Multi-level Spectroscopy of Two-Level Systems Coupled to a dc SQUID Phase Qubit

TL;DR

This study performs multi-level spectroscopy on two-level systems coupled to a dc SQUID phase qubit, revealing detailed energy levels, splittings, and coherence times, and providing insights into TLS behavior in superconducting qubits.

Contribution

It provides the first detailed multi-level spectroscopic analysis of TLSs coupled to a dc SQUID phase qubit, including measurements of energy levels, splittings, and coherence times.

Findings

Identified eight avoided level crossings with splittings from 10 MHz to 200 MHz.

Measured spectroscopic lifetimes ranging from 4 ns to 160 ns.

Distribution of splittings suggests non-interacting charged ions tunneling in the junction barrier.

Abstract

We report spectroscopic measurements of discrete two-level systems (TLSs) coupled to a dc SQUID phase qubit with a 16 \mu\m2 area Al/AlOx/Al junction. Applying microwaves in the 10 GHz to 11 GHz range, we found eight avoided level crossings with splitting sizes from 10 MHz to 200 MHz and spectroscopic lifetimes from 4 ns to 160 ns. Assuming the transitions are from the ground state of the composite system to an excited state of the qubit or an excited state of one of the TLS states, we fit the location and spectral width to get the energy levels, splitting sizes and spectroscopic coherence times of the phase qubit and TLSs. The distribution of splittings is consistent with non-interacting individual charged ions tunneling between random locations in the tunnel barrier and the distribution of lifetimes is consistent with the AlOx in the junction barrier having a frequency-independent loss tangent. To check that the charge of each TLS couples independently to the voltage across the junction, we also measured the spectrum in the 20-22 GHz range and found tilted avoided level crossings due to the second excited state of the junction and states in which both the junction and a TLS were excited.