Mesoscopic Hamiltonian for Josephson travelling-wave parametric amplifiers

• URL: http://arxiv.org/abs/1812.05907v5
• Date: Tue, 20 May 2025 08:05:43 GMT
• Title: Mesoscopic Hamiltonian for Josephson travelling-wave parametric amplifiers
• Authors: T. H. A. van der Reep,
• Abstract summary: We will focus on the process of four-wave mixing under the assumption of an undepleted pump.<n>The approach taken is quite general, such that a different parametric process or the process under different assumptions is easily derived.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. $\mathbf{113}:157001$] 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.

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