Light emission by free electrons in photonic time-crystals.

Photonic time-crystals (PTCs) are spatially homogeneous media whose electromagnetic susceptibility varies periodically in time, causing temporal reflections and refractions for any wave propagating within the medium. The time-reflected and time-refracted waves interfere, giving rise to Floquet modes with momentum bands separated by momentum gaps (rather than energy bands and energy gaps, as in photonic crystals). Here, we present a study on the emission of radiation by free electrons in PTCs. We show that a free electron moving in a PTC spontaneously emits radiation, and when associated with momentum-gap modes, the electron emission process is exponentially amplified by the modulation of the refractive index. Moreover, under strong electron-photon coupling, the quantum formulation reveals that the spontaneous emission into the PTC bandgap experiences destructive quantum interference with the emission of the electron into the PTC band modes, leading to suppression of the interdependent emission. Free-electron physics in PTCs offers a platform for studying a plethora of exciting phenomena, such as radiating dipoles moving at relativistic speeds and highly efficient quantum interactions with free electrons.

Higher-Order Topological Phase of Interacting Photon Pairs.

Topological phases open a door to such intriguing phenomena as unidirectional propagation and disorder-resilient localization at a stable frequency. Recently discovered higher-order topological phases further extend the concept of topological protection enabling versatile control over localization in multiple dimensions. Motivated by the recent advances in quantum technologies such as large coherently operating qubit ensembles, we predict and investigate the higher-order topological phase of photon pairs emerging due to effective photon-photon interaction and described by the extended version of Bose-Hubbard model. Being feasible for state-of-the-art experimental capabilities, the designed model provides an interesting example of interaction-induced topological transitions in the few-particle two-dimensional system.

Exceptional points for photon pairs bound by nonlinear dissipation in cavity arrays.

We theoretically study the dissipative Bose-Hubbard model describing the array of tunneling-coupled cavities with non-conservative photon-photon interaction. The bound two-photon states are formed in this system either in the limited range of the center-of-mass wave vectors or in the full Brillouin zone, depending on the strength of the dissipative interaction. Transition between these two regimes is manifested as an exceptional point in the complex energy spectrum. This improves fundamental understanding of the interplay of non-Hermiticity and interactions in the quantum structures and can potentially be used for on-demand nonlinear light generation in photonic lattices.

Amplified emission and lasing in photonic time crystals.

Photonic time crystals (PTCs), materials with a dielectric permittivity that is modulated periodically in time, offer new concepts in light manipulation. We study theoretically the emission of light from a radiation source placed inside a PTC and find that radiation corresponding to the momentum bandgap is exponentially amplified, whether initiated by a macroscopic source, an atom, or vacuum fluctuations, drawing the amplification energy from the modulation. The radiation linewidth becomes narrower with time, eventually becoming monochromatic in the middle of the bandgap, which enables us to propose the concept of nonresonant tunable PTC laser. Finally, we find that the spontaneous decay rate of an atom embedded in a PTC vanishes at the band edge because of the low density of photonic states.