Quantum optics with single spins

Lee C. Bassett

Quantum optics with single spins

T0 review · 0 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The chapter claims that coherent dispersive light-matter coupling, described by the Jaynes-Cummings Hamiltonian, is the common origin of both the Faraday effect and the optical Stark effect in single solid-state spins.

desk verdict A clear, honest review chapter that re-derives Faraday and optical Stark effects for NV centers from the Jaynes-Cummings Hamiltonian; no new results, but the pedagogy is sound and the claims are no stronger than the cited experiments. read the letter →

arxiv 1908.05566 v1 pith:2DQPKAZF submitted 2019-08-15 quant-ph cond-mat.mes-hallphysics.atom-ph

Lee C. Bassett This is my paper · ORCID

classification quant-phcond-mat.mes-hallphysics.atom-ph

keywords nitrogen-vacancycenterJaynes-CummingsmodelFaradayeffectopticalStarkcoherentpopulationtrappingstimulatedRamantransitionsultrafastcontrolsolid-statespinqubits

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 chapter establishes that a single theoretical picture—the Jaynes-Cummings Hamiltonian applied to a laser pulse in a well-defined spatial mode—accounts for both the spin-dependent phase shift of transmitted light (the Faraday effect) and the light-induced rotation of the spin (the optical Stark effect) in atom-like defects such as the nitrogen-vacancy center in diamond. The two effects are not separate phenomena: they are the light and spin components of the same polariton energy shift, linked by one constant $D$. If this is right, the same formalism explains all-optical initialization via coherent population trapping, arbitrary-axis rotations via stimulated Raman transitions in a $\Lambda$ configuration, and faster coherent control via ultrafast pulses that exploit excited-state spin-orbit coupling. A sympathetic reader would care because these are microwave-free, in-principle non-destructive tools for quantum networks and distributed quantum computers, and the chapter argues they generalize to any defect with a tunable $\Lambda$ configuration.

What carries the argument

The load-bearing object is the Jaynes-Cummings Hamiltonian $\hat{H}_{\mathrm{JC}}^{(j)} = E_{\mathrm{ph}}\hat a^\dagger\hat a + E_j \hat\sigma_z^{(j)}/2 + (\hbar\Omega_0/2)(\hat a\hat\sigma_+^{(j)} + \hat a^\dagger\hat\sigma_-^{(j)})$ in the basis of polariton states $|g_j,n+1\rangle$ and $|e_j,n\rangle$. Diagonalization gives the dispersive energy shift $\varepsilon_g(n,\Delta_j) = (\hbar\Delta_j/2)[\sqrt{1+\Omega_0^2/\Delta_j^2}-1]$, which, integrated over the pulse duration $\tau$, becomes the spin-dependent phase per photon $D/\Delta_j$. Tracing out the light leaves a spin rotation, while tracing out the spin leaves a light phase shift; the same constant $D$ appears in both, which is what unifies the Faraday and optical Stark effects. A Schrieffer-Wolff effective Hamiltonian for the strain-split excited state and a five-level Lindblad model for the $\Lambda$ system carry the all-optical control protocols.

What would settle it

Measure the Faraday phase shift and the optical-Stark rotation on the same spin transition while sweeping detuning from far-detuned through resonance, and compare both lineshapes to Eqs. (51) and (52) using the same fitted $\Omega_0$ and $\Gamma_j$. If the phase-shift lineshape is not the odd Lorentzian required by Kramers-Kronig, or if the ratio of Faraday phase to Stark rotation deviates from the predicted proportionality as $\Delta$ changes, the Jaynes-Cummings polariton account is falsified.

Watch

Extended reading notes

Core claim

The central claim is that coherent light-matter interaction for an individual solid-state spin is governed by the Jaynes-Cummings Hamiltonian, with the laser pulse playing the role of the cavity. In the dispersive limit $|\Delta_j|\gg \Omega_0$, each photon acquires a spin-dependent phase $\varphi_j = D/\Delta_j$ when the spin is in state $j$, and a coherent pulse rotates the spin by the accumulated phase $\langle n\rangle(\varphi_j-\varphi_k)$. This yields the Faraday effect in the transmitted light and the optical Stark effect on the spin, with $\Phi_{\mathrm{OSE}} = n \Phi_F$ in the far-detuned limit. The chapter further claims that the same polariton physics, extended to a $\Lambda$ configuration, produces dark states, coherent population trapping, and stimulated Raman transitions, so arbitrary single-qubit operations can be performed with light; and that with ultrafast pulses, free evolution under the excited-state Hamiltonian generates spin rotations at rates near 260 MHz, approaching microwave control speeds.

Load-bearing premise

The load-bearing premise is that each laser pulse has a smooth adiabatic turn-on, propagates as a single spatial mode with a well-defined phase, and has negligible spontaneous emission, spectral hopping, and laser noise during the interaction; if those conditions fail, the phase formulas and the predicted proportionality between the Faraday and optical Stark effects need correction.

Editorial extensions

If this is right

A single NV-center spin can be initialized, coherently controlled, and projectively read out using only light, without microwaves, through CPT initialization and SRT rotations.
The Faraday measurement is in principle non-destructive: the absorption falls as $1/\Delta^2$, while the phase shift falls as $1/|\Delta|$; in an optical cavity, the enhanced phase shift could allow spin readout without reinitialization.
Because the control only requires a $\Lambda$ configuration, the protocols transfer to other defects, such as silicon-vacancy centers and silicon carbide impurities, including systems without an intersystem crossing.
The relation $\Phi_{\mathrm{OSE}} = n \Phi_F$ lets one calibrate spin rotation and optical phase shift against each other using the same detuning-dependent constant $D$.
Ultrafast optical pulses bypass the dispersive approximation and use excited-state spin-orbit evolution directly, giving measured Rabi frequencies near 260 MHz and $\pi$-rotations in about 1.9 ns.

Reading between the lines

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

An editorial extension: if a single constant $D$ controls both the Faraday and optical Stark signals, a high-precision measurement of their ratio versus photon number would be a direct test of the coherent-state polariton model and a sensitive probe of decoherence during the pulse.
The chapter notes cavity-coupled silicon-vacancy spins but does not work out a two-spin gate; extending the same dispersive Hamiltonian to two defects in one cavity suggests a natural route to entangling operations, not just readout.
The adiabatic turn-on assumption implies that pulse shaping should matter: comparing smooth and abrupt pulse envelopes at fixed area would quantify non-adiabatic corrections to the phase formulas.
The time-domain quantum tomography technique described for the NV excited-state Hamiltonian could also map tunable strain and electric-field Hamiltonians in other defects, turning it into a general tool for choosing optimal control operating points.

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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

Colleague — good quick read. This is a review chapter, not a research paper, and it says so: much of the material is adapted from Buckley, Yale, and Bassett et al. What it does well is unify the Faraday and optical Stark effects under one Jaynes-Cummings polariton picture. That derivation (Sec. 3.1) is textbook-grade and the connection between phase-per-photon and spin rotation is stated cleanly. The lambda-system section and the ultrafast control part are compact summaries of published work, with the original references properly credited. If you teach NV quantum optics or want a single entry point for a student, this is a useful piece.

The main soft spot, as the reader notes, is that nothing here is new. The fitted parameters in Fig. 2(c) are extractions from Buckley et al. and are not predictions. The ultrafast section is a condensation of Bassett et al. That limits what peer review would need to check: the standard derivations and the fidelity of the reporting, not new claims. The math in Sections 3 and 4 checks out in the regimes stated, and the author is explicit about the adiabatic turn-on, single spatial mode, and no-decoherence assumptions. Those are real limitations for quantitative agreement, but they are stated rather than hidden.

One technical point worth knowing: Eq. (45) computes <α|ρ|α> rather than the true partial trace over light. The exact trace gives exp[-|α|^2(1-cos(φ_j-φ_k))] rather than exp[-|α|^2(2-e^{iφ_j}-e^{-iφ_k})] in the off-diagonal. Since both reduce to exp[-(φ_j-φ_k)^2/2] to leading order and the quoted phases are tiny (φ^2 ~ 10^-4), the optical-Stark rotation and the main argument survive; the error only affects the dephasing estimate, which is small. If the chapter gets revised, I'd suggest fixing the notation to do the trace honestly, but it is not a load-bearing flaw.

Bottom line: solid review for students and newcomers; not an advance. Worth sending to serious referees only in the sense that a proceedings chapter deserves checking for accuracy, and I'd accept it after minor cleanup. I wouldn't cite it as a primary source, and I'd only bring it to reading group if someone wants an NV optics primer.

Referee Report

0 major / 5 minor

Summary. This manuscript is a lecture/review chapter, based on the author's 2018 Enrico Fermi School lectures, that presents a pedagogical account of quantum optics with single solid-state spins, using the diamond nitrogen-vacancy (NV) center as the central example. Section 2 reviews the NV electronic structure and derives effective excited-state Hamiltonians in the low- and high-strain regimes via a Schrieffer-Wolff transformation. Section 3 derives the Jaynes-Cummings polariton picture and uses it to unify the Faraday effect and the optical Stark effect as two manifestations of the same dispersive light-matter interaction, with quantitative comparisons to the experiments of Ref. [1]. Section 4 extends the treatment to Lambda systems, covering coherent population trapping, stimulated Raman transitions, and all-optical initialization, control, and readout following Ref. [2]. Section 5 describes an alternative ultrafast, non-dispersive approach to spin control and time-domain quantum tomography following Ref. [3]. The manuscript explicitly states that much of the material is adapted from Refs. [1]-[3], and it carefully lists the assumptions (adiabatic pulse turn-on, single-mode propagation, neglect of spontaneous emission and spectral noise) and practical limitations (small Faraday phase without a cavity, dual-Lambda constraints on stimulated Raman transition speed).

Significance. If the derivation is taken as a review statement, the chapter is a valuable pedagogical resource. Its main strength is that it derives the Faraday phase and the optical Stark rotation from a single polariton energy-shift calculation, making the proportionality Phi_OSE = n Phi_F (Eq. (49)) and the lineshape comparison in Fig. 2(c) transparent. The standard Jaynes-Cummings calculation is carried out carefully, and the comparison with the published data of Refs. [1]-[3] is concrete. The text is honest about the conditions under which the derivation holds: Section 3.1 states the adiabatic and decoherence-free assumptions; Section 3.3 quantifies the smallness of the nondispersive phase; and Section 5 explicitly discusses the dual-Lambda limitation on the fidelity and speed of the stimulated Raman approach. Because the chapter is a review of published work and openly credits the original sources, there is no novelty or circularity concern. The main weakness is the imprecise treatment of the reduced spin density matrix in Section 3.2, which is local and does not affect the central conclusions.

minor comments (5)

[3.2, Eqs. (44)-(45)] The expression labeled rho_spin is defined as <alpha|rho|alpha>, which is a conditional projection onto the original coherent state rather than the reduced spin state Tr_light(rho). The exact partial trace yields off-diagonal elements proportional to exp[-|alpha|^2(1-cos(phi_j-phi_k))] e^{i|alpha|^2 sin(phi_j-phi_k)}, so the real dephasing factor in Eq. (45) is off by a factor of two relative to the correct result. The subsequent linearization in Eq. (47) retains only the leading phase, so the central Faraday/Stark relations are unaffected, but the derivation should be corrected for rigor.
[3.1, Eq. (27)] In Eq. (27), the n-dependence of Omega_0 is stated to enter through the field amplitude, but the Jaynes-Cummings matrix element in the basis of Eq. (26) involves sqrt(n+1), not sqrt(n). The authors should state explicitly that they neglect the difference between n and n+1, or redefine Omega_0(n) accordingly, since this is a notational shortcut that could confuse readers.
[3.2, after Eq. (47)] The condition under which the pure-state approximation for the spin is valid, namely |alpha|^2 (phi_j-phi_k)^2 << 1 for the relevant pairs, is not stated; adding this inequality would make the domain of validity of Eq. (48) quantitative.
[4.3 and Section 2.1 (typos)] There are typographical errors such as 'dissipate' for 'dissipate' in Section 4.3 and 'diagmagnetic' for 'diamagnetic' in Section 2.1; a careful proofreading pass is recommended.
[Fig. 2(c)] The text compares Eq. (50) to the data in Fig. 2(c) and states that extracted parameter values are obtained, but it does not specify the fitting procedure or the error bars on the extracted parameters; one or two sentences on this would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the polariton-based derivation is self-contained and the fitted parameters are presented as extractions, not predictions.

full rationale

The paper is a review/lecture chapter whose central derivation starts from the textbook Jaynes-Cummings Hamiltonian and obtains the dispersive phase shifts, Faraday effect, and optical Stark effect as derived consequences. The eigenenergy expression in Eq. (27) leads to the accumulated phase in Eq. (31), then to the Faraday phase in Eq. (43) and the spin-state phase in Eq. (48); the proportionality in Eq. (49) follows algebraically from those expressions. No equation is defined in terms of the quantity it is supposed to predict. The experimental parameters F_j, Γ_j, and Ω0 in Section 3.2 are explicitly described as extracted from data ('we extract experimental values'), so they are fits rather than predictions claimed from the model. The self-citations to Refs. [1–3] are used to credit the original experiments and models, not to provide an unexamined load-bearing premise; the derivation in the chapter is independent of those papers. The modeling assumptions (adiabatic turn-on, single-mode field, neglect of decoherence) are stated assumptions, not circular inputs. The minor technical point that Eq. (45) projects onto 〈α| rather than performing a full partial trace affects only the dephasing prefactor, not the optical-Stark phase, and in any case does not constitute circularity. No uniqueness theorem, ansatz-via-citation, or renaming of an empirical pattern is used to force the conclusions. The derivation is therefore self-contained, with no circular step that reduces an output to an input.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The chapter relies on standard quantum optics, the empirically parameterized NV Hamiltonian, and the author's prior experimental papers for all quantitative inputs. No new entities are introduced.

free parameters (7)

Debye-Waller factor F_DW = 0.04 +/- 0.01
Empirical reduction of the resonant dipole coupling due to nuclear-coordinate displacement; used in Eqs. (17), (22), (32).
Phase-per-photon scale D/2pi = approx 10 kHz
Typical value in high-NA experiments; scales the Faraday phase and optical Stark spin rotation in Eqs. (31)-(32), (43), (49).
Faraday amplitude F_0 = 2pi*6.9 urad.GHz
Fitted to Ref. [1] data in Fig. 2(c); used to compare the model to measurements without quoted uncertainty.
Absorption width Gamma_0 = 2pi*140 MHz
Fitted to the ms = 0 transition data in Fig. 2(c).
Faraday amplitude F_-1 = 2pi*7.6 urad.GHz
Fitted to the ms = -1 transition data in Fig. 2(c).
Absorption width Gamma_-1 = 2pi*300 MHz
Fitted to the ms = -1 transition data in Fig. 2(c).
Optical Rabi frequency Omega_0 = 2pi*70 MHz
Fitted to the data in Fig. 2(c); enters the optical Stark shift formula.

assumptions (5)

standard math Jaynes-Cummings model with rotating-wave approximation is valid for the NV optical transition.
Used in Section 3.1 to derive polariton eigenenergies and phase shifts; standard quantum optics result (Ref [19]).
domain assumption The optical pulse can be described as a single-mode coherent state with a cavity defined by the pulse duration, with adiabatic turn-on and no spontaneous emission or spectral diffusion.
Stated explicitly in Section 3.1; this idealization underlies Eqs. (29)-(32) and the spin phase shift formula.
domain assumption The NV excited-state Hamiltonian has the symmetry-allowed form of Eq. (2) with spin-orbit, spin-spin, Zeeman, diamagnetic, and strain terms.
Taken from Refs [9,10]; used throughout Section 2 to derive the effective Hamiltonians in Eqs. (15)-(16).
domain assumption The strain splitting 2delta dominates over other couplings, justifying the Schrieffer-Wolff expansion to lowest order in 1/delta.
Statement in Section 2.2 before Eq. (15); used to derive the block-diagonal effective Hamiltonians.
standard math Kramers-Kronig relation links the Faraday lineshape to the absorption resonance.
Invoked in Section 3.2 to extend the far-detuned expression to an odd Lorentzian (Eq. 51).

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Cite this review

Pith. "Pith review of Quantum optics with single spins." pith.science (2026). https://pith.science/paper/2DQPKAZF

@misc{pith2026190805566,
  author       = {Pith},
  title        = {Pith review of: Quantum optics with single spins},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2DQPKAZF}},
  note         = {Machine review of arXiv:1908.05566}
}

read the original abstract

Defects in solids are in many ways analogous to trapped atoms or molecules. They can serve as long-lived quantum memories and efficient light-matter interfaces. As such, they are leading building blocks for long-distance quantum networks and distributed quantum computers. This chapter describes the quantum-mechanical coupling between atom-like spin states and light, using the diamond nitrogen-vacancy (NV) center as a paradigm. We present an overview of the NV center's electronic structure, derive a general picture of coherent light-matter interactions, and describe several methods that can be used to achieve all-optical initialization, quantum-coherent control, and readout of solid-state spins. These techniques can be readily generalized to other defect systems, and they serve as the basis for advanced protocols at the heart of many emerging quantum technologies.

Figures

Figures reproduced from arXiv: 1908.05566 by the authors.

**Figure 1.** – Electronic structure of the diamond NV center. (a) At room temperature, rapid phonon transitions within the orbitals of the 3E excited state lead to an effective spintriplet with spin-dependent non-radiate decay channels, γ nr ms , through the ISC as shown. These dynamics produce the NV center’s spin-dependent PL. (b) At low temperature, the orbital fine structure within 3E is resolved. The unperturbed spin-orbit… view at source ↗

**Figure 2.** – Light-matter coupling in the diamond NV center. (a) The interaction between an atomic transition with ground and excited states {|gi, |ei} and a near-resonant laser field is described by the Jaynes Cummings Hamiltonian in terms of polariton states {|Gi, |Ei} with an energy shift ε. (b) Energy-resolved transitions for different spin sublevels in the NV center’s optical fine structure produce spin-dependent interact… view at source ↗

**Figure 3.** – Measurement setup. Schematic of the experimental setup used to measure Faraday and optical Stark effects. A tunable laser near the NV-center ZPL at 637 nm provides the coherent optical pulses. A second laser at 532 nm is used to initialize the NV-center spin and charge state. [AOM: Acousto-optic modulator; SBC: Soleil-Babinet compensator]. Adapted from Ref. [1] and reprinted with permission from AAAS. ms =−1 spin… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: – Physics of Λ configurations. (a) Three levels arranged in a Λ configuration. (b) Realization of a Λ system for the NV center from an excited-state avoided level crossing. then the amplitude for a transition to occur from state |gii to the excited state, |ei, is propo…

**Figure 5.** Figure 5: – All-optical control via coherent dark states. Experiments (points) and simulations (curves) of quantum dynamics in the NV-center ground state driven by optical pulses designed to achieve CPT (a) and SRT (b). Orange (top) and blue (bottom) trajectories correspond to…

**Figure 6.** Figure 6: – Coherent spin control with ultrafast pulses. (a) Orbital structure of the NV center at intermediate-to-high transverse strain. (b) Fine structure as a function of axial magnetic field in the |Li orbital branch when δ = 6.7 GHz. (c) PL excitation spectroscopy as a fun…

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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