Optical mode conversion via spatiotemporally modulated atomic susceptibility.

Light is an excellent medium for both classical and quantum information transmission due to its speed, manipulability, and abundant degrees of freedom into which to encode information. Recently, space-division multiplexing has gained attention as a means to substantially increase the rate of information transfer by utilizing sets of infinite-dimensional propagation eigenmodes such as the Laguerre-Gaussian "donut" modes. Encoding in these high-dimensional spaces necessitates devices capable of manipulating photonic degrees of freedom with high efficiency. In this work, we demonstrate controlling the optical susceptibility of an atomic sample can be used as powerful tool for manipulating the degrees of freedom of light that pass through the sample. Utilizing this tool, we demonstrate photonic mode conversion between two Laguerre-Gaussian modes of a twisted optical cavity with high efficiency. We spatiotemporally modulate the optical susceptibility of an atomic sample that sits at the cavity waist using an auxiliary Stark-shifting beam, in effect creating a mode-coupling optic that converts modes of orbital angular momentum l = 3 → l = 0. The internal conversion efficiency saturates near unity as a function of the atom number and modulation beam intensity, finding application in topological few-body state preparation, quantum communication, and potential development as a flexible tabletop device.

Observation of Laughlin states made of light.

Much of the richness in nature emerges because simple constituents form an endless variety of ordered states1. Whereas many such states are fully characterized by symmetries2, interacting quantum systems can exhibit topological order and are instead characterized by intricate patterns of entanglement3,4. A paradigmatic example of topological order is the Laughlin state5, which minimizes the interaction energy of charged particles in a magnetic field and underlies the fractional quantum Hall effect6. Efforts have been made to enhance our understanding of topological order by forming Laughlin states in synthetic systems of ultracold atoms7,8 or photons9-11. Nonetheless, electron gases remain the only systems in which such topological states have been definitively observed6,12-14. Here we create Laughlin-ordered photon pairs using a gas of strongly interacting, lowest-Landau-level polaritons as a photon collider. Initially uncorrelated photons enter a cavity and hybridize with atomic Rydberg excitations to form polaritons15-17, quasiparticles that here behave like electrons in the lowest Landau level owing to a synthetic magnetic field created by Floquet engineering18 a twisted cavity11,19 and by Rydberg-mediated interactions between them16,17,20,21. Polariton pairs collide and self-organize to avoid each other while conserving angular momentum. Our finite-lifetime polaritons only weakly prefer such organization. Therefore, we harness the unique tunability of Floquet polaritons to distil high-fidelity Laughlin states of photons outside the cavity. Particle-resolved measurements show that these photons avoid each other and exhibit angular momentum correlations, the hallmarks of Laughlin physics. This work provides broad prospects for the study of topological quantum light22.

Interacting Floquet polaritons.

Ordinarily, photons do not interact with one another. However, atoms can be used to mediate photonic interactions1,2, raising the prospect of forming synthetic materials3 and quantum information systems4-7 from photons. One promising approach combines highly excited Rydberg atoms8-12 with the enhanced light-matter coupling of an optical cavity to convert photons into strongly interacting polaritons13-15. However, quantum materials made of optical photons have not yet been realized, because the experimental challenge of coupling a suitable atomic sample with a degenerate cavity has constrained cavity polaritons to a single spatial mode that is resonant with an atomic transition. Here we use Floquet engineering16,17-the periodic modulation of a quantum system-to enable strongly interacting polaritons to access multiple spatial modes of an optical cavity. First, we show that periodically modulating an excited state of rubidium splits its spectral weight to generate new lines-beyond those that are ordinarily characteristic of the atom-separated by multiples of the modulation frequency. Second, we use this capability to simultaneously generate spectral lines that are resonant with two chosen spatial modes of a non-degenerate optical cavity, enabling what we name 'Floquet polaritons' to exist in both modes. Because both spectral lines correspond to the same Floquet-engineered atomic state, adding a single-frequency field is sufficient to couple both modes to a Rydberg excitation. We demonstrate that the resulting polaritons interact strongly in both cavity modes simultaneously. The production of Floquet polaritons provides a promising new route to the realization of ordered states of strongly correlated photons, including crystals and topological fluids, as well as quantum information technologies such as multimode photon-by-photon switching.