We present a method to systematically study multiphoton transmission in one-dimensional systems comprised of correlated quantum emitters coupled to input and output waveguides. Within the Green's function approach of the scattering matrix $(S$ matrix), we develop a diagrammatic technique to analytically obtain the system's scattering amplitudes while at the same time visualize all the possible absorption and emission processes. Our method helps to reduce the significant effort in finding the general response of a many-body bosonic system, particularly the nonlinear response embedded in the Green's functions. We demonstrate our proposal through physically relevant examples involving scattering of multiphoton states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators in the Bose-Hubbard model.We present a method to systematically study multiphoton transmission in one-dimensional systems comprised of correlated quantum emitters coupled to input and output waveguides. Within the Green's function approach of the scattering matrix $(S$ matrix), we develop a diagrammatic technique to analytically obtain the system's scattering amplitudes while at the same time visualize all the possible absorption and emission processes. Our method helps to reduce the significant effort in finding the general response of a many-body bosonic system, particularly the nonlinear response embedded in the Green's functions. We demonstrate our proposal through physically relevant examples involving scattering of multiphoton states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators in the Bose-Hubbard model.

arXiv:1702.01632Physical Review AMay 18, 201719 citations

Generalized linear input-output theory for quantum fluctuations

Jean-Michel Courty, Serge Reynaud

Scattering of quantum fluctuations by a linear system is entirely characterized by impedance functions that also allow the determination of the system fluctuations. We present a generalization of this linear input-output theory to the case of a nonlinear scattering system. We define response functions that are similar to the susceptibility functions of linear response theory, but behave as noncommuting quantities. These functions contain a ``dynamical'' part determined by the relaxation of the system and a ``structural'' one related to the commutators between the system observables. The generalized linear input-output theory provides us with a complete description of the system fluctuations as well as of the output reservoir fields. The consistency of the results is ensured by general relations existing between the response functions and the correlation functions.Scattering of quantum fluctuations by a linear system is entirely characterized by impedance functions that also allow the determination of the system fluctuations. We present a generalization of this linear input-output theory to the case of a nonlinear scattering system. We define response functions that are similar to the susceptibility functions of linear response theory, but behave as noncommuting quantities. These functions contain a ``dynamical'' part determined by the relaxation of the system and a ``structural'' one related to the commutators between the system observables. The generalized linear input-output theory provides us with a complete description of the system fluctuations as well as of the output reservoir fields. The consistency of the results is ensured by general relations existing between the response functions and the correlation functions.

Physical Review ASep 1, 199225 citations

Correlation Functions

Peter Millington

Springer thesesOct 29, 20130 citations

(S

matrix), we develop a diagrammatic technique to analytically obtain the system's scattering amplitudes while at the same time visualize all the possible absorption and emission processes. Our method helps to reduce the significant effort in finding the general response of a many-body bosonic system, particularly the nonlinear response embedded in the Green's functions. We demonstrate our proposal through physically relevant examples involving scattering of multiphoton states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators in the Bose-Hubbard model.