Spin-Polariton States: Hybrid Light–Matter Quasiparticles

• Spin-polariton states are hybrid light–matter quasiparticles whose dynamics integrate spin, polarization, and nonlinear interactions in semiconductor microcavities.
• They exhibit complex phenomena such as spontaneous symmetry breaking, TE-TM splitting induced spin-orbit coupling, and topologically nontrivial transport in engineered confinement.
• Control mechanisms via magnetic tuning, non-Hermitian engineering, and cavity coupling enable tailored spin dynamics, driving advances in spintronics and quantum optics.

Spin-polariton states are hybrid light–matter states in which the spin or polarization degree of freedom is an essential dynamical variable. In semiconductor microcavities, the term usually denotes two-component exciton-polariton states built from the circularly polarized components $\psi_{+}$ and $\psi_{-}$, with dynamics shaped by spin-dependent interactions, TE-TM splitting, Zeeman fields, gain and loss, and confinement geometry. In a broader cavity-QED usage, spin-polariton states are hybridized eigenstates of electronic spin excitations and cavity photons. Across these settings, the central theme is the same: spin is not a passive label, but part of the quasiparticle structure, the nonlinear dynamics, and the transport phenomenology (Rubo, 2012, Fischer et al., 25 Aug 2025).

1. Spinor structure and effective descriptions

The canonical description of semiconductor spin-polariton states uses a two-component order parameter in the circular basis, $\Psi=(\psi_{+},\psi_{-})^{T}$. In quasi-equilibrium mean-field theory, the condensate is described by a multicomponent Gross–Pitaevskii equation derived from a Hamiltonian density containing kinetic energy, interaction terms, and perturbations such as external fields. In the circular basis, the interaction energy distinguishes co-polarized and cross-polarized channels, and the Zeeman field enters as $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$. The same framework also extends to four-component exciton condensates containing bright $(\pm1)$ and dark $(\pm2)$ components, where spin-exchange terms phase-lock the bright and dark sectors (Rubo, 2012).

For driven condensates under non-resonant pumping, the basic model is an open-dissipative Gross–Pitaevskii equation coupled to rate equations for spin-selective reservoirs,

$$i\hbar\frac{\partial \psi_\sigma}{\partial t} = \left( -\frac{\hbar^2}{2m}\nabla^2 +u_a|\psi_\sigma|^2 +u_b|\psi_{-\sigma}|^2 +g_R n_\sigma +\frac{i\hbar}{2}[Rn_\sigma-\gamma_c] \right)\psi_\sigma +J\psi_{-\sigma},$$

with

$$\frac{\partial n_\sigma}{\partial t}=P_\sigma(r,t)-[\gamma_R+R|\psi_\sigma|^2]n_\sigma.$$

This form makes explicit the coexistence of coherent spin mixing through $J$, spin-anisotropic interactions through $u_a,u_b$, and driven-dissipative replenishment through the reservoir $\psi_{-}$0. A complementary pseudospin representation uses the Stokes components

$\psi_{-}$1

which place polarization dynamics on the Poincaré sphere and connect the problem to Josephson-type phase dynamics (Li et al., 2015).

In ring geometries, the spinor Gross–Pitaevskii model acquires explicitly angle-dependent TE-TM coupling,

$\psi_{-}$2

where $\psi_{-}$3 is half the Zeeman splitting and $\psi_{-}$4 is half the TE-TM splitting. The angular factors $\psi_{-}$5 encode the rotation of the effective in-plane field around the ring and are central to the geometric-phase effects discussed below (Zezyulin et al., 2017).

2. Nonequilibrium symmetry breaking and ordered spin phases

A major class of spin-polariton states arises through spontaneous symmetry breaking in driven-dissipative condensates. In a spatially trapped exciton-polariton condensate under nonresonant excitation, a critical bifurcation density induces spontaneous parity breaking to a ferromagnetic state: the condensate randomly adopts one of two elliptically polarized states with opposite handedness, reaching up to $\psi_{-}$6 circular polarization. At $\psi_{-}$7 these magnetized states remain stable for many seconds, while at higher temperatures they can flip between the two orientations. The dynamics are captured by a spinor equation with different loss rates and energy splittings for orthogonal linear polarizations, making the ferromagnetic states nonequilibrium attractors rather than equilibrium minima (Ohadi et al., 2015).

The same bifurcation mechanism generalizes to coupled condensates. In an infinite chain of uniformly coupled driven-dissipative condensate spins, the condensates become magnetized above a critical occupation threshold and form binary spin patterns. Minimization of the bifurcation threshold selects the ordered phase as a function of the coherent coupling $\psi_{-}$8: ferromagnetic order $\psi_{-}$9, antiferromagnetic order $\Psi=(\psi_{+},\psi_{-})^{T}$0, and a paired-spin state $\Psi=(\psi_{+},\psi_{-})^{T}$1. The paired state is enabled by the phase degree of freedom between condensates and appears as an intermediate order under adiabatic pump ramping (Sigurdsson et al., 2017).

Experiments on closed condensate chains showed the same sequence in finite systems. In 4-condensate rings, tuning the nearest-neighbor coupling optically drives transitions between ferromagnetic, antiferromagnetic, and an intermediate crossover phase composed of alternating FM and AFM bonds. In 8-condensate chains, spatial inhomogeneities become decisive, and feedback-controlled pump shaping is used to compensate disorder and prepare selected spin states. This establishes spin-polariton chains as controllable non-equilibrium spin lattices rather than simple analogues of equilibrium Ising models (Ohadi et al., 2017).

Under coherent driving, spin-polariton states also exhibit multistability and switching. A coherent polariton gas can display bistability between $\Psi=(\psi_{+},\psi_{-})^{T}$2-dominated and $\Psi=(\psi_{+},\psi_{-})^{T}$3-dominated states, and tristability when a mixed state becomes stable at higher pump power. Ultrafast $\Psi=(\psi_{+},\psi_{-})^{T}$4 optical pulses switch among these states, while nonlinear losses and the buildup of a non-radiative reservoir are crucial for the switching dynamics (Cerna et al., 2013). In a single-mode resonantly driven system with linear spin coupling, the symmetry-broken steady states can lose stability through Hopf bifurcation, leading to oscillatory and chaotic dynamics, including limit-cycle bistability and full-span oscillations of the circular-polarization degree analogous to the intrinsic Josephson effect (Gavrilov, 2021). Non-resonant spin-polarized pumping provides an additional control layer: well defined phase-locked steady states, self-trapped states, Josephson oscillations, and nontrivial stationary spin textures generated by spatially inhomogeneous pulses all emerge within the open-dissipative two-component model (Li et al., 2015).

3. TE-TM splitting, spin-orbit coupling, and confined geometries

In microcavity polariton systems, TE-TM splitting acts as a spin-orbit coupling that mixes circular polarizations in a momentum-dependent manner. In azimuthally symmetric traps, the single-particle Hamiltonian can be written as

$\Psi=(\psi_{+},\psi_{-})^{T}$5

with $\Psi=(\psi_{+},\psi_{-})^{T}$6. Unlike the electronic Rashba problem, the ground state of a trapped polariton can be non-degenerate and can possess a specific polarization vortex texture. For $\Psi=(\psi_{+},\psi_{-})^{T}$7, sufficiently strong spin-orbital coupling yields either an azimuthal vortex or a radial vortex, depending on the sign of $\Psi=(\psi_{+},\psi_{-})^{T}$8; in quasi-1D rings the effect is enhanced, and even weak TE-TM splitting can produce a definite-vorticity ground state. The effective ring Hamiltonian contains a linear-in-$\Psi=(\psi_{+},\psi_{-})^{T}$9 off-diagonal coupling proportional to the curvature $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$0, so the dispersion depends qualitatively on ring curvature (Rubo, 2022).

Nonlinear confined states inherit this spin-orbit structure. In radially periodic potentials,

$\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$1

with $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$2, spin-orbit coupling locks the topological charges of stationary vortex components through $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$3. The system supports single-ring and multiring vortices, dynamically stable multiring patterns, and rotating multipeaked solitons. A defining result is that the properties of rotating solitons depend on the sign of the rotation frequency as well as its magnitude, so clockwise and counterclockwise rotations are inequivalent even without an external Zeeman field (Zezyulin et al., 2019).

In one-dimensional polariton rings with both TE-TM and Zeeman splittings, the interplay of the rotating TE-TM field and the external field produces a geometric phase. Localized rotating defects—chiral solitons—then propagate differently in the clockwise and anticlockwise directions: their shape, energy, and stability differ for $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$4 and $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$5. In the adiabatic limit, the geometric phase behaves as a density-dependent synthetic gauge field, and the resulting chirality is interpreted as a solitonic analogue of the Aharonov–Bohm effect (Zezyulin et al., 2017).

The same TE-TM physics governs topological defects in the mean-field superfluid description. Two-component condensates support half-quantum vortices specified by phase and polarization windings $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$6, and TE-TM splitting warps the polarization and current patterns around these defects. In the geometric classification of polarization C-points, equilibrium half-vortices realize lemon and star morphologies; monstar configurations are excluded for energetic reasons in the analysis summarized by Rubo (Rubo, 2012). A different route to structured spin-orbit states appears in circularly confined first-excited manifolds, where polariton states with polarization and orbital angular momentum are organized on a spin-orbit Poincaré hypersphere. TE-TM splitting lifts the fourfold degeneracy into radial and azimuthal spin vortices plus two hyperbolic spin antivortices, and ultrafast Stark pulses with selected polarization provide state control on several distinct spin-orbit spheres (Li et al., 2016).

4. Spin transport, currents, and topological edge states

Spin-polariton states are also transport states. In microcavities with embedded (110)-oriented quantum wells, the spin dynamics is governed by the interplay of spin-orbit splitting odd in momentum and longitudinal-transverse splitting even in momentum. A linearly polarized optical pump generates pure spin currents because the two spin projections acquire opposite group velocities; tuning the excitation spot size changes the momentum distribution and switches the real-space spin texture between asymmetric spin-orbit-dominated patterns and symmetric LT-dominated patterns (Shahnazaryan et al., 2015).

In planar microcavities, an in-plane magnetic field applied in the Voigt geometry provides external control of propagating spin-polariton transport. The pseudospin precesses in an effective field whose components combine the LT splitting, a nonlinear self-induced Larmor term, and quadratic magnetic-field contributions originating from magneto-induced mixing of bright and dark exciton states. This mechanism changes the spin-beat frequency, suppresses the optical spin Hall effect at a critical field, and rotates the polarization pattern in real space (Caputo et al., 2018).

Lattice geometries introduce topological transport channels. In honeycomb arrays of exciton-polariton micropillars, TE-TM splitting together with an alternating Zeeman splitting shifts the Dirac points in energy rather than opening a global gap. Zigzag strips then support two pairs of antichiral edge states that propagate in the same direction on opposite edges, with the two edges carrying opposite circular polarizations. Because the system is gapless, the relevant topological invariant is a momentum-dependent winding number rather than a Chern number, and the edge modes can pass a $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$7 bend without reflection (Bao et al., 2022).

A related honeycomb-strip design adds onsite detuning between the two sublattices to Zeeman and spin-orbit couplings. The edge states then split in energy, and within a selected interval one fully spin-polarized edge state coexists only with gapless bulk states of opposite spin. The absence of a backward-propagating edge state with the same spin yields one-way reflection-free and feedback-suppressed transport, while the stronger localization of the edge mode compared with standard topological polariton systems makes the channel narrower (2002.01168).

Current-based diagnostics extend these ideas from continuous strips to coupled condensate graphs. In plaquettes and regular polygonal rings, spin-conserving tunnelling $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$8 and TE-TM-induced spin-flip tunnelling $\mathcal{H}'=\Omega(|\psi_{-1}|^2-|\psi_{+1}|^2)$9 generate circulating particle currents, hidden spin counterflows, and bond-dependent spin-current patterns. For minimal geometries such as the triangle and square, analytical expressions identify phases with uniform particle currents, bond-staggered spin currents, or torque-dominated links. For larger rings, per-component winding numbers $(\pm1)$0 and the common-phase coherence metric

$(\pm1)$1

organize the phase structure into hidden-vortex, semi-vortex, and topologically trivial domains (Kudlis et al., 2 Jul 2026).

5. Magnetic, semimagnetic, and non-Hermitian control

Magnetic control becomes especially direct in semimagnetic microcavities. By introducing Mn ions into the quantum wells while leaving the cavity photons unaffected, the exchange interaction produces giant Zeeman splitting of the excitonic component. In a CdTe-based semimagnetic microcavity containing four $(\pm1)$2-nm Cd$(\pm1)$3Zn$(\pm1)$4Mn$(\pm1)$5Te quantum wells, strong coupling yields lower and upper polariton branches with a vacuum-field Rabi splitting of $(\pm1)$6. Under non-resonant excitation at $(\pm1)$7, the lower polariton Zeeman splitting reaches $(\pm1)$8 at $(\pm1)$9, the condensation threshold at zero field is $(\pm2)$0, and the condensate emission becomes circularly polarized above $(\pm2)$1 in a moderate field of about $(\pm2)$2. Unlike nonmagnetic systems, increasing the excitation power increases the condensate spin polarization, providing a platform for testing predicted phenomena of spin-polarized condensates (Król et al., 2018).

This magnetic tunability connects directly to the broader theory of Zeeman-driven phase transitions in multicomponent superfluids. In the mean-field review literature, the Zeeman field changes the condensate polarization continuously up to a critical field $(\pm2)$3, above which one circular component is depleted and the condensate becomes fully circularly polarized. In four-component exciton condensates, differing $(\pm2)$4-factors for bright and dark excitons can produce more complex field-induced transitions between states with different numbers of occupied components (Rubo, 2012).

A newer control axis is non-Hermiticity. In exciton-polariton honeycomb lattices with sublattice-dependent gain and loss, non-Hermiticity couples to pre-existing topological edge physics and relocalizes edge states into hybrid skin-topological modes. Two regimes are identified: hybrid skin Chern states, whose localization is switchable by TE-TM splitting, and hybrid skin antichiral states, which preserve the spin-polarized property of the parent antichiral edge modes. In the antichiral case, spin-up and spin-down channels localize at opposite corners while retaining near-perfect circular polarization, thereby combining spin polarization, non-reciprocity, and skin accumulation in the same state class (Bao et al., 1 Dec 2025).

6. Spin-photon polaritons and extended cavity platforms

In a distinct but explicit usage, spin-polariton states are hybridized eigenstates of electronic spin excitations and cavity photons. For an effective spin-$(\pm2)$5 system coupled to a low-frequency optical cavity and an external static magnetic field, an effective spin-polariton Hamiltonian is derived from the Pauli–Fierz Hamiltonian beyond the dipole approximation by first-order quasi-degenerate perturbation theory. The effective Hamiltonian contains the conventional Zeeman term, a cavity Zeeman term coupling the spin to the cavity magnetic field, and the cavity photon Hamiltonian. When the cavity magnetic field is orthogonal to the static field, states such as $(\pm2)$6 and $(\pm2)$7 hybridize, producing avoided crossings, a spin-polariton Rabi splitting, modified Zeeman gaps, and a cavity-renormalized electronic $(\pm2)$8-factor observable in EPR spectroscopy (Fischer et al., 25 Aug 2025).

A circuit-QED implementation realizes related physics with molecular spin ensembles. In a superconducting chip containing pairs of capacitively coupled lumped-element resonators, droplets of PTMr and Tripak$(\pm2)$9 radicals placed on the inductors provide $$i\hbar\frac{\partial \psi_\sigma}{\partial t} = \left( -\frac{\hbar^2}{2m}\nabla^2 +u_a|\psi_\sigma|^2 +u_b|\psi_{-\sigma}|^2 +g_R n_\sigma +\frac{i\hbar}{2}[Rn_\sigma-\gamma_c] \right)\psi_\sigma +J\psi_{-\sigma},$$0 spin ensembles with $$i\hbar\frac{\partial \psi_\sigma}{\partial t} = \left( -\frac{\hbar^2}{2m}\nabla^2 +u_a|\psi_\sigma|^2 +u_b|\psi_{-\sigma}|^2 +g_R n_\sigma +\frac{i\hbar}{2}[Rn_\sigma-\gamma_c] \right)\psi_\sigma +J\psi_{-\sigma},$$1. Microwave transmission spectroscopy at $$i\hbar\frac{\partial \psi_\sigma}{\partial t} = \left( -\frac{\hbar^2}{2m}\nabla^2 +u_a|\psi_\sigma|^2 +u_b|\psi_{-\sigma}|^2 +g_R n_\sigma +\frac{i\hbar}{2}[Rn_\sigma-\gamma_c] \right)\psi_\sigma +J\psi_{-\sigma},$$2 shows that a spin ensemble coupled to one resonator can also couple remotely to the empty resonator through the circuit normal modes. When both resonators host spin ensembles and the upper polariton branches are tuned into resonance by magnetic field, an avoided level crossing directly reveals coherent polariton–polariton coupling. Pump–probe measurements further show that excitation of one polariton can be read out through the other, evidencing remote photon–photon and spin–spin correlations in a modular hybrid platform (Río et al., 20 Feb 2026).

Taken together, these developments show that spin-polariton states are not a single narrow object but a family of spinful hybrid modes spanning driven-dissipative condensates, confined spin-orbit textures, topological edge channels, semimagnetic condensates, non-Hermitian skin states, and cavity-mediated spin–photon hybrids. A plausible implication is that the unifying theoretical problem is no longer merely polarization dynamics, but the controlled co-design of spin, geometry, nonlinearity, and hybridization within a common quasiparticle language.