Abstract
There has been rapid development of systems that yield strong interactions between freely propagating photons in one-dimension via controlled coupling to quantum emitters. This raises interesting possibilities such as quantum information processing with photons or quantum many-body states of light, but treating such systems generally remains a difficult task theoretically. Here, we describe a novel technique in which the dynamics and correlations of a few photons can be exactly calculated, based upon knowledge of the initial photonic state and the solution of the reduced effective dynamics of the quantum emitters alone. We show that this generalized ‘input–output’ formalism allows for a straightforward numerical implementation regardless of system details, such as emitter positions, external driving, and level structure. As a specific example, we apply our technique to show how atomic systems with infinite-range interactions and under conditions of electromagnetically induced transparency enable the selective transmission of correlated multi-photon states.
Highlights
Systems in which individual photons can interact strongly with each other constitute an exciting frontier for the fields of quantum and nonlinear optics [1]
At the many-body level, it has been predicted that these systems can produce phenomena such as quantum phase transitions of light [3,4,5] or photon crystallization [6, 7]. Examples of such systems where strong interactions between photons could be observed consisted of individual atoms coupled to single modes of highfinesse optical cavities, within the context of cavity quantum electrodynamics (QEDs) [8, 9]
This paper is organized in the following way: first, we present a generalized input–output formalism to treat few-photon propagation in waveguides coupled to many atoms
Summary
Systems in which individual photons can interact strongly with each other constitute an exciting frontier for the fields of quantum and nonlinear optics [1]. At the many-body level, it has been predicted that these systems can produce phenomena such as quantum phase transitions of light [3,4,5] or photon crystallization [6, 7] Examples of such systems where strong interactions between photons could be observed consisted of individual atoms coupled to single modes of highfinesse optical cavities, within the context of cavity quantum electrodynamics (QEDs) [8, 9]. We show that the infinite degrees of freedom associated with the photonic modes can be effectively integrated out, yielding an open, interacting ‘spin’ model that involves only the internal degrees of freedom of the atoms This open system can be solved using a number of conventional, quantum optical techniques. To illustrate the ease of usage, we apply our technique to the study of nonlinear field propagation through an optically dense ensemble of atoms with Rydberg-like interactions
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