Saturation of Two Level Systems and Charge Noise in Josephson Junction Qubits

TL;DR

This paper investigates how two-level systems in Josephson qubits contribute to charge noise, revealing that saturation effects do not significantly alter the noise spectrum at different frequencies.

Contribution

The study provides a detailed analysis of TLS saturation effects on charge noise, using density matrix solutions to show saturation does not impact noise levels.

Findings

Charge noise exhibits 1/f behavior at low frequencies.

Charge noise remains constant at high frequencies.

TLS saturation does not affect charge noise spectrum.

Abstract

We study the charge noise $S_Q$ in Josephson qubits produced by fluctuating two level systems (TLS) with electric dipole moments in the substrate. The TLS are driven by an alternating electric field of angular frequency $\Omega$ and electric field intensity $I$. It is not widely appreciated that TLS in small qubits can easily be strongly saturated if $I\gg I_c$, where $I_c$ is the critical electric field intensity. To investigate the effect of saturation on the charge noise, we express the noise spectral density in terms of density matrix elements. To determine the dependence of the density matrix elements on the ratio $I/I_c$, we find the steady state solution for the density matrix using the Bloch-Redfield differential equations. We then obtain an expression for the spectral density of charge fluctuations as a function of frequency $f$ and the ratio $I/I_c$. We find $1/f$ charge noise at low frequencies, and that the charge noise is white (constant) at high frequencies. Using a flat density of states, we find that TLS saturation has no effect on the charge noise at either high or low frequencies.