No abstract

Given a weighted ℓ2 space with weights associated with an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond–Leontiev derivatives. This general class of operators includes many known examples, such as classic fractional derivatives and Dunkl operators. This allows us to establish a general framework, which goes beyond the classic Weyl–Heisenberg algebra. Concrete examples for its application are provided.

Collective interaction of emitter arrays has lately attracted significant attention due to its role in controlling directionality of
radiation, spontaneous emission and coherence. We focus on light interactions with engineered arrays of solid-state emitters in
photonic resonators. We theoretically study light interaction with an array of emitters or optical centers embedded inside a
microring resonator and discuss its application in the context of solid-state photonic systems. We discuss how such arrays can
be experimentally realized and how the inhomogeneous broadening of mesoscopic atomic arrays can be leveraged to study
broadband collective excitations in the array.

Given a weighted ℓ 2 space with weights associated to an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond-Leontiev derivatives. This general class of operators includes many known examples, like classic fractional derivatives and Dunkl operators. This allows us to establish a general framework which goes beyond the classic Weyl-Heisenberg algebra. Concrete examples for its application are provided.