Single-Photon Skyrmions in Quantum Photonics

• Single-photon skyrmions are topologically nontrivial quantum states of light defined by continuous mappings of polarization or momentum to a target manifold with a nonzero skyrmion number.
• They are realized through advanced spin–orbit coupling techniques using methods like SPDC and metasurface-integrated emitters, achieving high modal fidelity and robust single-photon generation.
• These topological states enable protected quantum information transport and hybrid light–matter interfaces, paving the way for scalable, on-chip quantum communication and sensing applications.

Single-photon skyrmions are topologically nontrivial quantum states of light in which the spatial polarization or momentum-spin configuration of a single photon forms a skyrmion texture—that is, a continuous mapping from physical space or momentum space (ℝ² or k-space) to a target manifold (such as the Poincaré sphere or spin-1 Bloch sphere) that carries a nonzero topological (skyrmion) number. This concept extends classical optical skyrmions and momentum-space analogs (Chern insulators, Dirac monopoles) to the fundamentally quantum single-photon regime, enabling topologically protected structures in quantum information, photonics, and light-matter interfaces (Mechelen et al., 2018, Koni et al., 30 Jul 2025, Liu et al., 10 Jan 2026).

1. Theoretical Foundations: Spin-1 Photonic Skyrmions

Single-photon skyrmions arise as physical manifestations of nontrivial topology in electromagnetic fields, particularly through the spin-1 structure of the photon. In photonic Chern insulators, the Maxwell–Dirac correspondence formalizes the analogy between photons and electrons, with the crucial distinction that photons (bosons) are described by spin-1 matrices $S_i$ generating SO(3) symmetry, while electrons (fermions) have spin-½ and SU(2) algebra.

For 2D photonic systems, the effective Hamiltonian

$$\mathcal{H}_1(k) = v(k_x S_x + k_y S_y) + \Lambda(k) S_z$$

with $\Lambda(k) = \Lambda_0 - \Lambda_2 k^2$, governs the emergence of massive photon states where the sign of $\Lambda_0 \Lambda_2$ determines topological (skyrmionic) phase versus trivial phase (Mechelen et al., 2018).

The eigenmodes of $\mathcal{H}_1$ are parametrized by a “skyrmion vector”

$\mathcal{M}(k) = (v k_x, v k_y, \Lambda(k))$

mapping momentum $k$ to the surface of a momentum-space sphere. The normalized spin-1 field

$$\hat{S}(k) = (\sin\theta \cos\phi,\,\sin\theta \sin\phi,\,\cos\theta)$$

with $\theta = \arctan(vk / \Lambda(k))$, determines the direction of the local photonic spin.

The skyrmion number (winding number)

$$N = \frac{1}{4\pi} \int_{\mathbb{R}^2} \hat{S} \cdot (\partial_{k_x} \hat{S} \times \partial_{k_y} \hat{S}) \, dk_x \, dk_y$$

classifies the topological phase. For photons, the Chern number per band is always even: $C_1 = 2N$ (Mechelen et al., 2018).

2. Quantum Photonic Skyrmions in Real Space: Polarization Textures

Real-space single-photon skyrmions are encoded in the transverse polarization structure of a quantum light field. For a heralded single photon with spin–orbit entanglement (e.g., superposition of circular polarization and orbital angular momentum (OAM) eigenstates), the polarization at each point $(x,y)$ is represented by the reduced density matrix $\bar{\rho}(x,y)$, yielding local Stokes parameters $S_0, S_1, S_2, S_3$.

The normalized local “spin” vector

$$\mathbf{s}(x,y) = [S_1(x,y), S_2(x,y), S_3(x,y)] / S_0(x,y)$$

maps the $(x, y)$ plane to the Poincaré sphere. The skyrmion number is then evaluated as

$$N = \frac{1}{4\pi} \int_{\mathbb{R}^2} \mathbf{s} \cdot (\partial_x \mathbf{s} \times \partial_y \mathbf{s}) \, dx \, dy$$

quantifying the topological degree of the mapping (Koni et al., 30 Jul 2025, Liu et al., 10 Jan 2026). Experimentally, typical values $N\approx \pm2$ indicate second-order skyrmions in photonic experiments.

3. Experimental Realizations: Heralded and On-Chip Single-Photon Skyrmions

A. Spin–Orbit Engineered Single-Photon Skyrmions

Experiments using spontaneous parametric down-conversion (SPDC) sources combined with liquid-crystal topological defects (q-plates) realize heralded single-photon skyrmions (Koni et al., 30 Jul 2025). The protocol involves:

• Generating entangled photon pairs with correlated OAM and polarization in a nonlinear crystal.
• Subjecting each photon to a spin–orbit coupling transformation by a liquid-crystal device with topological charge $q=+1$. Here, for a single photon $$\ell |R\rangle \to \sqrt{1-\eta}|ℓ\rangle|R\rangle + \sqrt{\eta}|ℓ-2\rangle|L\rangle$$ with electrically tunable efficiency $\eta$.
• Heralding on one photon (projecting onto a Gaussian OAM and specific polarization) yields a single-photon state exhibiting a spatial polarization skyrmion, confirmed by measuring local Stokes vectors and calculating the skyrmion number.

B. On-Chip Metasurface-Integrated Emitters

Metasurface-integrated quantum emitter (metaQE) platforms achieve deterministic single-photon skyrmion generation on chip (Liu et al., 10 Jan 2026). A quantum emitter coupled to a meta-atom array excites SPPs, whose scatterings by the metasurface imprint engineered spin–orbit phase relations:

$$|\psi(r, \phi)\rangle = A_R\, LG_{\ell_R, p_R}(r) e^{i \ell_R \phi} |R\rangle + A_L e^{i \Delta\varphi} LG_{\ell_L, p_L}(r) e^{i \ell_L \phi} |L\rangle$$

The device geometry defines charge combinations $(\ell_R, \ell_L)$ corresponding to anti-skyrmions ($N_{sk} \approx -1.86$) or skyrmionium ($N_{sk} \approx 0.07$), measured via Stokes parameter mapping and OAM holography.

Experimental parameters include:

Platform	Skyrmion Number $N$	Modal Purity (%)	$g^{(2)}(0)$ (Single-Photon Test)
LC-q-plate (heralded)	$\pm2$	>50 (Fidelity)	Confirmed by coincidence
Meta-QE (on chip)	-1.86 (anti-sk)	>90	0.19 (GeV center, $\tau\approx$8ns)

4. Momentum-Space (k-Space) Skyrmions and Topological Phases

Momentum-space skyrmions undergird the bulk-edge correspondence for photonic topological insulators. The spin-1 texture field $\hat{S}(k)$ defines the mapping $S^2\rightarrow S^2$, whose degree (skyrmion number) fixes the bulk Chern invariants.

The Berry connection and curvature are defined as

$$A(k) = -i \mathbf{e}_s^* \cdot \nabla_k \mathbf{e}_s,\quad F(k) = \nabla_k \times A(k)$$

In 2D photonic phases, the Berry curvature can be interpreted as a synthetic magnetic field

$$F(k) = \hat{S} \cdot (\partial_{k_x} \hat{S} \times \partial_{k_y} \hat{S})$$

and integrates to obtain the Chern number. The Dirac monopole charge $Q_s$ in k-space distinguishes photonic (integer) from electronic (half-integer) cases:

$Q_s = \frac{1}{4\pi} \oint_{S^2} F_s \cdot dS$

Bulk momentum-space skyrmions enforce the existence, number, and quantization of edge-localized, helically quantized topological edge states.

5. Strong Coupling and Light–Matter Hybrid Skyrmions

Single-photon skyrmion dynamics can be interfaced with solid-state topological textures, notably magnetic skyrmions in nano-discs. Coupling is achieved by Zeeman interaction between the resonator vacuum field and the total magnetic dipole of the skyrmion texture (Martínez-Pérez et al., 2018):

• The coupling Hamiltonian reads $$H_{\mathrm{int}} = g (a^\dagger b_\nu + b_\nu^\dagger a)$$, with $g$ determined by the vacuum field strength, magnetic susceptibility, and the skyrmion host volume.
• Numerical estimates yield $g/2\pi \sim 1$–3 MHz, exceeding both cavity decay and skyrmion dissipation rates by a factor $>10$, ensuring strong coupling.
• Skyrmion breathing and gyrotropic modes may be quantized and coherently exchanged with microwave photons.
• The device enables photon–skyrmion information transduction, generation of remote skyrmion entanglement via photons, and realization of nonreciprocal photon-magnon conversion elements.

Topological corrections from Dzyaloshinskii–Moriya interaction (DMI) modify both the skyrmion mode frequency and the coupling strength via the gyrotropic constant and the mode susceptibility.

6. Measurement, Tomography, and Topological Verification

Characterization of single-photon skyrmions universally requires spatially resolved polarization tomography:

• For real-space skyrmions, the field is analyzed at each pixel or spatial location $(x,y)$ via projective measurements onto polarization bases (RCP, LCP, H, V, D, A). Stokes vector fields are reconstructed, and the discrete version of the topological density $$\mathbf{s} \cdot (\partial_x \mathbf{s} \times \partial_y \mathbf{s})$$ is summed to estimate $N$.
• For k-space skyrmions, Fourier-plane polarization tomography is performed, and Berry curvature is accumulated over the sampled $k$-space.
• The quantum state fidelity $$F = [\mathrm{Tr}(\sqrt{\sqrt{\rho_t}\rho\sqrt{\rho_t}})]^2$$ quantifies agreement with the ideal skyrmion state; $F>0.5$ is seen when $|N|\approx 2$ (Koni et al., 30 Jul 2025).
• OAM holography and HOM-type measurements confirm OAM content and single-photon character ($g^{(2)}(0)<0.5$).

7. Applications and Prospects

Single-photon skyrmions present a robust, high-dimensional platform for:

• On-chip quantum communication, using discrete topological indices $(\ell, p, \text{spin})$ as quantum alphabet (Liu et al., 10 Jan 2026).
• Topologically protected quantum information transport, leveraging the resilience of skyrmion textures to perturbations and disorder.
• Hybrid interfaces, enabling photon–magnon–phonon interaction chains for complex quantum processing (Martínez-Pérez et al., 2018).
• Integrated quantum sensing and metrology exploiting the phase and polarization robustness carried by the skyrmion topology.
• Electrically reconfigurable and dynamically tunable sources via voltage-controlled spin–orbit couplers (e.g., liquid-crystal q-plates) (Koni et al., 30 Jul 2025).

A plausible implication is that the continued development of chip-integrated, high-purity single-photon skyrmion sources will advance scalable topological quantum photonic architectures and enable further examination of quantum matter–light hybrid skyrmionics in both condensed matter and quantum optics (Liu et al., 10 Jan 2026).