Transmon-phonon coupling of plasma oscillations and lattice vibrations

TL;DR

This paper investigates the coupling between plasma oscillations and lattice vibrations in transmon qubits, deriving spectral densities and estimating phonon-induced dephasing, which appears negligible for current experimental setups.

Contribution

It provides a theoretical analysis of transmon-phonon coupling, deriving spectral density functions and estimating dephasing rates, a novel insight into decoherence mechanisms.

Findings

Spectral density is ohmic and scales with I_c^2 and log(kR).

Phonon-induced dephasing rate is negligible compared to current experiments.

Coupling effects are derived from conservation laws and modeled with Fermi's Golden Rule.

Abstract

In the transmon qubit we expect from conservation of momentum and energy a coupling between the plasma oscillations and the vibrations of the underlying lattice. Specifically, the electron velocities and their kinetic energy density are boosted by the underlying lattice vibrations. We consider this effect in a representative transmon comprising two semi-circular superconducting charge islands joined by a Josephson junction. In particular, we solve the Fourier transform of a two-dimensional radial current density having inversion symmetry. The resulting spectral density is ohmic but also scales quadratically with the critical current I_c and logarithmically with the size of the transmon: J(w) ~ I_c^2 w log(kR). We make positive-definite Born-Markov approximations in a generalized Fermi's Golden Rule and estimate the phonon-induced dephasing rate is negligible compared to current experiments.