Machine-Learning-Empowered Quantum Sensing of the Plaquette Phase in a Three-Level Delta System

Dario Fasone; Elisabetta Paladino; Enrico Martello; Giuseppe Falci; Lorenzo Vitale; Luigi Giannelli; Shreyasi Mukherjee

REVIEW 2 major objections 5 minor 32 references

Machine-Learning-Empowered Quantum Sensing of the Plaquette Phase in a Three-Level Delta System

T0 review · 2 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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

Pith's one-line read A multilayer perceptron, trained on STIRAP transfer efficiencies measured under eight driving and detuning configurations, can reconstruct the gauge-invariant plaquette phase of a three-level Δ system across the full 2π interval.

desk verdict A clean simulation-level proof of principle for estimating the plaquette phase from STIRAP efficiencies; the 'sensing' language runs ahead of the evidence, and the sign-degeneracy objection doesn't survive contact with the paper. read the letter →

arxiv 2607.15040 v1 pith:6HSTI6JV submitted 2026-07-16 quant-ph

Lorenzo Vitale , Shreyasi Mukherjee , Dario Fasone , Enrico Martello , Elisabetta Paladino , Luigi Giannelli , Giuseppe Falci This is my paper · ORCID

classification quant-ph

keywords plaquettephasethree-levelΔsystemSTIRAPcoherentpopulationtrappingmachinelearningmultilayerperceptronquantumsensingsyntheticgaugefields

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

The paper proposes a method to measure the gauge-invariant plaquette phase of a closed-loop three-level system—a quantity that is not directly observable—by turning the known phase-dependent degradation of STIRAP population transfer into a sensing signal. The central claim is that a multilayer perceptron, trained on simulated STIRAP efficiencies collected under eight different driving and detuning conditions, can accurately reconstruct the phase across the full 2π range. If true, this gives a cheap, measurement-tolerant way to sense an effective magnetic flux in engineered quantum systems, with applications to synthetic gauge fields and quantum metrology. The insight is that an imperfection—the breakdown of coherent population trapping—carries precisely the information one wants.

What carries the argument

The gauge-invariant plaquette phase φ = φ0 + φs − φp, which remains after all local gauge transformations are exhausted; the generalized dark-state (trapped-state) condition that defines the detuning baseline; the dark state |D⟩ = cosθ|0⟩ − sinθ|1⟩; and the fact that for φ ≠ 0 the dressed states acquire a component along |D⟩ proportional to sin φ, which produces phase-dependent leakage. The sensing protocol uses eight STIRAP efficiencies (three driving configurations × detuning settings) as features, and a two-output MLP trained with mean-squared error on the circular encoding.

What would settle it

Sweep the plaquette phase on a controllable platform (or simulate the full Lindblad master equation with realistic noise) and record the eight efficiencies; if two distinct phases in [−π,π] yield fingerprint vectors that are statistically indistinguishable at the experimental noise level, or if the network's prediction error grows sharply once noise is added to the ideal efficiencies, then the central sensing claim fails. A numerical check: compute the Jacobian of the eight-efficiency map with respect to φ; if its singular values collapse toward zero anywhere, the map is locally non-invertible

Watch

Extended reading notes

Core claim

The paper demonstrates that the plaquette phase φ, a gauge-invariant quantity that cannot be directly measured, is encoded in the transfer efficiency of STIRAP. When the detuning is set to the value that would ensure perfect trapping at φ=0, any nonzero φ causes leakage from the dark manifold proportional to sin φ, so the final population of the target state becomes a phase-dependent observable. The authors construct an eight-dimensional fingerprint of efficiencies from three driving conditions and three detuning schemes, and show that a multilayer perceptron trained on noiseless simulated data predicts φ across the full interval with small error. The MLP outputs (cos φ, sin φ), avoiding the

Load-bearing premise

The eight measured transfer efficiencies form a well-conditioned, effectively invertible fingerprint of the plaquette phase, so a network trained on ideal noiseless simulations will infer the phase from real measurements made with noise and experimental imperfections.

Editorial extensions

If this is right

A single final-population measurement per configuration replaces full state tomography, making the phase estimate cheap and experimentally accessible.
The phase-dependent degradation of STIRAP, normally a drawback, becomes the physical resource that carries the sensing signal.
Because the method relies only on the closed-loop geometry, it transfers to any engineered platform—superconducting circuits, NV centers, quantum dots—with the same fingerprint structure.
The circular (cos φ, sin φ) output means the estimator works uniformly across the 2π boundary, so no phase discontinuity artifacts appear.

Reading between the lines

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

The paper only tests noiseless synthetic data; the immediate next experiment is to add measurement noise and parameter fluctuations. If the eight-efficiency mapping is not robust, the authors will need to augment the training set or the feature vector.
The choice of eight features is heuristic (three driving conditions, three detunings, two matched configurations). A cheaper protocol with fewer features may be possible; the paper lists reducing the number of input features as future work.
In a lattice of many triangular plaquettes, the same method could serve as a local magnetometer for synthetic gauge fields: measuring each plaquette's phase map would reconstruct the effective magnetic-field texture.
The network's generalization is only demonstrated within the same parameter range used for training (fixed pulse width, delay, and amplitude ratio). Whether the estimator is robust to changes in pulse shape or timing is an untested extension.

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.

Desk Editor's Note

read the letter

Quick read, before you spend referee time: this is a competent numerical proof-of-principle, not a field-changer. The genuinely new piece is using an MLP to estimate the gauge-invariant plaquette phase from eight simulated STIRAP transfer efficiencies. The phase-dependent STIRAP physics comes from Pope et al. [15], and the ML approach is a direct continuation of the group's own noise-classification work [23,24], but I don't know of an earlier demonstration of this specific estimation task. The circular (cos phi, sin phi) target encoding is the right call, the test set is genuinely held out, and the reported training/validation behavior is consistent with a stable fit.

Soft spots, in order of importance. No noise, no error bars, no experimental data, no baseline comparison, no code or data release. The abstract's phrase 'experimentally accessible observables' is defensible in principle—final populations are measurable—but calling this 'quantum sensing' overstates what is shown: the mapping is learned and evaluated on the same noiseless model that defines the phase. Section 5 explicitly defers noise robustness. That is a scope issue, not a fatal flaw. The conditioning of the 8-dimensional fingerprint is also never characterized; they note the inverse problem is 'generally non-invertible' but do not say where the ambiguities are.

On the stress-test: the exact phi -> -phi degeneracy worry does not hold up. H(-phi)=H(phi)* is a time-reversal relation, and complex conjugation alone does not map the forward STIRAP evolution at phi to the forward evolution at -phi—the counterintuitive pulse sequence breaks time-reversal symmetry. The paper's own dressed-state leakage is proportional to sin phi, so the efficiencies are not obviously even in phi. If the eight features were exactly two-to-one, the reported test-set error over [-pi,pi] would be impossible; I see no hidden symmetry forcing that. A one-line symmetry comment in the paper would have preempted this, but the concern does not invalidate the result.

Who should read it: anyone working on ML-assisted quantum control, STIRAP in closed-loop systems, or synthetic gauge-field characterization. It deserves a serious referee. I would send it out with the request that the authors add a noise model, a baseline comparison, and ideally a small experimental or analog demonstration before the word 'sensing' is used. As-is, it is a solid simulation-level extension with a clearly bounded claim.

Referee Report

2 major / 5 minor

Summary. The paper proposes a machine-learning approach to estimate the plaquette phase φ in a closed-loop three-level Δ system from STIRAP population transfer efficiencies. The Hamiltonian (2) contains a residual complex coupling e^{±iφ}; Sec. 2.3 shows that a non-zero φ breaks coherent population trapping, producing a phase-dependent transfer efficiency. Sec. 3 describes an eight-efficiency feature vector built from three driving conditions and several detuning protocols, and an MLP with circular output (cos φ, sin φ). Sec. 4 reports low test error on a synthetic dataset of 2000 phases. The authors conclude that the phase can be accurately reconstructed from experimentally accessible observables.

Significance. The analytical treatment of the dark-state breakdown is standard and the data-generation pipeline is transparent, including a held-out test set and early stopping; these are strengths. However, the central sensing claim is invalidated by an exact symmetry: all eight input efficiencies are invariant under φ→-φ while the target is not. Thus the reported MLP performance cannot be reproduced as stated, and the proposed method does not sense the signed plaquette phase. The practical significance of the work therefore hinges on a symmetry obstruction that is not addressed; the paper would need a fundamentally different observable or a reduced target (e.g., |φ|) to be salvageable.

major comments (2)

[Secs. 3.3 and 4, Eq. (2)] For the Hamiltonian in Eq. (2), H(−φ)=H(φ)^*. Since the pulses in Eq. (10) are real, the detunings are real, and the STIRAP initial state is |0⟩, the propagator satisfies U(−φ)=U(φ)^*. Every feature is a final population η=|<1|ψ(t_f)>|² (Eq. 12), so η_k(−φ)=η_k(φ) for each of the eight configurations. The input vector therefore satisfies x(−φ)=x(φ) while the target (cos φ, sin φ) in Eq. (13) is not invariant under φ→−φ. A deterministic MLP cannot separate φ and −φ from identical inputs. The low test error in Fig. 4 is inconsistent with the stated data-generation protocol unless the symmetry is broken by an unstated step. This is a load-bearing flaw, not a noise issue: it persists in the ideal noiseless limit.
[Abstract; Sec. 5] The abstract claims estimation from 'experimentally accessible observables' and the conclusions frame the result as a quantum-sensing protocol. However, the entire study uses noiseless synthetic data with no detector noise, no parameter fluctuations, no error bars, and no comparison with a direct estimator or baseline. The only generalization demonstrated is interpolation within the same model distribution. This overstates the experimental scope and should be corrected even if the symmetry issue were resolved.

minor comments (5)

[Sec. 5, first paragraph] 'three-level ∆ system with.' contains a dangling 'with'.
[Abstract] 'STImulated' should be 'Stimulated'.
[Eq. (8)] The notation eδ_p is undefined; it presumably denotes the shifted detuning defined in Eq. (7).
[Sec. 3.3, Table 2] The definitions of δ_pump and δ_Stokes are described only in prose; the table would be clearer if the matched detuning formulas were written explicitly.
[Sec. 4 and Fig. 4] The conversion from the two output components to a predicted angle is not specified; the convention used to report 'predicted phase' should be stated.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation; physics is from external Ref. [15], ML test is held-out interpolation, self-citations are motivational only.

full rationale

The derivation chain is self-contained. The trapping condition, dark state, and dressed-state leakage (Eqs. (4)-(8)) are taken from Ref. [15], an external reference, and the MLP is trained on numerically integrated Schrödinger dynamics of Eq. (2) with held-out test phases; the target y=(cos φ, sin φ) is not used as an input and no fitted parameter is renamed as a prediction. The only self-citations [23,24] appear as motivation ('we take inspiration') and for a normalization convention; they carry no load in the sensing argument. The paper itself flags the inverse problem as 'generally non-invertible' (Sec. 1) and defers noise robustness to future work (Sec. 5); these are limitations of the protocol, not circularity. Any φ→−φ identifiability issue would be a physical correctness concern rather than a definitional/fitted-input circularity and is not counted here.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

All training data are generated from the same Hamiltonian that defines the target phase, and the paper provides no experimental noise model or invertibility proof; these are the main uncharged premises.

free parameters (4)

Pulse width T = ΩT = 15
Chosen simulation parameter; the phase-efficiency mapping and thus the sensing fidelity depend on the adiabaticity of the STIRAP pulses.
Pulse delay τ = 0.7 T
Chosen for counterintuitive STIRAP sequence; affects transfer efficiency and the shape of the phase-dependent signal.
Detuning δ_p = 0
Set to zero; part of the driving conditions used to generate the eight input features.
Pulse amplitude ratios = Ω_p/Ω_s ∈ {1, 2, 1/2}
Chosen driving configurations; essential for disambiguating the phase since a single efficiency is non-invertible.

assumptions (5)

domain assumption Rotating-wave three-level Δ Hamiltonian with complex couplings, Eqs. (1)-(2)
All training data are generated from this model; if the model does not describe a real device, the sensing claim fails.
domain assumption The trapped-state/dressed-state analysis from Ref. [15] (Sec. 2.3) remains valid under the operational detuning of Eq. (9)
Used to predict phase-dependent leakage that the ML exploits.
ad hoc to paper The mapping from phase φ to the 8-dimensional efficiency vector is well-posed (unique and stable enough to invert)
No proof; the paper relies on empirical training success to justify the chosen feature set (Sec. 3.3, Table 2).
standard math An MLP can approximate this mapping and generalize to unseen phases
Universal approximation / supervised learning; standard but not proven for this task.
domain assumption Measured transfer efficiencies are noiseless and exact
Synthetic data are generated by solving the Schrödinger equation with no detection noise; real efficiencies will have noise, and robustness is deferred to future work (Sec. 5).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Machine-Learning-Empowered Quantum Sensing of the Plaquette Phase in a Three-Level Delta System." pith.science (2026). https://pith.science/paper/6HSTI6JV

@misc{pith2026260715040,
  author       = {Pith},
  title        = {Pith review of: Machine-Learning-Empowered Quantum Sensing of the Plaquette Phase in a Three-Level Delta System},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6HSTI6JV}},
  note         = {Machine review of arXiv:2607.15040}
}

abstract

We propose a machine-learning-empowered approach to the quantum sensing of the plaquette phase, a gauge-invariant quantity arising in three-level $\Delta$ systems. This phase profoundly affects the system dynamics, breaking coherent population trapping and inducing a non-trivial phase dependence of the dynamics. We demonstrate that a multi-layer perceptron (MLP), trained in a supervised-learning framework, can accurately estimate the plaquette phase from STImulated Raman Adiabatic Passage (STIRAP) population transfer efficiencies measured under different driving conditions, which provide experimentally accessible observables. Our results highlight how the combination of coherent control and machine learning (ML) enables effective phase identification in closed-loop quantum systems, opening new perspectives for quantum technologies, specifically quantum sensing applications including synthetic gauge fields.

Figures

Figures reproduced from arXiv: 2607.15040 by the authors.

**Figure 1.** Three-level system in a ∆ configuration. sensing of the plaquette phase in a three-level ∆ system. By exploiting the phase-dependent degradation of STIRAP transfer efficiency under different driving conditions, we train a NN to reconstruct the phase from experimentally accessible observables. This approach highlights how coherent control protocols, when combined with data-driven methods, can be repurposed as flexib… view at source ↗

**Figure 2.** Time- and phase-resolved population of the target state |1⟩ during the STIRAP protocol, obtained under the operational two-photon detuning condition of Eq. (9). The Gaussian pulses given by Eq. (10) are taken with equal peak amplitudes, Ωmax p = Ωmax s = Ω. Simulation parameters: ΩT = 15, τ = 0.7 T, and δp = 0. specifically a MLP. The network is trained on a labeled dataset, {(xi , ˆyi)}i=1,...,N , where each input … view at source ↗

**Figure 3.** Training progress. The value of the cost function, given by Eq. (14), for the training sets (solid blue line) and the validation sets (solid orange line) vs. the number of epochs of training. quently optimized through gradient-based minimization of the loss function Eq. (14). The training process of the model is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Performance of the neural network on the test dataset. Left: predicted phase versus the corresponding target value (the true value). Right: prediction accuracy as a function of the test sample index. 5 Conclusions In this work, we have proposed a ML–assisted approach t…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

32 extracted references · 6 canonical work pages

[15]

Coherent Trapping in Small Quantum Networks

T. J. Pope et al. “Coherent Trapping in Small Quantum Networks”. In:Journal of Statistical Mechanics: Theory and Experiment2019.12 (2019), p. 124024.issn: 1742-5468.doi:10.1088/1742-5468/ab54b7

work page doi:10.1088/1742-5468/ab54b7 2019
[1]

The Quantum Technologies Roadmap: A European Community View

A. Ac ´ ın et al. “The Quantum Technologies Roadmap: A European Community View”. In:New Journal of Physics20 (2018), p. 080201. issn: 1367-2630.doi:10.1088/1367-2630/aad1ea

doi:10.1088/1367-2630/aad1ea 2018
[2]

Quantum Technology: The Sec- ond Quantum Revolution

J. P. Dowling and G. J. Milburn. “Quantum Technology: The Sec- ond Quantum Revolution”. In:Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences361 (2003). Ed. by A. G. J. MacFarlane, pp. 1655–1674.issn: 1364-503X, 1471-2962.doi:10.1098/rsta.2003.1227

arXiv 2003
[3]

Quantum Sensing

C. L. Degen, F. Reinhard, and P. Cappellaro. “Quantum Sensing”. In:Reviews of Modern Physics89 (2017), p. 035002.issn: 0034-6861, 1539-0756.doi:10.1103/RevModPhys.89.035002

doi:10.1103/revmodphys.89.035002 2017
[4]

Coherent Manipulations of Atoms Using Laser Light

B. Shore. “Coherent Manipulations of Atoms Using Laser Light”. In: Acta Physica Slovaca. Reviews and Tutorials58.3 (2008).issn: 1336- 040X, 0323-0465.doi:10.2478/v10155-010-0090-z

work page doi:10.2478/v10155-010-0090-z 2008
[5]

Nonabsorbing Atomic Coherences by Coherent Two-Photon Transitions in a Three-Level Optical Pumping

E. Arimondo and G. Orriols. “Nonabsorbing Atomic Coherences by Coherent Two-Photon Transitions in a Three-Level Optical Pumping”. In:Lettere al Nuovo Cimento (1971-1985)17.10 (1976), pp. 333–338. issn: 1827-613X.doi:10.1007/BF02746514

work page doi:10.1007/bf02746514 1971
[6]

Coherent Trapping of Atomic Populations

H. R. Gray, R. M. Whitley, and C. R. Stroud. “Coherent Trapping of Atomic Populations”. In:Optics Letters3.6 (1978), pp. 218–220.issn: 1539-4794.doi:10.1364/OL.3.000218. 13

doi:10.1364/ol.3.000218 1978
[7]

V coherent population trapping in laser spectroscopy

E. Arimondo. “V coherent population trapping in laser spectroscopy”. In:Progress in optics35 (1996), pp. 257–354.doi:10.1016/S0079- 6638(08)70531-6

doi:10.1016/s0079- 1996

Show all 32 references

[8]

Coherent Population Transfer among Quantum States of Atoms and Molecules

K. Bergmann, H. Theuer, and B. W. Shore. “Coherent Population Transfer among Quantum States of Atoms and Molecules”. In:Re- views of Modern Physics70.3 (1998), pp. 1003–1025.doi:10.1103/ RevModPhys.70.1003

1998
[9]

Stimulated Raman Adiabatic Passage in Physics, Chemistry, and Beyond

N. V. Vitanov et al. “Stimulated Raman Adiabatic Passage in Physics, Chemistry, and Beyond”. In:Reviews of Modern Physics89.1 (2017), p. 015006.doi:10.1103/RevModPhys.89.015006

2017 doi
[10]

Stimulated Raman Adiabatic Passage in a Three- Level Superconducting Circuit

K. S. Kumar et al. “Stimulated Raman Adiabatic Passage in a Three- Level Superconducting Circuit”. In:Nature Communications7.1 (2016), p. 10628.issn: 2041-1723.doi:10.1038/ncomms10628

2016 doi
[11]

Advanced Control with a Cooper- pair Box: Stimulated Raman Adiabatic Passage and Fock-state Gen- eration in a Nanomechanical Resonator

J. Siewert, T. Brandes, and G. Falci. “Advanced Control with a Cooper- pair Box: Stimulated Raman Adiabatic Passage and Fock-state Gen- eration in a Nanomechanical Resonator”. In:Physical Review B79.2 (2009), p. 024504.doi:10.1103/PhysRevB.79.024504

2009 doi
[12]

Design of a Lambda System for Population Transfer in Superconducting Nanocircuits

G. Falci et al. “Design of a Lambda System for Population Transfer in Superconducting Nanocircuits”. In:Physical Review B87.21 (2013), p. 214515.doi:10.1103/PhysRevB.87.214515

2013 doi
[13]

Advances in Quantum Control of Three-Level Super- conducting Circuit Architectures

G. Falci et al. “Advances in Quantum Control of Three-Level Super- conducting Circuit Architectures”. In:Fortschritte der Physik65.6-8 (2017), p. 1600077.issn: 1521-3978.doi:10.1002/prop.201600077

2017 doi
[14]

Population Transfer in a Lambda System In- duced by Detunings

P. G. Di Stefano et al. “Population Transfer in a Lambda System In- duced by Detunings”. In:Physical Review B91.22 (2015), p. 224506. doi:10.1103/PhysRevB.91.224506

2015 doi
[16]

Atomic Physics and Quantum Optics Using Superconducting Circuits

J. Q. You and F. Nori. “Atomic Physics and Quantum Optics Using Superconducting Circuits”. In:Nature474 (2011), pp. 589–597.issn: 0028-0836, 1476-4687.doi:10.1038/nature10122

2011 doi
[17]

Optical Selection Rules and Phase-Dependent Adiabatic State Control in a Superconducting Quantum Circuit

Y. Liu et al. “Optical Selection Rules and Phase-Dependent Adiabatic State Control in a Superconducting Quantum Circuit”. In:Physical Review Letters95 (2005), p. 087001.doi:10.1103/PhysRevLett.95. 087001

2005 doi
[18]

Observation of chiral solitary waves in a nonlinear Aharonov-Bohm ring

I. Velkovsky et al. “Observation of chiral solitary waves in a nonlinear Aharonov-Bohm ring”. In:arXiv preprint arXiv:2406.01732(2024). 14

2024 arXiv
[19]

Machine Learning and Quantum Devices

F. Marquardt. “Machine Learning and Quantum Devices”. In:SciPost Physics Lecture Notes(2021), p. 29.issn: 2590-1990.doi:10.21468/ SciPostPhysLectNotes.29

2021
[20]

Artificial intelligence and machine learning for quan- tum technologies

M. Krenn et al. “Artificial intelligence and machine learning for quan- tum technologies”. In:Phys. Rev. A107 (1 2023), p. 010101.doi: 10.1103/PhysRevA.107.010101

2023 doi
[21]

Reinforcement learning-enhanced protocols for co- herent population-transfer in three-level quantum systems

J. Brown et al. “Reinforcement learning-enhanced protocols for co- herent population-transfer in three-level quantum systems”. In:New Journal of Physics23.9 (2021), p. 093035.doi:10.1088/1367-2630/ ac2393

2021 doi
[22]

A Tutorial on Optimal Control and Reinforcement Learning Methods for Quantum Technologies

L. Giannelli et al. “A Tutorial on Optimal Control and Reinforcement Learning Methods for Quantum Technologies”. In:Physics Letters A 434 (2022), p. 128054.issn: 03759601.doi:10 . 1016 / j . physleta . 2022.128054

2022
[23]

Noise Classification in Three-Level Quantum Net- works by Machine Learning

S. Mukherjee et al. “Noise Classification in Three-Level Quantum Net- works by Machine Learning”. In:Machine Learning: Science and Tech- nology5.4 (2024), p. 045049.issn: 2632-2153.doi:10 . 1088 / 2632 - 2153/ad9193

2024
[24]

Fasone et al.Detection of Noise Correlations in Two Qubit Systems by Machine Learning

D. Fasone et al.Detection of Noise Correlations in Two Qubit Systems by Machine Learning. 2025.doi:10.48550/arXiv.2509.03389. arXiv: 2509.03389 [quant-ph]

2025 doi arXiv
[25]

Artificial Gauge Fields with Ultracold Atoms

V. Galitski, G. Juzeli¯ unas, and I. B. Spielman. “Artificial Gauge Fields with Ultracold Atoms”. In:Physics Today72.1 (2019), pp. 38–44.issn: 0031-9228, 1945-0699.doi:10.1063/PT.3.4111

2019 doi
[26]

Atomic Interferometers: Phase-dependence in Mul- tilevel Atomic Transitions

S. J. Buckle et al. “Atomic Interferometers: Phase-dependence in Mul- tilevel Atomic Transitions”. In:Optica Acta: International Journal of Optics33.9 (1986), pp. 1129–1140.issn: 0030-3909.doi:10 . 1080 / 713822082

1986
[27]

Laser-Induced Adiabatic Atomic Reorientation with Control of Diabatic Losses

R. G Unanyan et al. “Laser-Induced Adiabatic Atomic Reorientation with Control of Diabatic Losses”. In:Optics Communications139 (1997), pp. 48–54.issn: 00304018.doi:10.1016/S0030-4018(97)00099-0

1997 doi
[28]

Burkov.The Hundred-Page Machine Learning Book

A. Burkov.The Hundred-Page Machine Learning Book. Vol. 1. 2019

2019
[29]

D. P. Kingma and J. Ba.Adam: A Method for Stochastic Optimization. 2014.doi:10.48550/arXiv.1412.6980. arXiv:1412.6980 [cs.LG]

2014 doi arXiv
[30]

Abadi et al.TensorFlow: Large-Scale Machine Learning on Het- erogeneous Systems

M. Abadi et al.TensorFlow: Large-Scale Machine Learning on Het- erogeneous Systems. Software available from tensorflow.org. 2015.url: https://www.tensorflow.org/

2015
[31]

Chiral Ground-State Currents of Interacting Pho- tons in a Synthetic Magnetic Field

P. Roushan et al. “Chiral Ground-State Currents of Interacting Pho- tons in a Synthetic Magnetic Field”. In:Nature Physics13 (Feb. 2017), pp. 146–151.issn: 1745-2473, 1745-2481.doi:10.1038/nphys3930. 15

2017 doi
[32]

Phase-Controlled Coherent Dynamics of a Single Spin under Closed-Contour Interaction

A. Barfuss et al. “Phase-Controlled Coherent Dynamics of a Single Spin under Closed-Contour Interaction”. In:Nature Physics14 (Nov. 2018), pp. 1087–1091.issn: 1745-2481.doi:10.1038/s41567-018-0231-8. 16

2018 doi

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [15]

Coherent Trapping in Small Quantum Networks

T. J. Pope et al. “Coherent Trapping in Small Quantum Networks”. In:Journal of Statistical Mechanics: Theory and Experiment2019.12 (2019), p. 124024.issn: 1742-5468.doi:10.1088/1742-5468/ab54b7

work page doi:10.1088/1742-5468/ab54b7 2019

[2] [1]

The Quantum Technologies Roadmap: A European Community View

A. Ac ´ ın et al. “The Quantum Technologies Roadmap: A European Community View”. In:New Journal of Physics20 (2018), p. 080201. issn: 1367-2630.doi:10.1088/1367-2630/aad1ea

doi:10.1088/1367-2630/aad1ea 2018

[3] [2]

Quantum Technology: The Sec- ond Quantum Revolution

J. P. Dowling and G. J. Milburn. “Quantum Technology: The Sec- ond Quantum Revolution”. In:Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences361 (2003). Ed. by A. G. J. MacFarlane, pp. 1655–1674.issn: 1364-503X, 1471-2962.doi:10.1098/rsta.2003.1227

arXiv 2003

[4] [3]

Quantum Sensing

C. L. Degen, F. Reinhard, and P. Cappellaro. “Quantum Sensing”. In:Reviews of Modern Physics89 (2017), p. 035002.issn: 0034-6861, 1539-0756.doi:10.1103/RevModPhys.89.035002

doi:10.1103/revmodphys.89.035002 2017

[5] [4]

Coherent Manipulations of Atoms Using Laser Light

B. Shore. “Coherent Manipulations of Atoms Using Laser Light”. In: Acta Physica Slovaca. Reviews and Tutorials58.3 (2008).issn: 1336- 040X, 0323-0465.doi:10.2478/v10155-010-0090-z

work page doi:10.2478/v10155-010-0090-z 2008

[6] [5]

Nonabsorbing Atomic Coherences by Coherent Two-Photon Transitions in a Three-Level Optical Pumping

E. Arimondo and G. Orriols. “Nonabsorbing Atomic Coherences by Coherent Two-Photon Transitions in a Three-Level Optical Pumping”. In:Lettere al Nuovo Cimento (1971-1985)17.10 (1976), pp. 333–338. issn: 1827-613X.doi:10.1007/BF02746514

work page doi:10.1007/bf02746514 1971

[7] [6]

Coherent Trapping of Atomic Populations

H. R. Gray, R. M. Whitley, and C. R. Stroud. “Coherent Trapping of Atomic Populations”. In:Optics Letters3.6 (1978), pp. 218–220.issn: 1539-4794.doi:10.1364/OL.3.000218. 13

doi:10.1364/ol.3.000218 1978

[8] [7]

V coherent population trapping in laser spectroscopy

E. Arimondo. “V coherent population trapping in laser spectroscopy”. In:Progress in optics35 (1996), pp. 257–354.doi:10.1016/S0079- 6638(08)70531-6

doi:10.1016/s0079- 1996