Photon emission without quantum jumps

When modelling photon emission, we often assume that the emitter experiences a random quantum jump. When a quantum jump occurs, the emitter transitions suddenly into a lower energy level, while spontaneously generating a single photon. However, this point of view is misleading when modelling quantum optical systems which rely on far-field interference effects for applications like distributed quantum computing and non-invasive photonic quantum sensing. In this paper, we highlight that the dynamics of an emitter in the free radiation field can be described by simply solving a Schrödinger equation based on a locally-acting Hamiltonian without invoking the notion of quantum jumps. Our approach is nevertheless consistent with quantum optical master equations.