Dissipative Spin-Orbital-Angular-Momentum Coupling

• Dissipative SOAMC is a process where spin couples to orbital angular momentum in the presence of loss, enabling chiral transport and state manipulation.
• It utilizes classical and quantum models with coupled angular motions, non-Hermitian dynamics, and exceptional points to achieve spin filtering and vortex control.
• Applications range from cold-atom experiments and exciton-polariton condensates to atomistic spin-lattice simulations, offering practical insights into novel quantum phases.

Dissipative spin–orbital–angular‐momentum coupling (SOAMC) is a generalized form of spin–orbit coupling (SOC) wherein the spin degree of freedom is coupled specifically to the orbital angular momentum (OAM) of particles or fields, in the presence of dissipation. SOAMC has emerged as a central concept in the study of quantum transport, non-Hermitian dynamics, and emergent phenomena in driven-dissipative many-body and condensed-matter systems, with broad relevance from cold-atom experiments and exciton-polariton condensates to atomistic spin-lattice simulations.

1. Fundamental Principles and Model Hamiltonians

SOAMC is characterized by kinetic or dynamical cross-terms that couple the "spin" (which may be a real spin, a pseudo-spin, or an internal degree of freedom) to the angular motion (typically to OAM about a specific axis). In classical and quantum mechanical frameworks, minimal models capture the essential physics:

• Classical Model: Two independent angular coordinates, θ₁ ("orbit") and θ₂ ("spin"), are coupled by a Lagrangian of the form

$$L[θ₁, θ₂, \dot{θ}_1, \dot{θ}_2] = \frac{1}{2}β_1 \dot{θ}_1^2 + \frac{1}{2}β_2 \dot{θ}_2^2 + γ \dot{θ}_1 \dot{θ}_2 f(θ_2 - θ_1)$$

where β₁, β₂ are moments of inertia, γ is the SOAMC strength, and $f(δ)$ is a $2π$-periodic function encoding the angular dependence of the coupling. The canonical quantum analogue is a Hamiltonian featuring

$$\hat{H} = \frac{\hat{L}_z^2}{2I} + (\alpha_R / \hbar) \hat{L}_z \hat{σ}_z$$

which directly couples OAM and spin, as realized in cold-atom and condensed-matter platforms (Varshney et al., 2024, Liu et al., 2 Jan 2026, Yang et al., 2024).

• Dissipation is incorporated by Rayleigh-type friction terms (classical) or non-Hermitian loss terms (quantum), which break energy conservation and open channels for nonreciprocal dynamics, spin relaxation, and novel transport effects. In quantum SOAMC systems, non-Hermiticity typically enters as spin-dependent losses or gain, e.g., $\omega = h - i\gamma$ where $γ$ is a spin-dependent decay rate (Liu et al., 2 Jan 2026).

2. Dissipative SOAMC in Quantum and Classical Dynamics

The interplay of SOAMC and dissipation produces robust transport asymmetries and nonreciprocal phenomena:

• In classical rotor models, the inclusion of Rayleigh damping ($\alpha>0$) leads to analytic solutions for the dynamics and enables "spin filtering": the total distance traversed in the orbital channel depends on the initial spin polarization, yielding a spin-dependent traversal asymmetry (Varshney et al., 2024):

$$Δθ_1^f(s) = \frac{2}{\alpha}\left( c_1 - \frac{\gamma}{2} s |c_2| \right)$$

and the corresponding filtering asymmetry

$$A = \frac{Δθ_1^f(-1) - Δθ_1^f(+1)}{Δθ_1^f(-1) + Δθ_1^f(+1)} = \frac{\gamma |c_2|}{2c_1}$$

Such filtering provides a classical analogue to chiral quantum transport and demonstrates the minimal ingredients (SOAMC, chirality, and dissipation) necessary for spin-selective effects.

• In quantum non-Hermitian SOAMC systems, exceptional points (EPs) emerge as degeneracies where eigenvalues and eigenstates coalesce. SOAMC, implemented via Raman coupling with co-propagating Laguerre–Gaussian beams (carrying defined OAM), mixes the spin and orbital motion and introduces spin-dependent decay, resulting in rich multi-band structures and the appearance of both intra- and inter-band EPs. The spectral Riemann surfaces near these EPs govern the chiral transfer of population among modes, enabling deterministic, path-dependent manipulation of quantum states in the presence of loss (Liu et al., 2 Jan 2026).

3. Driven–Dissipative SOAMC in Bose–Einstein and Polariton Condensates

SOAMC has been experimentally implemented in two-component Bose–Einstein condensates and generalized to exciton-polariton condensates under driven-dissipative conditions:

• The open-dissipative Gross–Pitaevskii framework, modified to include spatially inhomogeneous Raman coupling $\Omega_R(r)$ with orbital angular momentum, yields coupled equations for pseudo-spinor condensates. SOAMC manifests as an off-diagonal term mixing the spin components, with the angular structure inherited from the Raman beams' OAM difference (Yang et al., 2024).
• The competition between boundary-driven rotation (from finite-radius pump and loss) and the internal spin–OAM torque from SOAMC produces a rich phase diagram for vortex formation and stability:
  • Weak SOAMC ($\Omega'_R \sim 1$) generates a robust central vortex–antivortex pair.
  • Strong SOAMC ($\Omega'_R \gtrsim 50$) disrupts lattice-wide vortex order and can destroy global coherence, especially for weak interactions.
  • Moderate repulsive interactions stabilize vortex patterns against disruption by SOAMC, while dissipation and spatially varying coupling can both pin and destabilize vortices depending on parameter regimes (Yang et al., 2024).

4. Non-Hermitian Topology, Exceptional Points, and Chiral Dynamics

Non-Hermitian SOAMC systems, particularly in cold-atom platforms, feature a hierarchy of exceptional points due to the interplay of spin–OAM coupling and dissipation:

• Exceptional Points (EPs): For each OAM quantum number $m$ and band index $n$, the condition for an EP is

$$(h - i\gamma)^2 + \Omega_{n\uparrow,n\downarrow}^2 = 0 \quad \Longrightarrow \quad h = 0, \gamma = \pm\Omega_{n\uparrow,n\downarrow}$$

where $h$ is two-photon detuning and $\Omega_{n\uparrow,n\downarrow}$ the intra-band Raman coupling. Inter-band EPs arise from non-zero inter-band couplings and can be mapped numerically as curves in the $(h, \gamma)$ plane (Liu et al., 2 Jan 2026).

• Chiral Encircling of EPs: By adiabatically modulating $h$ and $\gamma$ around closed loops that enclose EPs, robust nonreciprocal state transfer between bands is realized:
  • Clockwise traversal of the EP branch cut flips the occupancy between band branches (e.g., from upper to lower).
  • Counterclockwise traversal can return the population to its original state, contingent on the topology of the Riemann surface and the detailed time-dependence.
  • Composite loops involving multiple EPs facilitate transfer into higher bands, providing novel routes to populate otherwise inaccessible SOAMC-dressed states (Liu et al., 2 Jan 2026).
• Dominance of Loss and Non-Adiabaticity: Increasing dissipation ($\gamma \gg \Omega$) projects the system into subspaces with largest decay rates, causing adiabatic encirclement to fail and final-state populations to be determined by the imaginary parts of the eigenenergies along the loop.

5. SOAMC in Atomistic Spin–Lattice Dynamics

The extension of atomistic simulations to include dissipative SOAMC enables fully coupled simulations of lattice and spin with direct angular-momentum exchange:

• Classical atoms with positions $r_i$ and velocities $v_i$, bearing classical spins $S_i$, are governed by a total Hamiltonian $H = H_{lat} + H_{spin} + H_{soc}$, where $H_{soc}$ models spin–orbit-induced local anisotropies due to symmetry-breaking from lattice vibrations or defects (Perera et al., 2016).
• The explicit SOAMC terms,

$$H_{soc} = -C_1 \sum_i K_i(r) \cdot S_i - C_2 \sum_i S_i^{T} \Lambda_i(r) S_i$$

with local "easy axis" $K_i$ and Hessian $\Lambda_i$, provide a microscopic channel for angular-momentum transfer between spin and lattice, which is essential for simulating thermalization, demagnetization, and phonon–magnon coupling.

• Introduction of $H_{soc}$ enables the lattice–spin system to equilibrate: in its absence, magnetic moments remain frozen when only the lattice is thermostatted. When SOAMC is implemented, spin temperature rises and magnetization decays toward the target value on the picosecond timescale. The rates can be quantified and controlled by varying the local anisotropy strengths $C_1$, $C_2$, or by introducing defects, which strongly enhance relaxation rates (Perera et al., 2016).

6. Experimental Realizations and Physical Implications

Dissipative SOAMC is readily implementable in several experimental platforms:

• Cold Atom Gases: SOAMC is generated by employing pairs of Raman beams with different OAM (e.g., Laguerre–Gaussian modes), spin-selective loss by optical pumping, and tunable detuning and coupling strengths. The time scales and parameter spaces required for observing EP topology and chiral population transfer are accessible within typical coherence times (Liu et al., 2 Jan 2026).
• Exciton-Polariton Systems: Spatially structured optical pumping combined with resonantly driven SOAMC can control the formation, stability, and disruption of vortex configurations over a wide regime of pump strengths and interaction parameters (Yang et al., 2024).
• Atomistic Simulations: Multiscale modeling of spintronic materials and ultrafast magnetic processes benefits from inclusion of SOAMC, especially when local structural disorder or phonon activity is significant (Perera et al., 2016).

The physical consequences of SOAMC, particularly when coupled with dissipation, include the breakdown of conventional angular-momentum conservation (in the presence of loss), spin-selective transport and filtering, topological band reconstruction at EPs, and the emergence or destabilization of complex many-body configurations such as vortex lattices. While classical models capture the essential chiral and dissipative aspects, quantum SOAMC offers richer physics due to non-Abelian spin structure, geometric phases, and non-Hermitian topology.

7. Limitations and Outlook

Classical SOAMC models, while illustrative, are limited by their treatment of "spin" as a continuous variable, lacking the SU(2) quantum structure of real electronic spin, precluding effects such as entanglement and geometric phases (Varshney et al., 2024). Quantum non-Hermitian SOAMC, as realized in cold atoms and polariton condensates, provides a platform for exploring chiral dynamics, exceptional-point topology, and dissipative control over band populations. In atomistic magnetic simulations, the accuracy of angular-momentum transfer depends on parameterization of local anisotropies and the treatment of spin–lattice coupling.

Continued development in experimental techniques and computational modeling is expected to further elucidate the regimes in which dissipative SOAMC can be exploited for quantum technologies, chiral transport, and the engineering of many-body quantum phases.

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Key References:

• "Classical 'spin' filtering with two degrees of freedom and dissipation" (Varshney et al., 2024)
• "Chiral Dynamics Near Intra- and Inter-Band Exceptional Points under Dissipative Spin-Orbital-Angular-Momentum Coupling" (Liu et al., 2 Jan 2026)
• "Stability of vortices in exciton-polariton condensates with spin-orbital-angular-momentum coupling" (Yang et al., 2024)
• "Reinventing atomistic magnetic simulations with spin-orbit coupling" (Perera et al., 2016)