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arXiv:2512.17889

Simulation of topological superconductors and their competing orders using photon-mediated interactions

Anjun Chu, Joyce Kwan, Eric Yilun Song, Seth Hew Peng Chew, James K. Thompson, Ana Maria Rey

quant-phcond-mat.quant-gasphysics.atom-phSubmitted Dec 19, 2025• Announced Dec 22, 2025• 0 citations
v1 · Dec 19, 2025v2 · Oct 15, 2026
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Abstract

Realizing and controlling the unconventional pairing featured by topological superconductors remains a central challenge. We introduce a cavity QED quantum simulator that engineers competing chiral $p_x+ip_y$ and $d_{x^2-y^2}+id_{xy}$ orders by tailoring cavity-mediated couplings between atomic pseudospins that emulate momentum-dependent pairing channels. The desired spatially inhomogeneous cavity-mediated couplings can be engineered in a 2D optical lattice using incommensurate cavity-lattice wavelengths naturally occurring in cavity QED systems. This minimal and fully tunable platform enables controlled state preparation and continuous measurement of superconducting order parameters, revealing phases in both equilibrium and sudden-quench settings with a single dominant pairing channel, as well as coexistence regimes with competing pairing channels. Crucially, our implementation allows direct observation of topological transitions in and out of equilibrium, providing a powerful route to the quantum simulation of competing topological superconducting phases that remain elusive in solid-state and ultracold-atom systems.

Comments
11+12 pages, 5+5 figures

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Realizing and controlling the unconventional pairing featured by topological superconductors remains a central challenge. We introduce a cavity QED quantum simulator that engineers competing chiral px+ipyp_x+ip_ypx​+ipy​ and dx2−y2+idxyd_{x^2-y^2}+id_{xy}dx2−y2​+idxy​ orders by tailoring cavity-mediated couplings between atomic pseudospins that emulate momentum-dependent pairing channels. The desired spatially inhomogeneous cavity-mediated couplings can be engineered in a 2D optical lattice using incommensurate cavity-lattice wavelengths naturally occurring in cavity QED systems. This minimal and fully tunable platform enables controlled state preparation and continuous measurement of superconducting order parameters, revealing phases in both equilibrium and sudden-quench settings with a single dominant pairing channel, as well as coexistence regimes with competing pairing channels. Crucially, our implementation allows direct observation of topological transitions in and out of equilibrium, providing a powerful route to the quantum simulation of competing topological superconducting phases that remain elusive in solid-state and ultracold-atom systems.
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Understanding how pairing correlations in superconductors evolve out of equilibrium is a central challenge in quantum many-body physics. In systems with sss-wave pairing, the character of Cooper pairing evolves continuously from a BCS regime of weakly bound, overlapping pairs to a BEC regime of tightly bound molecules, each with distinct excitation spectra. Here we realize and probe pairing dynamics across these regimes using cold, non-degenerate 87^{87}87Rb atoms coupled to an optical cavity with Floquet dressing. Our cavity-QED platform emulates fermionic superfluids through a mapping onto Anderson pseudospins, while optical and microwave control tunes the ratio of interactions to single-particle energies, providing a flexible approach complementary to ultracold Feshbach and ultrafast solid-state platforms. Following a quench, we observe persistent pairing and transient oscillations of the order parameter associated with a collective amplitude (Higgs) mode. We find that the decay of these oscillations sharply distinguishes weak- and strong-pairing regimes: in the weak-pairing regime, oscillations decay with a power-law exponent ∣α∣=0.65(8)|α|=0.65(8)∣α∣=0.65(8), whereas in the strong-pairing regime the decay is substantially faster, with ∣α∣>1|α|>1∣α∣>1. The oscillation frequency is set by the minimum quasiparticle excitation energy, directly linking nonequilibrium dynamics to the underlying excitation spectrum. Our results establish nonequilibrium dynamics as a direct probe of pairing character and collective excitations in interacting quantum systems.
Engineering the photonic environment using lattices of coupled resonators, which we refer to as lattice quantum electrodynamics (QED), provides a route to control both the spontaneous emission of individual quantum emitters and the photon-mediated interactions between them. Here we introduce an optical lattice QED platform based on individual dibenzoterrylene (DBT) molecules embedded in anthracene crystals and coupled to lattices of open optical microcavities. This hybrid architecture benefits from narrow-linewidth molecular emitters, site-resolved optical access, engineered coupled-resonator bands, and compatibility with established molecular frequency-tuning techniques. As a proof-of-principle demonstration, we observe emitter-photon bound states formed when the optical transition of a single molecule is tuned to the band gap of a Su-Schrieffer-Heeger (SSH) cavity lattice. These in-gap states display directional localization and photon emission on a single sublattice, inherited from the vacancy-induced topological edge modes of the underlying SSH lattice. Our results establish open-cavity lattices coupled to DBT molecules as a versatile architecture for engineering many-emitter quantum optical systems with controllable photon-mediated interactions.
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