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Controllable interaction between photons and distant spins via vacuum Rabi oscillations

T0 review · 2 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper reports the first time-domain observation of vacuum Rabi oscillations between a single electron spin and a single microwave photon, using two silicon double-quantum-dot spin qubits coupled to a superconducting cavity.

desk verdict A real milestone in spin-photon circuit QED, though the Fock-state claim needs tempering and the vacuum initialization deserves direct evidence. read the letter →

arxiv 2608.03809 v1 pith:N6EF2XSG submitted 2026-08-04 cond-mat.mes-hall quant-ph

Xiao Xue , Jurgen Dijkema , Tobias Bonsen , Patrick Harvey-Collard , Maximilian Rimbach-Russ , Sander L. de Snoo , Guoji Zheng , Amir Sammak
show 2 more authors
Giordano Scappucci Lieven M. K. Vandersypen
This is my paper · ORCID
classification cond-mat.mes-hallquant-ph
keywords vacuumRabioscillationsspinqubitcircuitQEDsuperconductingresonatorFockstatequantumtransfersilicondoubledotJaynes-Cummingsmodel
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 tries to show that a single electron spin and a single microwave photon can coherently exchange a quantum of energy back and forth in real time, a process called vacuum Rabi oscillation. If true, it closes a gap left open since strong spin-photon coupling was first demonstrated: the interaction is now probed in the time domain, not just spectroscopically. The authors go further and use this exchange to transfer an excitation from one spin to another spin located 250 micrometers away, with the photon acting as the messenger. They also show that the photon left in the cavity after such a transfer is a Fock state: its presence accelerates the vacuum Rabi oscillation of the receiving spin, as the Jaynes-Cummings model predicts.

What carries the argument

The workhorse is the flopping-mode spin qubit: a single electron delocalized across a double quantum dot, with a micromagnet providing a transverse magnetic-field gradient. The delocalized charge dipole couples strongly to the resonator, and spin-charge hybridization produces an effective spin-photon coupling described by the Jaynes-Cummings Hamiltonian. Rapid detuning pulses switch the system between the uncoupled regime (for spin manipulation and readout), the resonant regime (for vacuum Rabi oscillations), and the dispersive regime (for readout), all within the same device. The signature that carries the argument is the time-domain oscillation of the cavity transmission, whose frequency g

What would settle it

Measure the vacuum Rabi frequency starting from a cavity whose photon population is independently calibrated, for example by preparing n=0 and n=1 and comparing the first oscillation period. If the extracted single-excitation frequency deviates from sqrt(Delta^2 + 4g_s^2) with g_s fixed by spectroscopy, or if the acceleration after one swap does not track the independently measured photon number, the vacuum-state interpretation fails. Concretely, a spurious thermal population n_bar would shift the fitted g_s upward by a factor sqrt(1+n_bar), which could be detected by repeating the experiment

Watch

Extended reading notes

Core claim

The central discovery is the observation of multiple periods of vacuum Rabi oscillation between a single electron spin and a single microwave photon in a gate-defined silicon double quantum dot coupled to a superconducting resonator. Starting with the spin excited and the cavity empty, the authors watch the excitation oscillate between spin and photon and extract spin-photon coupling strengths of 27.3 MHz and 20.1 MHz for the two qubits. They then concatenate two half-oscillations: a calibrated pi/2 interaction maps the first spin's excitation onto the cavity, and a second pi/2 interaction transfers that photon into the second spin, demonstrating coherent spin-to-spin state transfer through

Load-bearing premise

The cavity must truly start empty—no leaked microwave photons from the spin-flip pulse and negligible thermal population—when the spin-photon interaction begins; otherwise the observed oscillation frequency would be dressed by the photon number and the Fock-state analysis would be biased.

Editorial extensions

If this is right

  • A spin qubit's state can be mapped into a real microwave photon and back, making the resonator a coherent quantum bus that connects spins separated by hundreds of micrometers on the same chip.
  • The same concatenated half-oscillation sequence can, with different interaction times, entangle two distant spins; the paper notes that quantum state tomography would be needed to verify such entanglement.
  • Repeating the swap protocol in lower-loss devices should prepare higher-photon-number Fock states, enabling bosonic quantum information processing in the same resonator.
  • The time-domain observation of the sqrt(n) accelerated Rabi frequency verifies the Jaynes-Cummings ladder for a spin-photon system, not just for superconducting or atomic qubits.
  • Resonant photon-mediated transfer and dispersive iSWAP gates now coexist on one platform, so the same device can serve as a testbed for modular spin-qubit architectures.

Reading between the lines

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

  • If spin relaxation and cavity loss were improved by about an order of magnitude, the same protocol should prepare near-deterministic single-photon Fock states, making the measured acceleration approach the ideal sqrt(2) factor.
  • The extracted initial photon numbers (p around 0.65 and 0.55) give a quantitative budget for how much fidelity is lost to decoherence during the first swap; reducing that loss would directly boost state-transfer fidelity.
  • The second spin acts as a photon-number analyzer; by measuring the vacuum Rabi frequency at several interaction times, one could reconstruct more of the photon-number distribution than just its mean, effectively performing Fock-state tomography without a separate detector.
  • A partial swap followed by a second partial swap implements a beam-splitter-like transformation in the spin-photon Hilbert space, which could be extended to generate photon-mediated entanglement beyond the dispersive regime.
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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

2 major / 4 minor

Summary. The paper reports time-domain vacuum Rabi oscillations between individual electron spin qubits in two distant silicon double quantum dots and a shared superconducting microwave resonator. The protocol initializes one spin in |↑> with the cavity nominally empty, rapidly pulses the double dot into resonance, and reads out the spin via a dispersive transmission measurement after a variable interaction time. Multiple oscillation periods are observed for both qubits, and the extracted 2g_s values (27.3 MHz and 20.1 MHz) agree with earlier spectroscopic vacuum-Rabi splittings on the same device. The paper then concatenates two half-period oscillations to transfer an excitation from one spin to the other through a real cavity photon, showing an interference pattern in a two-dimensional interaction-time sweep. Finally, by first swapping a spin excitation into the cavity, the authors observe an accelerated vacuum-Rabi oscillation and interpret the acceleration as evidence for a predominantly single-photon Fock state, extracting initial photon numbers p≈0.65 and 0.55.

Significance. If the claims hold, this is a milestone for spin-circuit QED: it would be the first time-domain observation of coherent, reversible exchange of a single quantum of energy between a single electron spin and a single microwave photon, and it adds a real-photon quantum link between distant spin qubits. The manuscript has several concrete strengths: multiple oscillation periods are visible in the raw transmission data; the extracted coupling strengths match independent spectroscopic values; the Jaynes-Cummings sqrt(n) acceleration is a genuine model prediction rather than a fitted effect; and the paper shares data and fitting code in a public repository. The state-transfer and Fock-state results are plausibly supported by master-equation simulations with tabulated parameters. However, the 'vacuum' qualification and the quantitative Fock-state interpretation rest on an unverified cavity-initialization assumption and on model-dependent fitting, which need additional experimental support before the central claims can be regarded as fully established.

major comments (2)
  1. [Table I / Section IV-V] The central 'vacuum Rabi' claim rests on the assertion that the resonator is initially in |0>. Section III states 'the cavity empty (|n=0>)' and Appendix A2 sets ρ_init,res=|0><0|, but no measurement or calibration is provided to verify this. The spin-flip burst is applied to LP at ≈6.904 GHz, resonant with the cavity; if any part of this burst leaks into the resonator, the initial photon number nbar is nonzero and the observed frequency is sqrt(1+nbar) g_s, not g_s. This would also inflate the p values extracted in Section V. Please provide a quantitative upper bound on nbar (e.g., calibrate the cavity photon population through a dispersive/ac-Stark measurement, or directly measure the cavity transmission while applying the spin-flip burst with the spin far off resonance), or perform a power-dependence test showing that the extracted g_s is independent of burst power.
  2. [Table I / Section IV-V] The Fock-state evidence is an inferred p from a master-equation fit, not a direct photon-number measurement. The 'empty-cavity' baseline and the 'loaded-cavity' trajectory are fit with the same model, and the spin-flip initialization is assumed perfect; the observed ratio 1.28/1.24 could in principle be mimicked by a combination of imperfect vacuum initialization and detuning miscalibration. The cross-check p≈0.69/0.67 from the first VRO is useful but again uses the same model. Please provide an independent validation of the photon number—for example, a fit to the analytical form (1-p)cos²(g t)+p cos²(√2 g t), or a measurement that is more directly sensitive to the photon-number distribution—to strengthen the Fock-state claim.
minor comments (4)
  1. [Abstract / Section V] The abstract says 'the cavity is prepared in a Fock state,' while the actual prepared state has p≈0.65 and is a statistical mixture (1-p)|0><0|+p|1><1|. Please qualify this as an approximate or predominantly single-photon state to avoid overclaiming.
  2. [Fig. 2 caption / Table I] The caption states 'A vacuum Rabi frequency of 27.3 MHz (20.1 MHz) is extracted,' but Table I lists g_s/2π. Please clarify in the caption that these numbers are 2g_s, to avoid confusion.
  3. [Appendix A, Eq. (A5)] The prefactor in Eq. (A5) appears as 'ℏ 2 g_c^2' in the text; this is likely a typo for ℏ^2 g_c^2 or a missing superscript. Please double-check the expression.
  4. [Reference [28]] The DOI in reference [28] is written as 'https://doi.org/0.4121/...'; this should probably be 'https://doi.org/10.4121/...'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are independent empirical tests of the Jaynes-Cummings model.

full rationale

The paper's central claims—time-domain vacuum Rabi oscillations, spin-to-spin excitation transfer, and the accelerated Rabi frequency from a populated cavity—are presented as measurements compared against the externally established Jaynes-Cummings model. The extracted spin-photon coupling g_s, relaxation rates, scaling factors, and offsets are fitting parameters, not outputs derived from the claims. The accelerated-oscillation experiment fits an initial photon number p to the data, but p is not predetermined by the model and the observed acceleration itself is a nontrivial qualitative prediction of the model; the cross-check using the first vacuum Rabi oscillation is model-dependent but uses a separate dataset, so it is parameter estimation rather than circular reasoning. Self-citations to refs. [4], [18], [19], and [34] provide device details, calibration procedures, and input-output linearization, but none of these supply the central result or serve as a load-bearing uniqueness/ansatz argument. The assumption that the resonator starts in the vacuum state is an experimental precondition, not a derived conclusion, and the paper's own comparison of fitted g_s values with earlier spectroscopic splittings provides an external cross-check. No step reduces, by construction or by self-citation, to its own inputs.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central analysis rests on a master equation fit with five free parameters per dataset (g_s, gamma_1,s, a, b, t_0), plus the extracted photon number p in the Fock-state experiments. The model assumes the Jaynes-Cummings Hamiltonian, spin on resonance, negligible pure dephasing, and a diagonal mixed state for the prepared photon. No new entities are introduced. The qualitative detuning simulations add extra chosen parameters (DeltaB_z, gamma_1,c).

free parameters (7)
  • Spin-photon coupling strength g_s = 13.66±0.10 MHz (Q1, Fig. 2a); 10.06±0.08 MHz (Q2, Fig. 2b); 8.90±0.11 MHz (Q1, Fig. 3c); 9.40±0.14 MHz (Q2, inset); 9.83
    Effective spin-photon coupling strength fitted independently for each vacuum Rabi oscillation dataset.
  • Spin relaxation rate gamma_1,s = 2.68±0.26, 2.80±0.22, 2.60±0.52, 2.46±0.31, 2.37±0.25, 1.37±0.22 MHz across datasets; 3.0 MHz (estimated, Fig. 3d)
    Fitted spin relaxation rate in the Lindblad master equation for each dataset.
  • Initial delay t_0 = 5.40±0.29, 6.91±0.35, 0.0 (bounded), 1.03±0.63, 1.02±0.52, 1.34±0.48 ns; 7.0/5.0 ns (estimated, Fig. 3d)
    Initial delay accounts for spin-photon interaction during the detuning ramps; fitted per dataset.
  • Readout linear mapping parameters a, b = a from 1.22e-3 to 1.80e-3; b from 2.28e-4 to 4.36e-4
    Parameters converting simulated P_up to transmission signal via linear mapping |S21|_sim = a P_up + b.
  • Initial photon number p = 0.65 (Q2 prepares, Fig. 4a); 0.55 (Q1 prepares, Fig. 4b); 0.65 (Q1 in Fig. 3c); 0 (Q2 in Fig. 3c)
    In Fock-state experiments, p is manually varied until the simulation matches the accelerated oscillation; no error bars reported.
  • Longitudinal field gradient DeltaB_z = 4 mT (DQD1), 0.5 mT (DQD2)
    Chosen in the full-Hamiltonian simulation (Section A4) to reproduce the observed asymmetry in detuning maps.
  • Charge relaxation rate gamma_1,c = 1 GHz
    Chosen so that simulated vacuum Rabi visibility roughly matches experimental data in Section A4.
assumptions (6)
  • standard math Jaynes-Cummings model with rotating-wave approximation after eliminating the charge degree of freedom
    The effective spin-photon model (Eq. A4) is derived under the condition max(hbar*g_c, g*mu_B*DeltaB_x) << 2 t_c, stated in Appendix A1.
  • domain assumption Spin on resonance with the shifted cavity: omega_q = omega*_r
    Assumed in the fitting procedure (Appendix A3); the magnetic field is tuned to satisfy this.
  • domain assumption Perfect spin state preparation (rho_init,q = |up><up|)
    Statement in Appendix A2: 'We assume the spin state preparation to be perfect.'
  • domain assumption Pure spin dephasing neglected (gamma_phi,s = 0)
    Appendix A3 says 'the observed vacuum Rabi oscillations are mainly limited by relaxation' and sets gamma_phi,s = 0.
  • ad hoc to paper Prepared cavity state is a diagonal mixture (1-p)|0><0| + p|1><1|
    Appendix A3 uses this mixture to model the imperfect Fock-state preparation; it assumes no coherences in the photon state.
  • domain assumption Truncated resonator Hilbert space with N_max = 5 photons is sufficient
    Appendix A2 states the simulations truncate at N_max = 5, assuming convergence for the low photon numbers involved.

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Cite this review

Pith. "Pith review of Controllable interaction between photons and distant spins via vacuum Rabi oscillations." pith.science (2026). https://pith.science/paper/N6EF2XSG

@misc{pith2026260803809,
  author       = {Pith},
  title        = {Pith review of: Controllable interaction between photons and distant spins via vacuum Rabi oscillations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N6EF2XSG}},
  note         = {Machine review of arXiv:2608.03809}
}
read the original abstract

Vacuum Rabi oscillations between a single photon and a single spin demonstrate the capability of harnessing light-matter interaction at the level of a single quantum of energy. Since the observation of strong spin-photon coupling in gate-defined quantum dots, probing this interaction in the time-domain has been a major objective. Here, we carefully engineer a device composed of two spatially separated double quantum dots hosting single electron spin qubits and a superconducting cavity to accommodate microwave photons. We observe multiple vacuum Rabi oscillations between each spin qubit and the cavity. By concatenating vacuum Rabi oscillations involving the two spins, an energy excitation in one qubit can be emitted as a photon and then transferred to the other qubit. When a single photon is emitted, the cavity is prepared in a Fock state, leading to an accelerated vacuum Rabi frequency. These results serve as building blocks not only in exploring light-matter interactions, but also in interfacing semiconductor spin qubits to photonic links.

Figures

Figures reproduced from arXiv: 2608.03809 by the authors.

Figure 1
Figure 1. A distributed quantum computation architecture enabled by superconducting resonators. a. Vision of a spin-based quantum processor. The processor contains multiple two-dimensional quantum dot arrays with densely patterned quantum dots that host electron (or hole) spin qubits. Each module is connected to superconducting resonators at its corners. The quantum information encoded in spin qubits can be exchanged into mic… view at source ↗
Figure 2
Figure 2. Vacuum Rabi oscillations. a,b. Vacuum Rabi oscillations of (a) Q1 and (b) Q2 . The data points show the magnitude of the measured transmission signal through the resonator as a function of the interaction time tint between the resonator and the corresponding qubit. Solid lines are fits to the data using a numerical model of the spin-photon system, including coupling to its environment (see Section A for details). A … view at source ↗
Figure 3
Figure 3. Transfer of excitations between distant spins. a. Circuit schematic implemented in the experiment. b. Schematics showing the double dot configuration leading to vacuum Rabi oscillations for Q2 and Q1 respectively. c. With the resonator being populated and Q1 in its ground state, a vacuum Rabi oscillation with inverted phase is observed. The oscillation frequency is fitted to be 17.8 MHz. Inset, vacuum Rabi oscillati… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Accelerated vacuum Rabi oscillations. a. The top panel shows the circuit schematic. Both qubits start in their excited state. Then the spin excitation in Q2 is completely swapped into the resonator and subsequently, the vacuum Rabi oscillation between Q1 and the photon…
Figure 5
Figure 5. Figure 5: Asymmetry in the vacuum Rabi oscillations versus interdot detuning. a,b. Simulated spin-up probability as a function of interdot detuning ε and interaction time tint. In these simulations, we use ωr/2π = 6.9105 GHz, κ/2π = 1.8 MHz, gc/2π = 192 MHz, γ1,c/2π = 1 GHz, and…
Figure 6
Figure 6. Figure 6: Detuning ramp simulations. a-d Simulated spin (|↑⟩) and photon (|n = 1⟩) excitation probabilities for several interaction times tint, throughout the shown interdot detuning profiles ε(t). The simulation parameters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p…
Figure 7
Figure 7. Figure 7: Coherent spin-photon coupling with detuning-pulsed dispersive readout. a. Probed resonator frequency as function of double-dot detuning. At zero detuning, the charge degree of freedom of the double dot induces a dispersive shift of the resonator frequency. As the spin …

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    M. Newville, R. Otten, A. Nelson, T. Stensitzki, A. In- gargiola, D. Allan, A. Fox, F. Carter, Michał, R. Osborn, D. Pustakhod, S. Weigand, lneuhaus, A. Aristov, Glenn, Mark, mgunyho, C. Deil, A. L. R. Hansen, G. Pasque- vich, L. Foks, N. Zobrist, O. Frost, Stuermer, J.-C. Jas...

    2024

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    The effect of nonzeroεand∆B z will be investigated in Section A4

    Effective spin-photon model To enable iterative fitting of the simulations to the experimental data, we eliminate the charge degree of freedom in the limitmax(ℏgc,gµB∆Bx)≪2t c and setε= 0,∆B z = 0[18]. The effect of nonzeroεand∆B z will be investigated in Section A4. We then a...

  30. [38]

    ThesimulationsareimplementedusingQuTip[33], with a truncated resonator Hilbert space including up toNmax = 5photons in the resonator

    Numerical simulations and decoherence The system dynamics are simulated using the Lindblad master equation dρ dt =− i ℏ(Hρ−ρH) + ∑ i Di(ρ)(A7) withLindbladdissipationtermsD i(ρ) =γ i ( LiρL† i− 1 2{L† iLi,ρ} ) . ThesimulationsareimplementedusingQuTip[33], with a truncated reso...

  31. [39]

    Fitting procedure To fit the experimental data, we perform a master equation simulation using the effective spin-photon Hamiltonian HJC, and include the following dissipation terms in Eq. (A7) γ1 =κ∗ L1 =a,(A8) γ2 =γ 1,s L2 =σ−,(A9) γ3 =γ ϕ,s L3 =σ z.(A10) Similar to the reson...

  32. [40]

    Asymmetry versus interdot detuning In this section, we numerically reproduce the observed asymmetry in the vacuum Rabi oscillations versus interdot detuning seen in main text Fig. 2c,d. As discussed in the main text, we expect this asymmetry to originate from a difference in m...

  33. [41]

    As discussed in the main text, we attribute this initial phase to the spin-photon interaction during the detuning ramps

    Phase accumulation during the detuning ramps Finally, we investigate the origin of the observed initial phase attint = 0of the vacuum Rabi oscillations, which was accounted for in the effective spin-photon model (Section A1) by including an initial delayt0 as a fitting paramet...

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Reviewed August 5, 2026 · model on record in the stance chip above.