2018/12/14 by T. H. A. van der Reep, van der Reep, T. H. A.
Physics and Astronomy · Computer Science · #Quantum optics and atomic interactions #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.1812.05907
We present a theory describing parametric amplification in a Josephson junction embedded transmission line. We will focus on the process of four-wave mixing under the assumption of an undepleted pump. However, the approach taken is quite general, such that a different parametric process or the process under different assumptions is easily derived. First the classical theory of the coupled-mode equations as presented by O'Brien et al. [Phys. Rev. Lett. 113:157001] is shortly reviewed. Then a derivation of the full quantum theory is given using mesoscopic quantisation techniques in terms of discrete mode operators. This results in a Hamiltonian that describes the process of parametric amplification. We show that the coupled-mode equations can be derived from this Hamiltonian in the classical limit and elaborate on the validity of the theory.