Model of multiphoton transitions in a current-biased Josephson junction

TL;DR

This paper develops a simple theoretical model for multiphoton transitions in current-biased Josephson junctions, explaining experimental observations and predicting how transition rates depend on bias current and ac voltage parameters.

Contribution

The paper introduces a straightforward model for multiphoton transitions in Josephson junctions, including calculations of transition matrix elements and absorption spectra, aligning with recent experimental results.

Findings

Transition rates decrease with higher photon number n.

Absorption coefficient exhibits an even-odd effect with bias current.

Model qualitatively matches experimental observations.

Abstract

We present a simple model for multiphoton transitions between the quasi-bound states of a current-driven Josephson junction. The transitions are induced by applying an ac voltage with controllable frequency and amplitude across the junction. The voltage induces transitions when the ac frequency equals n times the splitting between the ground and first excited quasi-bound state of the junction. We calculate the transition matrix elements as functions of the dc bias current I, and the frequency and amplitude of the ac voltage, for representative junction parameters. We also calculate the frequency-dependent absorption coefficient by solving the relevant Bloch equations when the ac amplitude is sufficiently small. In this regime, the absorption coefficient is a sum of Lorentzian lines centered at the n-photon absorption frequency, of strength proportional to the squared matrix elements. For fixed ac voltage amplitude, the n-photon transition rate usually decreases with increasing n. We also find a characteristic even-odd effect: The absorption coefficient typically increases with I for n even but decreases for n odd. Our results agree qualitatively with recent experiments.