Abstract
Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena. In the usual scenario, optical nonlinearities originate from the interactions between polaritons, which are hybrid quasi-particles mixing matter and light degrees of freedom. Here we introduce a type of polariton which is intrinsically nonlinear and emerges as the natural quasi-particle in presence quantum degenerate fermionic matter. It is a composite object made of a fermion trapped inside an optical soliton forming a topological defect in a spontaneously formed crystalline structure. Each of these soliton-polaritons carries a Z2 topological quantum number, as they create a domain wall between two crystalline regions with opposite dimerization so that the fermion is trapped in an interphase state. These composite objects are formally equivalent to those appearing in the Su-Schrieffer-Heeger (SSH) model for electrons coupled to lattice phonons.
Highlights
Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena
In this one-dimensional (1D) configuration, the fermionic cloud is unstable toward density modulations with wavenumber equal to twice the Fermi momentum kF—analogous to the Peierls instability known since the 1950s in the context of solids6—so that photon-mediated Umklapp scattering of atoms between the Fermi points induces crystallization
Spatially ordered fermionic patterns coupled to multimode fields are sensitive to commensurability effects, and the resulting structures can accommodate hybrid light–matter defects as low-lying excitations. The latter consist of a fermion trapped in an interphase state located at a solitonic deformation of the electromagnetic potential
Summary
Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena. We show that a different situation can arise, where a new type of long-lived hybrid quasi-particle emerges This type of polariton is not a linear superposition of non-interacting atomic and photonic degrees of freedom, but rather a result of the optical nonlinearity of the system in the presence of an atomic Fermi surface. It is a composite object made of a fermion trapped inside an optical soliton forming a topological defect in an emergent crystalline structure
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