Higher-order nonlinear effects in a Josephson parametric amplifier

Bogdan A. Kochetov; Arkady Fedorov

doi:10.1103/PhysRevB.92.224304

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Higher-order nonlinear effects in a Josephson parametric amplifier

Bogdan A. Kochetov, Arkady Fedorov

DOI 10.1103/PhysRevB.92.224304 · Physical Review B

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Abstract

Nonlinearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA) as well as for a Josephson traveling-wave parametric amplifier, the only devices in which the quantum limit for added noise has so far been approached at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) nonlinearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type nonlinearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction nonlinearity in the linear response regime. We then analyze gain saturation effect for stronger signals within a semiclassical approach. Our results reveal nonlinear effects of higher orders and their implications for operation of a JPA.