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REVIEW 3 major objections 4 minor 14 references

Quantum optical experiments towards atom-photon entanglement

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A single optically trapped rubidium atom and a single photon it emits are entangled, with an entanglement fidelity of 0.82, verified through correlations in complementary measurement bases.

desk verdict Careful theory and methods chapters, but the posted text truncates before the experimental results, so the headline 0.82 fidelity claim is not evidenced in this manuscript. read the letter →

arxiv 2507.22166 v1 pith:2XZVJUIP submitted 2025-07-29 quant-ph

Markus Weber This is my paper · ORCID
classification quant-ph MSC 81P4081P1581V80 PACS 03.65.Ud42.50.-p32.80.Qk
keywords atom-photonentanglementsingletrappedatomspontaneousemissionfidelityBellinequalitySTIRAPopticaldipoletrap87Rb
topics The Measurement Problem
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 thesis reports the experimental creation of entanglement between a single optically trapped 87Rb atom and a single photon emitted by that atom in spontaneous decay. The atom is excited to a state with two decay channels, and because those channels are spectrally and otherwise indistinguishable, the atomic spin and the photon polarization end up in the maximally entangled state |Ψ+⟩. Entanglement is verified by correlation measurements in complementary bases, giving a fidelity of 0.82. The result matters because atom-photon entanglement is the building block for entangling distant atoms through photon interference, which could enable a loophole-free Bell test and quantum communication tasks such as remote state preparation.

What carries the argument

The central mechanism is spontaneous emission from a single excited state with two equally probable, indistinguishable decay paths: decay to |1,−1⟩ emits a σ+ photon, while decay to |1,+1⟩ emits a σ− photon. Angular-momentum conservation creates the correlation between photon polarization and atomic Zeeman state, and indistinguishability of the paths creates the coherence; collecting light along the quantization axis removes the π decay channel, leaving |Ψ+⟩. The atomic state is read out with a phase-sensitive STIRAP pulse whose polarization angle sets the measurement basis, and the photon is analyzed with a rotatable half-wave plate and polarizing beam splitter.

What would settle it

Measure the atom-photon correlation fidelity while sweeping the magnetic field from below 100 mGauss upward: if coherence relies on spectral indistinguishability, the fidelity should fall from 0.82 toward 0.5 as the Zeeman splitting approaches the 6 MHz natural linewidth, and a direct spectral resolution of the σ+ and σ− emission lines would reveal any resolvable splitting that contradicts the claim.

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Extended reading notes

Core claim

The central experimental claim is that a single optically trapped 87Rb atom, after excitation to the 2P3/2, |0,0⟩ state, spontaneously decays into the entangled atom-photon state |Ψ+⟩ = 1/√2 (|1,−1⟩|σ+⟩ + |1,+1⟩|σ−⟩) with an entanglement fidelity of 0.82. The author argues that, because the residual magnetic field is below 100 mGauss, the Zeeman splitting between the mF=±1 ground states is two orders of magnitude smaller than the natural linewidth, so the two decay channels are spectrally indistinguishable and the required coherence is preserved. Detection along the quantization axis selects only the σ± decay channels, leaving a maximally entangled state, and correlated measurements of photon polarization and atomic spin in complementary bases certify entanglement.

Load-bearing premise

The two decay paths must be spectrally indistinguishable; the experiment assumes the residual magnetic field is below 100 mGauss so the Zeeman splitting of mF=±1 is much smaller than the natural linewidth, and if that fails the state degrades from an entangled superposition to a mixture.

Editorial extensions

If this is right

  • The generated state, with fidelity 0.82, exceeds the 0.5 threshold for entanglement and lies above the 0.78 fidelity needed to violate a Bell inequality under a white-noise model, making it a candidate building block for a loophole-free test.
  • Two such atom-photon sources could be combined by sending each photon to an intermediate Bell-state measurement, leaving the two distant atoms entangled even though they never interacted.
  • The atomic readout based on STIRAP and destructive push-out achieves a minimum detection efficiency of 0.95, close to the near-perfect atom detection needed to close the detection loophole.
  • Remote state preparation of a single atom becomes feasible, since the emitted photon carries the full spin information of the atom and can be transported over long distances.
  • A direct corollary of the fidelity result is that the atom-photon pair is a usable interface for mapping quantum information between a stable matter qubit and a photonic communication channel.

Reading between the lines

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

  • A natural control experiment would be to sweep the magnetic field upward from the sub-100 mGauss regime: the entanglement fidelity should drop toward 0.5 as the Zeeman splitting approaches the natural linewidth, directly testing the spectral-indistinguishability assumption.
  • The same polarization-defined STIRAP readout could be reused as a general phase-sensitive atomic qubit measurement in other atom-photon or atom-atom entanglement protocols.
  • The fidelity estimate assumes a white-noise admixture; a full two-qubit tomography would reveal whether the remaining infidelity is noise-like or comes from coherent errors such as residual π-photon contamination or imperfect STIRAP transfer.
  • Improving the collection geometry, which the thesis notes can raise the maximal fidelity to 0.99, would bring the same setup close to the threshold for a loophole-free Bell test with two separated atoms.
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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 manuscript is a dissertation by Markus Weber reporting on experiments towards atom-photon entanglement with a single optically trapped 87Rb atom. The theory sections (Chapters 2–4) develop the Weisskopf–Wigner treatment of spontaneous emission, the resulting atom-photon state of Eq. (6.1), a four-level optical Bloch model for resonance fluorescence, and a STIRAP-based scheme for measuring atomic Zeeman superposition states. Chapter 5 demonstrates state preparation and detection with a raw fringe visibility of 0.57±0.01, corrected to 0.71±0.01 under a three-level model. Chapter 6 describes the entanglement generation process and states that the residual magnetic field is below 100 mGauss, making the two decay channels spectrally indistinguishable. The abstract claims that the generated atom-photon state yields an entanglement fidelity of 0.82. However, the posted text truncates in the middle of §6.2, and the section '6.3 Experimental results' listed in the table of contents is absent, so no correlation data, no fidelity calculation, and no error analysis are actually provided.

Significance. If the experimental claim holds, this is a significant milestone: it would be a direct observation of entanglement between a single localized neutral atom and a single spontaneously emitted photon at a telecommunication-compatible wavelength, an important step toward quantum repeaters and loophole-free Bell tests. The manuscript gives credit where due for careful technical work: the four-level optical Bloch equations are aligned with a published PRA article, the measured g^(2)(0)=0.02±0.14 demonstrates single-atom antibunching, and the hyperfine-state detection efficiency of 0.95±0.01 is quantified. The STIRAP-based atomic-state detection is described in detail with an explicit visibility measurement. However, the central assertion of the paper—the entanglement fidelity of 0.82—is not supported by any data in the posted text, and the reported fidelity appears to rely on model corrections and a Werner-state ansatz. The significance of the work therefore cannot be assessed from the submitted manuscript alone.

major comments (3)
  1. [§6.2/§6.3] The posted text truncates mid-sentence in §6.2 (after 'until a photon is de…'), and the table-of-contents entry '6.3 Experimental results' has no corresponding content. This is the central evidence for the paper's claim: correlation measurements in complementary bases, the calculation of the entanglement fidelity 0.82, error bars, background subtraction, and detection-efficiency corrections. Without this section the abstract's assertion 'It is shown, that the generated atom-photon state yields an entanglement fidelity of 0.82' is unsubstantiated. The authors must provide the complete experimental-results section, including raw coincidence counts in at least two mutually unbiased bases, the fitted visibilities, and the explicit formula used to convert visibilities into fidelity.
  2. [Eq. (2.27) and Sec. 5.3.4] The fidelity derivation appears to rest on the Werner-state ansatz ρ = p|Ψ+⟩⟨Ψ+| + (1−p)I/4, with F = p + (1−p)/4 (Eqs. 2.27–2.28), and on model-corrected STIRAP visibilities: Sec. 5.3.4 reports a raw visibility of 0.57±0.01, corrected to 0.71±0.01 by a numerical three-level model that accounts for imperfect state preparation and imperfect STIRAP transfer. The manuscript does not show how these intermediate numbers combine to yield the quoted 0.82, nor does it justify the white-noise assumption. The reported fidelity is therefore an inferred, model-dependent quantity rather than a directly measured one. The authors should present the measured two-particle correlation probabilities in the σz, σx, and σy bases, the background subtraction, and a transparent error propagation to F, and they should state whether the Werner-state ansatz is assumed or derived from the data.
  3. [§5.3.3 vs §6.2] There is an inconsistency in the residual magnetic field: §5.3.3 reports a Larmor-precession measurement of 132 mGauss and an upper bound of 300 mGauss, while §6.2 states that the residual field is smaller than 100 mGauss. The spectral indistinguishability of the two decay channels, and hence the coherence of the entangled state of Eq. (6.1), depends on this value. The manuscript must either reconcile these numbers or report the dedicated in-situ magnetic-field measurement used for the entanglement runs, including the uncertainty.
minor comments (4)
  1. [Eq. (3.40)] The notation for the mean kinetic energy, 'Ekin = ... = (110 ± 15)+14 −25 µK ·kB', is confusing; the result should be written as k_B T = (110 ± 15_stat) μK with a separate systematic error.
  2. [Fig. 5.15 and §5.3.4] The caption of Fig. 5.15 states that the prepared state is (|1,−1⟩+|1,+1⟩)/√2, whereas the text and Eq. (5.19) define the prepared state as (|1,−1⟩−|1,+1⟩)/√2; the sign convention should be made consistent throughout.
  3. [General] Reference [35] appears to be a published report of the same or closely related result; the manuscript should clarify the relation between this dissertation and [35], and state what new material the present arXiv posting adds.
  4. [§3.2.2] The phrase 'red-detuned from the cycling transition ... up to 5 natural linewidths' should be reworded for clarity, e.g., 'red-detuned by up to 5 natural linewidths from the cycling transition'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the atom-photon entanglement state is derived from first-principles angular-momentum conservation and stated indistinguishability conditions; the 0.82 fidelity claim is unauditable because §6.3 is truncated, but no circular reduction can be exhibited.

full rationale

The derivation chain from spontaneous emission to the entangled state (Eqs. 2.39–2.41 and 6.1) uses angular-momentum conservation, Clebsch–Gordan coefficients, and the stated spectral-indistinguishability condition (residual magnetic field <100 mG, Zeeman splitting two orders of magnitude below the natural linewidth). None of these inputs contains the target entanglement fidelity, so the generation mechanism is not circular. The fidelity definition (Eq. 2.25) is a standard measure, and the lower-bound expression (Eq. 2.26) is cited from [35] as a mathematical inequality; even if [35] is same-group work, this citation is not load-bearing because the inequality is a parameter-free mathematical statement that does not assume the measured fidelity. The Werner-state ansatz (Eq. 2.27) is explicitly described as a model of imperfect detection, with Eq. 2.28 following by direct substitution; the available text never shows this ansatz being fitted to data and then renamed as the 0.82 result. The STIRAP visibility correction in Sec. 5.3.4 is an efficiency calibration obtained from a simplified three-level master equation; it is not used in the posted text as an input that predicts the atom-photon correlations. The experimental-results section (§6.3) is truncated before any fidelity calculation, raw correlation histogram, or error bar appears, so a claimed reduction of the 0.82 fidelity to a fitted parameter cannot be quoted or exhibited. Absence of evidence is an evidential gap, not circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim is an experimental measurement, so the ledger contains the modeling assumptions used to convert raw correlations into a fidelity, plus a few fitted parameters from the supporting trap and photon-statistics chapters. No new physical entities are postulated.

free parameters (3)
  • single-particle loss rate gamma = 0.2 s^-1
    Chosen in Sec. 3.2.3 as 'consistent with our observations' and used in the loading-rate model (Eq. 3.36). It affects the trap statistics model but not the entanglement fidelity.
  • motional correlation decay amplitude A and time constant tau0 = tau0 = 1.8 microseconds (A not stated)
    Fit to the microsecond-scale decay of g2 in Sec. 4.3.2 (Fig. 4.6) and used to multiply the four-level OBE prediction. This is a phenomenological fit to the photon-correlation data, not the central entanglement claim.
  • STIRAP correction fractions = 84 percent population in F=1, 5 percent leakage
    Obtained from a three-level master-equation model in Sec. 5.3.4 to correct the raw STIRAP visibility from 0.57 to 0.71. This correction feeds into the atomic-analysis fidelity chain and is not independently measured.
assumptions (4)
  • domain assumption The prepared atom-photon state is a Werner-like mixture rho = p|Psi+><Psi+| + (1-p)I/4
    Eq. 2.27 in Sec. 2.3.3 is used to convert correlation measurements into an entanglement fidelity. If the noise is not white, Eq. 2.28 can misestimate the true fidelity.
  • domain assumption Detection along the quantization axis collects only sigma-plus and sigma-minus photons, so the pi channel is absent
    Sec. 2.4.3 and Sec. 3.3.4 assume the NA=0.29 objective along z does not collect pi-polarized photons; the residual pi contribution is claimed to limit fidelity to 0.99. If this fails, the detected state is not the maximally entangled state of Eq. 6.1.
  • domain assumption STIRAP transfer is adiabatic and state-selective with no population leakage
    Sections 5.3.4 and 6.2 rely on the dark-bright decomposition of the atomic superposition. The measured visibility is 0.71 after correction, so the ideal STIRAP behavior is not fully realized and the correction itself uses a model.
  • standard math Weisskopf-Wigner spontaneous emission and the quantum regression theorem
    Standard background used to derive the emitted photon state (Sec. 2.4.1) and the g2 correlation functions (Sec. 4.2.1). These are accepted textbook results.

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Cite this review

Pith. "Pith review of Quantum optical experiments towards atom-photon entanglement." pith.science (2026). https://pith.science/paper/2XZVJUIP

@misc{pith2026250722166,
  author       = {Pith},
  title        = {Pith review of: Quantum optical experiments towards atom-photon entanglement},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2XZVJUIP}},
  note         = {Machine review of arXiv:2507.22166}
}
read the original abstract

In 1935 EPR used the assumption of local realism to conclude in a Gedankenexperiment with two entangled particles that quantum mechanics is not complete. Based on this idea Bell constructed an inequality whereby experimental tests could distinguish between quantum mechanics and local-realistic theories. Many experiments have since been done that are consistent with quantum mechanics, disproving the concept of local realism. But all these tests suffered from loopholes allowing a local-realistic explanation of the experimental observations. In this context, of special interest is entanglement between different quantum objects like atoms and photons, because it allows one to entangle distant atoms by the interference of photons. The resulting space-like separation together with the almost perfect detection efficiency of the atoms will allow a first event-ready Bell test closing detection and locality loopholes. The primary goal of the present thesis was the experimental realization of entanglement between a single localized atom and a single spontaneously emitted photon. In the experiment a single optically trapped R87 atom is excited to a state which has two selected decay channels. In the following spontaneous decay a photon is emitted coherently with equal probability into both decay channels. This accounts for perfect correlations between the polarization state of the emitted photon and the Zeeman state of the atom after spontaneous decay. Because these decay channels are spectrally and in all other degrees of freedom indistinguishable, the spin state of the atom is entangled with the polarization state of the photon. To verify entanglement, appropriate correlation measurements in complementary bases of the photon polarization and the internal quantum state of the atom were performed. It is shown, that the generated atom-photon state yields an entanglement fidelity of 0.82.

Figures

Figures reproduced from arXiv: 2507.22166 by the authors.

Figure 1.1
Figure 1.1. Atomic dipole transition to generate atom-photon entan [PITH_FULL_IMAGE:figures/full_fig_p012_1_1.png] view at source ↗
Figure 2.1
Figure 2.1. An arbitrary spin-1/2 state |Ψi and the three complementary bases x,y,z in the Bloch sphere representation. 2.2.2. Quantum measurements A measurement in quantum mechanics is inherently indeterministic. If we ask (measure) whether |Ψi is in the state |↑i, we obtain this result with probability |h↑|Ψi|2 = |a| 2 . After the measurement, the state is projected to |↑i. In this ideal Von Neumann mea￾surement, it is not po… view at source ↗
Figure 2.2
Figure 2.2. Expected spin correlations of an entangled state [PITH_FULL_IMAGE:figures/full_fig_p018_2_2.png] view at source ↗
Figures from the paper (56 more)
Figure 2.3
Figure 2.3. Figure 2.3: : Experimental apparatuses measuring one of the dichot [PITH_FULL_IMAGE:figures/full_fig_p020_2_3.png]
Figure 2.4
Figure 2.4. Figure 2.4: : Principle of quantum teleportation using two-particle ent [PITH_FULL_IMAGE:figures/full_fig_p025_2_4.png]
Figure 2.5
Figure 2.5. Figure 2.5: : Principle of entanglement swapping. Two sources produc [PITH_FULL_IMAGE:figures/full_fig_p027_2_5.png]
Figure 2.6
Figure 2.6. Figure 2.6: : Spontaneous emission of a photon. At time [PITH_FULL_IMAGE:figures/full_fig_p028_2_6.png]
Figure 2.7
Figure 2.7. Figure 2.7: : Emission characteristics of light emitted from dipole trans [PITH_FULL_IMAGE:figures/full_fig_p029_2_7.png]
Figure 2.8
Figure 2.8. Figure 2.8: Atomic level structure in 87Rb used to generate atom-photon entanglement. Provided the emission frequencies for σ +, σ − and π polarized transitions are indistinguishable within the natural linewidth of the transition, the polar￾ization of a spontaneously emitted pho…
Figure 3.1
Figure 3.1. Figure 3.1: : Schematic setup for the detection of light emitted from a [PITH_FULL_IMAGE:figures/full_fig_p032_3_1.png]
Figure 3.2
Figure 3.2. Figure 3.2: : Light shifts for a two-level atom. Red-detuned light (∆ [PITH_FULL_IMAGE:figures/full_fig_p038_3_2.png]
Figure 3.3
Figure 3.3. Figure 3.3: Reduced level scheme in 87Rb. Dipole matrix elements for π-polarized light are shown as multiples of hJ||er||J ′ i. On the basis of Eq. 3.19, the Wigner-Eckart theorem and Eq. 3.22 one can derive a general expression for the light-shift of any atomic hyperfine state …
Figure 3.4
Figure 3.4. Figure 3.4: 52S1/2 ground- (dashed blue line) and 52P3/2 excited-state (solid red line) light-shift ∆ν as a function of the dipole laser wavelength λ. At 1.4 µm both states have the same light shift. In contrast to the ground state, the excited state Zeeman sub levels m′ F exper…
Figure 3.5
Figure 3.5. Figure 3.5: : Schematical drawing of a focused Gaussian laser beam an [PITH_FULL_IMAGE:figures/full_fig_p041_3_5.png]
Figure 3.6
Figure 3.6. Figure 3.6: : Schematic diagram of processes leading to trap loss in an o [PITH_FULL_IMAGE:figures/full_fig_p045_3_6.png]
Figure 3.7
Figure 3.7. Figure 3.7: Average number N of trapped atoms as a function of the loading rate R for different values of the waist w0 (red line: w0 = 4µm; green line: w0 = 8µm; blue line: w0 = 12µm), (a) without and (b) with two-body collisions. In presence of light-induced two-body collisions…
Figure 3.8
Figure 3.8. Figure 3.8: : Stationary atom number distributions for different loadin [PITH_FULL_IMAGE:figures/full_fig_p048_3_8.png]
Figure 3.9
Figure 3.9. Figure 3.9: : Detailed picture of the experimental setup. [PITH_FULL_IMAGE:figures/full_fig_p049_3_9.png]
Figure 3.10
Figure 3.10. Figure 3.10: : Laser frequencies used in the present experiment for [PITH_FULL_IMAGE:figures/full_fig_p051_3_10.png]
Figure 3.11
Figure 3.11. Figure 3.11: : Geometry of a magneto optical trap (MOT). The magne [PITH_FULL_IMAGE:figures/full_fig_p052_3_11.png]
Figure 3.12
Figure 3.12. Figure 3.12: Photograph of the experimental apparatus. On the vertical base plate above the vacuum chamber optics for the MOT and the cycling laser can be seen. The optics on the right hand side of the MOT chamber is for focussing the dipole laser beam collecting atomic fluoresc…
Figure 3.13
Figure 3.13. Figure 3.13: Experimental setup of the dipole trap and fluorescence detection. The dipole laser is focussed at the intersection of three counterpropagat￾ing laser beams for optical cooling. Fluorescence light is collected with a confocal microscope into a single-mode optical fib…
Figure 3.14
Figure 3.14. Figure 3.14: Single atom detection. Number of photons counted by an avalanche photodiode per 100 ms. Due to the small trap volume and light induced two-body collisions we observe either one or no atom at a time. The dipole trap is loaded by simply overlapping it with the atomic …
Figure 3.15
Figure 3.15. Figure 3.15: : Single atom detection. Histogram of photon counts per [PITH_FULL_IMAGE:figures/full_fig_p056_3_15.png]
Figure 3.16
Figure 3.16. Figure 3.16: : Fraction of single atoms in the dipole trap as a function of [PITH_FULL_IMAGE:figures/full_fig_p057_3_16.png]
Figure 3.17
Figure 3.17. Figure 3.17: (a) Loading rate R and (b) 1/e lifetime in presence of cooling light as a function of the MOT current. Increasing the MOT current reduces the trap lifetime due to an increase of the loading rate. 50 [PITH_FULL_IMAGE:figures/full_fig_p057_3_17.png]
Figure 3.18
Figure 3.18. Figure 3.18: : Histograms of detected photon counts in 100 ms for diffe [PITH_FULL_IMAGE:figures/full_fig_p058_3_18.png]
Figure 3.19
Figure 3.19. Figure 3.19: : Measured atom number distributions for different loadin [PITH_FULL_IMAGE:figures/full_fig_p059_3_19.png]
Figure 3.20
Figure 3.20. Figure 3.20: : Setup for the measurement of the resonance fluores [PITH_FULL_IMAGE:figures/full_fig_p060_3_20.png]
Figure 3.21
Figure 3.21. Figure 3.21: : Measured spectra of the single atom resonance fluore [PITH_FULL_IMAGE:figures/full_fig_p061_3_21.png]
Figure 4.1
Figure 4.1. Figure 4.1: Second-order correlation function g (2)(τ ) of a two-level atom versus the di￾mensionless delay time Γτ for ΩR/Γ = 4 (green solid line) and ΩR/Γ = 0.4 (red dashed line, respectively). values. Performing some calculations [49], the second-order correlation function is…
Figure 4.2
Figure 4.2. Figure 4.2: Effective level structure in 87Rb used for fluorescence detection. The cooling laser field (CL) couples F = 2 → F ′ = 3 and F = 2 → F ′ = 2, whereas the repump laser field (RL) couples only F = 1 → F ′ = 2. Optical Bloch equations In the following I will focus on an …
Figure 4.3
Figure 4.3. Figure 4.3: : Calculated intensity correlation function [PITH_FULL_IMAGE:figures/full_fig_p071_4_3.png]
Figure 4.4
Figure 4.4. Figure 4.4: : Hanbury-Brown-Twiss setup to measure the photon pa [PITH_FULL_IMAGE:figures/full_fig_p075_4_4.png]
Figure 4.5
Figure 4.5. Figure 4.5: Second-order correlation function g (2)(τ ) of the resonance fluorescence of a single 87Rb atom. (a) On long timescales, g (2)(τ ) shows a monotonous de￾cay for | τ |≤ 2..3µs. (b) On short timescales, clear photon anti-bunching at τ = 0 and oscillations due to Rabi f…
Figure 4
Figure 4. Figure 4: shows the resulting correlation function [PITH_FULL_IMAGE:figures/full_fig_p077_4.png]
Figure 4.6
Figure 4.6. Figure 4.6: : Background corrected second-order correlation fun [PITH_FULL_IMAGE:figures/full_fig_p078_4_6.png]
Figure 4.7
Figure 4.7. Figure 4.7: Intensity correlation function g (2)(τ ) (background corrected) of the reso￾nance fluorescence from a single 87Rb atom in the dipole trap for two dif￾ferent trap depths. Red solid line: calculation. Experimental parameters: ICL = 103 mW/cm2 , IRL = 12 mW/cm2 , ∆/2π =…
Figure 5.1
Figure 5.1. Figure 5.1: : Three-level system coupled by two lasers of angular fre [PITH_FULL_IMAGE:figures/full_fig_p081_5_1.png]
Figure 5.2
Figure 5.2. Figure 5.2: : Time dependence of the Rabi frequencies required for e [PITH_FULL_IMAGE:figures/full_fig_p082_5_2.png]
Figure 5.3
Figure 5.3. Figure 5.3: : Four-level system of tripod-STIRAP coupled by three la [PITH_FULL_IMAGE:figures/full_fig_p084_5_3.png]
Figure 5.4
Figure 5.4. Figure 5.4: : Coupling scheme for the analysis of coherent superposit [PITH_FULL_IMAGE:figures/full_fig_p085_5_4.png]
Figure 5.5
Figure 5.5. Figure 5.5: : Geometry of the experiment. The two circularly polarized [PITH_FULL_IMAGE:figures/full_fig_p086_5_5.png]
Figure 5.6
Figure 5.6. Figure 5.6: : Probability to detect the atom in the hyperfine ground st [PITH_FULL_IMAGE:figures/full_fig_p087_5_6.png]
Figure 5.7
Figure 5.7. Figure 5.7: : Probability to detect a single atom in the hyperfine ground [PITH_FULL_IMAGE:figures/full_fig_p088_5_7.png]
Figure 5.8
Figure 5.8. Figure 5.8: : (a) Histogramm of photon counts per 60 ms during redet [PITH_FULL_IMAGE:figures/full_fig_p089_5_8.png]
Figure 5.9
Figure 5.9. Figure 5.9: : Zeeman-splitting of a hyperfine transition [PITH_FULL_IMAGE:figures/full_fig_p091_5_9.png]
Figure 5.10
Figure 5.10. Figure 5.10: : Probability to detect the atom in the dipole trap after ap [PITH_FULL_IMAGE:figures/full_fig_p093_5_10.png]
Figure 5.11
Figure 5.11. Figure 5.11: : Preparation of a Zeeman-superposition state [PITH_FULL_IMAGE:figures/full_fig_p094_5_11.png]
Figure 5.12
Figure 5.12. Figure 5.12: : Experimentel setup of the STIRAP-lasers. (ST [PITH_FULL_IMAGE:figures/full_fig_p095_5_12.png]
Figure 5.13
Figure 5.13. Figure 5.13: : Schematic view of the experimental setup to investigat [PITH_FULL_IMAGE:figures/full_fig_p096_5_13.png]
Figure 5.14
Figure 5.14. Figure 5.14: : Coupling scheme for the analysis of coherent superpos [PITH_FULL_IMAGE:figures/full_fig_p097_5_14.png]
Figure 5.15
Figure 5.15. Figure 5.15: (a) Probability to detect the atom in the hyperfine ground state F = 1 after application of a state-selective STIRAP and detection laser pulse as a function of the linear polarization angle α of the STIRAP laser. Initially the atom was prepared by a 5-µs pump pulse …
Figure 6.1
Figure 6.1. Figure 6.1: : The experimental process (time not to scale). [PITH_FULL_IMAGE:figures/full_fig_p101_6_1.png]
Figure 6.2
Figure 6.2. Figure 6.2: : Simplified setup of the experimental apparatus. The [PITH_FULL_IMAGE:figures/full_fig_p102_6_2.png]
Figure 6.3
Figure 6.3. Figure 6.3: : Number of scattered photons as a function of time durin [PITH_FULL_IMAGE:figures/full_fig_p103_6_3.png]
Figure 6.4
Figure 6.4. Figure 6.4: : Probability of detecting the atom in the ground state [PITH_FULL_IMAGE:figures/full_fig_p106_6_4.png]
Figure 7.1
Figure 7.1. Figure 7.1: : Principle of Remote State Preparation. [PITH_FULL_IMAGE:figures/full_fig_p108_7_1.png]
Figure 7.2
Figure 7.2. Figure 7.2: : Atom-atom entanglement by two-photon interference [PITH_FULL_IMAGE:figures/full_fig_p109_7_2.png]

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