Spontaneously generated coherence–mediated orbital angular momentum transfer: experimental realization, tolerances, and robustness in a near-degenerate V-type atomic medium

A 2019 theoretical study (Sabegh, Mohammadi, Maleki and Mahmoudi, J. Opt. Soc. Am. B 36, 2757) predicted that spontaneously generated coherence (SGC) — quantum interference between two spontaneous-emission channels in a V-type atom — transfers orbital angular momentum (OAM) from a weak Laguerre–Gaussian beam to a generated weak plane-wave field in a medium with two near-degenerate excited states, with no transfer when the SGC parameter $\eta=\cos\theta$ vanishes. The prediction rests on idealizations — steady state, exact resonance, equal and closed decay channels, $\eta$ up to 0.99 — and specifies no experimental protocol or tolerances. The open problem is to make this mechanism real and quantitatively understood: engineer a real medium whose level structure attains a large effective $\eta$ within stated tolerances, verify the OAM transfer (topological charge, phase structure, efficiency), and map its robustness to detuning, transients, Doppler and collisional dephasing, and non-ideal decay branching.

Background

Light beams with a helical wavefront, such as Laguerre–Gaussian (LG) modes whose field carries an azimuthal phase factor $\exp(il\varphi)$, possess an orbital angular momentum (OAM) of $l\hbar$ per photon, distinct from the spin angular momentum of polarization. Because the integer topological charge $l$ is unbounded, OAM provides a high-dimensional basis for encoding quantum information, which motivates schemes to transfer OAM between light fields inside a controllable medium.

Spontaneously generated coherence (SGC, also called vacuum-induced coherence) is a quantum-interference effect in a three-level $V$-type atom — two excited states $|2\rangle$ and $|3\rangle$ decaying to a common ground state $|1\rangle$ — in which the two spontaneous-emission channels are indistinguishable and therefore interfere. Indistinguishability requires (i) an excited-state splitting comparable to or smaller than the transition linewidth and (ii) non-orthogonal transition dipole moments $\vec{\mu}_{21}$ and $\vec{\mu}_{31}$. The SGC strength is $\eta=\vec{\mu}_{31}\cdot\vec{\mu}_{21}/(|\vec{\mu}_{31}||\vec{\mu}_{21}|)=\cos\theta$, and it enters the atomic density-matrix (Bloch) equations as cross-damping terms proportional to $\eta\sqrt{\gamma_R\gamma_L}$, where $\gamma_R$ and $\gamma_L$ are the spontaneous decay rates of the two excited states.

Sabegh, Mohammadi, Maleki and Mahmoudi [J. Opt. Soc. Am. B 36, 2757 (2019); arXiv:1906.01855] solved the steady-state Bloch equations coupled to Maxwell's propagation equation (in the electric-dipole, rotating-wave and slowly-varying-envelope approximations) for a $V$-type medium with two near-degenerate excited states driven by a weak LG 'right' field and a weak plane-wave 'left' field. They showed analytically that the SGC alone mediates OAM transfer: the generated left field acquires the full intensity and phase structure of the right LG field, whereas for $\eta=0$ the generated field vanishes and no transfer occurs. As a candidate real medium they proposed the sodium D2 line, with the ground state $|3^2S_{1/2},F=1\rangle$ and the hyperfine sublevels $|3^2P_{3/2},F'=0\rangle$ and $|3^2P_{3/2},F'=1\rangle$ as the near-degenerate excited states. Their calculations used idealized conditions: exact two-photon resonance ($\Delta_R=\Delta_L=0$), equal decay rates, a closed decay manifold, optical depth $\alpha=100$, and steady state. At moderate SGC ($\eta=0.5$) the output-field intensity is heavily reduced, while strong SGC ($\eta=0.99$) raises it about tenfold relative to the first, microwave-induced scheme of the same paper. The paper provides no experimental protocol and no tolerances for the level engineering that a large $\eta$ demands.

For context, OAM exchange between optical fields in atomic vapors has been demonstrated experimentally, but only through resonant four-wave mixing, a mechanism unrelated to SGC. SGC itself has been studied almost exclusively theoretically (electromagnetically induced transparency and refractive properties, atom localization, optical switching, quantum wells and dots), and the experimental accessibility of spontaneous-emission-induced coherences has so far been shown mainly in laser-cooling settings. Whether SGC — a spontaneous-emission interference effect requiring delicate near-degeneracy and dipole alignment — can be engineered strongly enough to transfer OAM in a real medium, and how robust such transfer would be, has not been established.

Problem Statement

The problem is to establish whether spontaneously generated coherence is a realizable mechanism for orbital angular momentum transfer between weak optical fields, by answering, for a concrete real medium, three linked questions that jointly serve this single objective:

1. Level engineering and protocol. Identify a real atomic (or atom-like) medium and specify a complete experimental protocol — level structure, field frequencies, polarizations and geometry, quantization-axis control, medium optical depth and length, temperature — with quantified tolerances, that attains a large effective SGC parameter $\eta$. The tolerances must state how close to degeneracy the two excited levels must be relative to the transition linewidth, how well aligned the two transition dipoles must be (including the Zeeman-sublevel selection and polarization purity this requires), and how the non-ideal decay branching of the chosen levels (decay channels outside the ideal closed $V$ system) constrains the scheme.

2. Transfer verification. Demonstrate — experimentally, or with a quantitative model validated against the original ideal-limit predictions — that the generated field carries the orbital angular momentum of the incident Laguerre–Gaussian field (its topological charge and azimuthal phase structure), and quantify the transfer efficiency.

3. Robustness map. Quantify how the transfer efficiency and phase fidelity degrade with detuning from resonance, finite $\eta$, Doppler and collisional dephasing, transient (non-steady-state) operation, and non-ideal decay branching, and quantify the signal-to-noise and gain–absorption tradeoff of the weak generated field at moderate $\eta$.

An answer may take the form of an experimental demonstration with the above characterization, or a validated quantitative protocol-and-robustness analysis; a quantified infeasibility result — showing that no accessible medium attains the required effective $\eta$ within stated tolerances — is also an acceptable resolution. Either way it must engage the real level structure of the chosen medium rather than the idealized closed model, and it must be explicit about which parts of the original generality (e.g., the sodium D2 hyperfine proposal) it confirms, refines, or replaces.

References

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