & Gershoni, D

    Avinadav, C., Fischer, R., London, P. & Gershoni, D. Time-optimal universal control of two-level systems under strong driving.Phys. Rev. B89, 245311, DOI: 10.1103/PhysRevB.89.245311 (2014)

    2014 doi

  27. [35]

    & Lupascu, A

    Deng, C., Orgiazzi, J.-L., Shen, F., Ashhab, S. & Lupascu, A. Observation of Floquet states in a strongly driven artificial atom.Phys. Rev. Lett.115, 133601, DOI: 10.1103/PhysRevLett.115.133601 (2015)

    2015 doi

  28. [36]

    K.et al.Experimentally simulating the dynamics of quantum light and matter at deep strong coupling.Nat

    Langford, N. K.et al.Experimentally simulating the dynamics of quantum light and matter at deep strong coupling.Nat. Commun.8, 1715, DOI: 10.1038/s41467-017-01061-x (2017). 37.Fregosi, A.et al.Floquet space exploration for the dual-dressing of a qubit.Sci. Reports13, 15304 (2023)

    2017 doi

  29. [38]

    & Fregosi, A

    Bevilacqua, G., Biancalana, V ., Dancheva, Y . & Fregosi, A. Tri-axial time-dependent magnetic field calibrated in-situ by harmonic analysis of adiabatically evolving atomic spins (2025). 2404.14574

    2025 arXiv

  30. [39]

    Forster, F.et al.Landau-Zener interference at bichromatic driving.Phys. Rev. B92, 245422, DOI: 10.1103/PhysRevB.92. 245422 (2015)

    2015 doi

  31. [40]

    Fregosi, A.et al.Magnetic induction imaging with a cold-atom radio frequency magnetometer.Appl. Phys. Lett.117, 144102, DOI: 10.1063/5.0020415 (2020)

    2020 doi

  32. [41]

    & Vigilante, A

    Bevilacqua, G., Biancalana, V ., Dancheva, Y . & Vigilante, A. Sub-millimetric ultra-low-field MRI detected in situ by a dressed atomic magnetometer,.Appl. Phys. Lett.115, 174102, DOI: 10.1063/1.5123653 (2019)

    2019 doi

  33. [42]

    R., Zagoskin, A

    Ashhab, S., Johansson, J. R., Zagoskin, A. M. & Nori, F. Two-level systems driven by large-amplitude fields.Phys. Rev. A 75, 063414, DOI: 10.1103/PhysRevA.75.063414 (2007)

    2007 doi

  34. [43]

    & Weitz, M

    Kling, S., Salger, T., Grossert, C. & Weitz, M. Atomic Bloch-Zener oscillations and Stückelberg interferometry in optical lattices.Phys. Rev. Lett.105, 215301, DOI: 10.1103/PhysRevLett.105.215301 (2010)

    2010 doi

  35. [44]

    & Arimondo, E

    Zenesini, A., Ciampini, D., Morsch, O. & Arimondo, E. Observation of Stückelberg oscillations in accelerated optical lattices.Phys. Rev. A82, 065601, DOI: 10.1103/PhysRevA.82.065601 (2010)

    2010 doi

  36. [45]

    Rahman, T.et al.Bloch oscillation phases investigated by multipath Stückelberg atom interferometry.Phys. Rev. Res.6, L022012, DOI: 10.1103/PhysRevResearch.6.L022012 (2024)

    2024 doi

  37. [46]

    & Halperin, B

    Martin, I., Refael, G. & Halperin, B. Topological frequency conversion in strongly driven quantum systems.Phys. Rev. X 7, 041008, DOI: 10.1103/PhysRevX.7.041008 (2017)

    2017 doi

  38. [47]

    M.et al.Amplitude spectroscopy of a solid-state artificial atom.Nature455, 51–57, DOI: 10.1038/nature07262 (2008)

    Berns, D. M.et al.Amplitude spectroscopy of a solid-state artificial atom.Nature455, 51–57, DOI: 10.1038/nature07262 (2008)

    2008 doi

  39. [48]

    Yang, Z.-X.et al.Phase-sensitive Landau-Zener-Stückelberg interference in superconducting quantum circuit*.Chin. Phys. B30, 024212, DOI: 10.1088/1674-1056/abd753 (2021)

    2021 doi

  40. [49]

    Neilinger, P.et al.Landau-Zener-Stückelberg-Majorana lasing in circuit quantum electrodynamics.Phys. Rev. B94, 094519, DOI: 10.1103/PhysRevB.94.094519 (2016)

    2016 doi

  41. [50]

    I., Ivakhnenko, O

    Ryzhov, A. I., Ivakhnenko, O. V ., Shevchenko, S. N., Gonzalez-Zalba, M. F. & Nori, F. Alternative fast quantum logic gates using nonadiabatic Landau-Zener-Stückelberg-Majorana transitions.Phys. Rev. Res.6, 033340, DOI: 10.1103/ PhysRevResearch.6.033340 (2024)

    2024

  42. [51]

    & Rice, S

    Demirplak, M. & Rice, S. A. Assisted adiabatic passage revisited.J. Phys. Chem. B109, 6838–44, DOI: 0.1021/jp040647w (2005)

    2005

  43. [52]

    Reports688, 1–35, DOI: https://doi.org/10.1016/j.physrep.2017.05.003 (2017)

    Weinberg, P.et al.Adiabatic perturbation theory and geometry of periodically-driven systems.Phys. Reports688, 1–35, DOI: https://doi.org/10.1016/j.physrep.2017.05.003 (2017)

    2017 doi

  44. [53]

    EuPRAXIA Advanced Photon Sources (EuAPS)

    NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/, Release 1.0.23 of 2019-06-15 (2019). F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller and B. V . Saunders, eds. Acknowledgements All authors than...

    2019

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.