Projected dipole moments of individual two-level defects extracted using circuit quantum electrodynamics

TL;DR

This paper measures the dipole moments of individual two-level defects in superconducting devices using circuit QED, revealing a distribution of dipole sizes and enabling characterization of defect properties without volume-based electric field measurements.

Contribution

It introduces a method to extract individual TLS dipole moments using a tunable electric field in a cQED system, providing detailed defect characterization.

Findings

Distribution of dipole moments with two characteristic magnitudes

Values of dipole moments: approximately 2.8 and 8.3 Debye

Ability to measure vacuum-Rabi splitting using dipole moments

Abstract

Material-based two-level systems (TLSs), appearing as defects in low-temperature devices including superconducting qubits and photon detectors, are difficult to characterize. In this study we apply a uniform dc-electric field across a film to tune the energies of TLSs within. The film is embedded in a superconducting resonator such that it forms a circuit quantum electrodynamical (cQED) system. The energy of individual TLSs is observed as a function of the known tuning field. By studying TLSs for which we can determine the tunneling energy, the actual $p_z$, dipole moments projected along the uniform field direction, are individually obtained. A distribution is created with 60 $p_z$. We describe the distribution using a model with two dipole moment magnitudes, and a fit yields the corresponding values $p=p_1= 2.8\pm 0.2$ Debye and $p=p_2=8.3\pm0.4$ Debye. For a strong-coupled TLS the vacuum-Rabi splitting can be obtained with $p_z$ and tunneling energy. This allows a measurement of the circuit's zero-point electric field fluctuations, in a method that does not need the electric-field volume.