Spin-Entangled Optical Transitions

• Spin-entangled optical transitions are quantum processes that couple spin states with optical excitations, creating nontrivial correlations across photonic and orbital modes.
• They are realized in systems such as cold-atom lattices, solid-state spin–photon interfaces, and 2D van der Waals magnets, offering diverse experimental platforms.
• Experimental studies show that external magnetic fields and anisotropic interactions can modulate these transitions, paving the way for advanced quantum networks and metrology.

Spin-entangled optical transitions are quantum processes in which the evolution, manipulation, or observation of internal spin degrees of freedom in matter is directly intertwined with optical excitation or emission events. In such transitions, the resultant quantum states encode nontrivial spin correlations—entanglement—between localized or extended regions, which are coupled to photonic, spatial, or orbital degrees of freedom. This phenomenon underlies quantum simulation in cold-atom superlattices, the design of scalable solid-state spin–photon interfaces, ultrafast spectroscopy of correlated organic materials, and the exploration of fundamental magnetic interactions in van der Waals antiferromagnets.

1. Fundamental Mechanisms of Spin–Entangled Optical Transitions

Spin–entangled optical transitions arise in systems where light-matter interactions couple electronic/spin degrees of freedom with the spatial, charge, or photonic modes:

• In spinor cold-atom lattices, as in the Bose–Hubbard spin-1 model, the Hamiltonian incorporates both orbital and spin-dependent terms:

$$H_0 = \frac{U_0}{2} \sum_{i=L,R} n_i(n_i-1) - t \sum_\sigma (\hat{L}_\sigma^\dagger\hat{R}_\sigma + \hat{R}_\sigma^\dagger\hat{L}_\sigma) + \epsilon(n_L-n_R) + \frac{U_2}{2} \sum_{i=L,R} (\vec{S}_i^2 - 2n_i)$$

The interplay of spin-exchange interactions ($U_2$), orbital transitions (tunneling $t$), and onsite interactions ($U_0$) leads to optical transitions whose rates and allowedness depend on the spin state, embedding spin entanglement in spatially resolved tunneling events (Wagner et al., 2011).

• In van der Waals antiferromagnets, spin-entangled transitions manifest as on-site spin-flip excitations in d-electron systems, often detected as photoluminescence or absorption resonances (the "X-feature"). An absorbed photon induces a $\Delta S=1$ spin flip confined to a magnetic atom (e.g., Mn in MnPS₃, Ni in NiPS₃), with transition energies and oscillator strengths modulated by the underlying magnetic order and anisotropy (Jana et al., 3 Oct 2025).
• Spin–photon interfaces in quantum dots, NV centers, and SiC divacancies exploit cyclic optical transitions: transitions that preserve spin state, allow repeated photon cycling, and exhibit spin-selectivity in emission. By engineering selection rules and photonic environments (e.g., photonic crystal waveguides, optical cavities), cyclicity can be massively enhanced (values up to 409 demonstrated), enabling coherent manipulation/readout of spin qubits via optical means (Koong et al., 17 Sep 2025, Appel et al., 2020, Antoniuk et al., 2023).

2. Spin–Orbit Interplay and Bipartite Entanglement Structure

Spin–entangled optical transitions are characterized by nonlocal quantum correlations arising from hybridization of spin, spatial/orbital, and photonic degrees. The total entanglement between two subsystems—for example, sites in a double-well—can be decomposed:

$$E(|\Psi\rangle) \geq E_{\text{orbital}} + E_{\text{spin}}$$

where %%%%6%%%% quantifies spin entanglement and $E_{\text{orbital}}$ quantifies uncertainty in particle number or mode occupation (Wagner et al., 2011). For states of two spin-1 bosons with total spin zero, the spin contribution reaches $\log_2 3$, corresponding to maximal two-qutrit singlet entanglement.

In photonic systems, eigenmodes with combined spin (polarization) and orbital angular momentum (OAM) yield single-photon spin–orbit entangled states, which can be mathematically represented as:

$$|\ell, m\rangle_{\text{OAM}} \propto \text{HE}_{\text{even}}^{+1,m} \pm i\,\text{HE}_{\text{odd}}^{+1,m} \propto F_m(r) e^{\pm i \ell \phi}$$

Such encoding enables high-dimensional entanglement in optical fibers and expanded quantum information capacity (Yang et al., 2021).

3. Influence of Magnetic Fields and Anisotropic Interactions

External magnetic fields introduce both linear and quadratic Zeeman effects, modifying spin-energy spectra and causing mixing of spin states. In spin-1 cold-atom systems, the quadratic Zeeman term breaks conservation of spin magnitude ($S^2$), yielding hybridization among $S_{\text{tot}}$ sectors and altering the position/width of transitions:

• Linear Zeeman term: $p S_z^{\text{tot}}$, splitting multiplets.
• Quadratic term: $q \sum m_\sigma^2 n_{i,\sigma}$, mixing states.

In van der Waals antiferromagnets with pronounced in-plane and out-of-plane anisotropies (e.g., NiPS₃ and MnPS₃), magnetic field orientation modulates the splitting and polarization of spin-flip optical transitions:

$E_X(B) = E_X(0) - g \mu_B B \cos\Psi(B)$

where $\Psi(B)$ encodes the angle between sublattice magnetization and field. Above the spin-flop field $B_{\text{sf}}$, spin reorientation leads to collapse or quadratic field dependence (Jana et al., 3 Oct 2025, Jana et al., 2023). Experimental PL and absorption data provide direct probes of anisotropy parameters and effective exchange couplings.

4. Experimental Realization and Platform Capabilities

Platforms exploiting spin-entangled optical transitions span several domains:

• Cold-atom superlattices: Manipulation of tunneling rates and site offsets in double-well potentials enables control and measurement of spin–orbital entanglement, with magnetic fields tuning spin-coupling and Zeeman hybridization (Wagner et al., 2011, Kessler et al., 2013).
• Solid-state photonic systems: Photonic crystal waveguides and resonant cavities manipulate transition rates and selection rules, achieving cyclicity necessary for efficient spin–photon interfaces, multi-photon entanglement, and scalable quantum gates (Koong et al., 17 Sep 2025, Appel et al., 2020, Antoniuk et al., 2023).
• Organic and correlated materials: Ultrafast spectroscopy of $\pi$-conjugated systems reveals hidden spin-entangled triplet-pair components in optically dark singlet states, with selective optical projection yielding spatially separated, long-lived entangled triplets (Pandya et al., 2020).
• 2D magnets: Ab initio GW and dynamical mean-field theory calculations elucidate atom- and orbital-resolved band structure, allowing direct interpretation of orbital- and spin-resolved spectroscopic observations in van der Waals antiferromagnets (Jana et al., 3 Oct 2025).

5. Quantification and Analysis of Entanglement

Entanglement measures depend on system, context, and observable:

• Cold atoms: Particular bipartite entanglement structures are accessed via Schmidt decomposition, as in

$$|\Psi\rangle = c_1 |2,0\rangle_L |0,0\rangle_R + c_2 |1,1\rangle_L |1,1\rangle_R + c_3 |0,2\rangle_L |0,0\rangle_R$$

with $$E(|\Psi\rangle) = -\sum_i c_i^2 \log_2 c_i^2 + c_2^2 \log_2 3$$.

• Fermionic lattices: Spin entanglement between sites is quantified via concurrence:

$$C_{i,j}(t) = \max \left\{ 0, -\frac{1}{2} - 6 \frac{\langle S_i^z S_j^z \rangle}{\langle n_i^s n_j^s \rangle} \right\}$$

The spatial distribution of entangled pairs can be manipulated by onsite interaction $U$ and time-dependent tunneling $J(t)$ (Kessler et al., 2013).

• Photonics: In spin–orbit entangled photons, the full state can represent a qudit using both polarization and OAM; device engineering allows deterministic, high-fidelity initialization and control (Yang et al., 2021, Appel et al., 2020).

6. Technological and Fundamental Implications

Spin–entangled optical transitions have direct relevance to quantum networks, metrology, and ultrafast opto-magnetism:

• Deterministic spin–photon interfaces support quantum memory, quantum transduction between microwave and optical domains, and scalable multi-photon cluster state generation (Koong et al., 17 Sep 2025, Antoniuk et al., 2023, Ortu et al., 2017, Welinski et al., 2018).
• High-dimensional encoding using spin–orbit entangled photons increases channel capacity and error resilience in quantum communication (Yang et al., 2021).
• Magneto-optical spectroscopies enable ultrafast control of antiferromagnetic order and probe fundamental magnetic interactions in low-dimensional materials (Jana et al., 3 Oct 2025, Jana et al., 2023).
• In organic materials, the direct projection and manipulation of spin-entangled triplet pairs informs singlet fission photovoltaics and room-temperature quantum coherence (Pandya et al., 2020).

7. Outlook and Future Directions

Future work will explore:

• Advanced ab initio and DMFT theoretical methods to systematically predict and tailor spin–entangled optical transitions in correlated materials and nanostructures (Jana et al., 3 Oct 2025).
• Engineering cyclic optical transitions, strain, and light–hole mixing in quantum dots and color centers to optimize spin–photon coupling, cyclicity, and repeatability for on-chip quantum information processing (Koong et al., 17 Sep 2025, Antoniuk et al., 2023).
• Manipulation of anisotropic magnetic interactions in 2D van der Waals magnets for ultrafast spin-control and optically driven quantum phase manipulation (Jana et al., 2023, Jana et al., 3 Oct 2025).
• Integration of spin–orbit photonic modes into fiber-based quantum networks and high-dimensional quantum communication platforms (Yang et al., 2021).
• Quantitative exploration of combined orbital, spin, and photonic entanglement contributions across diverse experimental and simulation platforms.

Spin-entangled optical transitions constitute a unifying quantum resource, enabling precision metrology, scalable communication, and probing of correlated matter, with their structure, magnitude, and control increasingly accessible across atomic, solid-state, and photonic architectures.