Abstract
The effective description of the weak interaction between an emitter and a bosonic field as a sequence of two-body collisions provides a simple intuitive picture compared to traditional quantum optics methods as well as an effective calculation tool of the joint emitter-field dynamics. Here, this collisional approach is extended to many emitters (atoms or resonators), each generally interacting with the field at many coupling points ("giant" emitter). In the regime of negligible delays, the unitary describing each collision in particular features a contribution of a chiral origin resulting in an effective Hamiltonian. The picture is applied to derive a Lindblad master equation (ME) of a set of giant atoms coupled to a (generally chiral) waveguide field in an arbitrary white-noise Gaussian state, which condenses into a single equation and extends a variety of quantum optics and waveguide-QED MEs. The effective Hamiltonian and jump operators corresponding to a selected photodetection scheme are also worked out.
Highlights
A major focus of quantum optics is the interaction of quantum emitters, such as atoms or resonators, with a field modeled as a continuum of bosonic modes
Thereby, for τN − τ1 t (1/γ, 1/γ ), the joint dynamics can be represented by an effective collision model, where at each collision the emitters jointly collide with a right-going and a left-going time bin, at once being subject to an internal coherent dynamics governed by the secondorder Hamiltonian (25)
The collisional picture maps the field into a stream of discrete time-bin modes interacting with the emitters in a conveyor-belt-like fashion
Summary
A major focus of quantum optics is the interaction of quantum emitters, such as (artificial) atoms or resonators, with a field modeled as a continuum of bosonic modes. While the regimes of both negligible and long time delays are discussed, our main focus is the former In this case it will be proven that each collision can be effectively represented as a collective coupling of all the emitters with one field time bin plus an internal coherent dipole-dipole interaction between the emitters described by a Hamiltonian originating from the intrinsic system’s chirality (in the conveyor-belt picture of Fig. 1 time bins travel from left to right). While the presented collisional framework has many potential uses, here we apply it to derive the Lindblad master equation of a set of giant emitters coupled to a, generally chiral, one-dimensional waveguide when the field starts in an arbitrary Gaussian state. The diagram encodes the coupling points topology. (d) Implementation of the setup in (a) via a looped unidirectional waveguide
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