Collisional picture of quantum optics with giant emitters

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.

Modelling quantum light-matter interactions in waveguide-QED with retardation and a time-delayed feedback: matrix product states versus a space-discretized waveguide model

“…An alternative, but less well developed, approach to modelling waveguide QED is to use a "collision model" where the system repeatedly interacts with discrete slices (or bins) of the environment [41,44,48,49]. This model can be integrated with the physical insight of QT theory [84][85][86] and an intuitive strategy for modelling non-Markovian dynamics emerges.…”

“…The aim of this paper is to present and compare two powerful, but quite different, approaches for solving several classes of non-Markovian feedback and waveguide QED, which can be applied to study both vacuum dynamics and nonlinear (i.e., multi-photon) excitation regimes. Specifically, these methods are based on: (a) matrix product states (MPSs) [15,[38][39][40] and (b) a new space-discretized waveguide (SDW) model, using a collision approach for the waveguide environment [41][42][43][44]. The collision model is solved explicitly by allowing for 1 or 2 photons in the waveguide, which helps to show when several photons need to be included in the model, while the MPS model is not restricted in the number of photons.…”

“…This approach extends the recent approach introduced by Whalen [42], and is substantially easier for a researcher to implement computationally than MPSs. In essence, the SDW model discretizes the waveguide field in the spatial domain over the waveguide length of interest and follows a "collisional" model for the interaction with the quantum optic system of interest [41,44,48,49]. In contrast to MPS theory, the SDW model has a simple and intuitive implementation, without all the added complexities that come with MPSs and tensor networks in general.…”

Mechanism of decoherence-free coupling between giant atoms

“…Next, we come back to (23) and extend it to a bidirectional waveguide using the newly introduced operators as (see Ref. [40] for more details)…”

Microscopic biasing of discrete-time quantum trajectories

“…To achieve the above, we use a quantum collision model (CM): in fact the natural and simplest microscopic framework for describing quantum trajectories and weak measurements [20][21][22][23][24]. In a CM [see Fig.…”