[Paper Review] Spectroscopy of random two-level systems in insulating films

Bahman Sarabi, Aruna Ramanayaka+3 more|arXiv (Cornell University)|Jan 23, 2015

Quantum optics and atomic interactions3 citations

TL;DR

This study introduces degenerate well resonator (DWR) spectroscopy to measure individual two-level systems (TLSs) in insulating films using a calibrated dc electric field and a superconducting microwave resonator at millikelvin temperatures. It precisely determines the electric dipole moment $p_z$ and tunneling strength of 60 TLSs in silicon nitride, revealing distinct dipole types at 3.3 and 8.3 Debye, with vacuum fluctuation fields measured consistently via quantum electrodynamics and volume integration.

ABSTRACT

Using a calibrated uniform dc electric field, we modify the energy potential of randomly occurring two-level systems (TLSs) in an insulating film and probe them using a superconducting microwave resonator at millikelvin temperatures. This allows measurement of the excitation energies of individual TLSs dependent on the $z$-component of their electric dipole moment $p_{z}$. The hyperbolic energy dependence of TLSs reveals the state of double well degeneracy which allows for a precise measurement of $p_{z}$ and the tunneling strength for each individual TLS. This method of degenerate well resonator (DWR) spectroscopy resolves multiple dipole types from a thick insulating film, and in silicon nitride we observe distinct types with maxima at $p_{z}=3.3$ and $8.3$ Debye. Sixty TLSs are measured with this technique, and the loss tangent microscopic observations is consistent with ensemble-averaged data. The TLS-resonator ac coupling is also measured and, with $p_{z}$, provides a quantum electrodynamical measurement of the vacuum fluctuation field. The same fluctuation field calculated from the electric field volume is only 16% smaller.

Motivation & Objective

• To develop a method for probing individual two-level systems (TLSs) in disordered insulating films with high precision.
• To measure the electric dipole moment $p_z$ and tunneling matrix element of individual TLSs by applying a calibrated dc electric field.
• To resolve multiple TLS dipole types in thick insulating films using resonant microwave probing.
• To validate the vacuum fluctuation field via quantum electrodynamical coupling between TLS and resonator, comparing with volume-integrated estimates.

Proposed method

• A superconducting microwave resonator is used to probe individual TLSs in insulating films at millikelvin temperatures.
• A calibrated uniform dc electric field is applied to shift the energy potential of TLSs, enabling control and measurement of their excitation energies.
• The hyperbolic energy dependence of TLSs under the dc field reveals double-well degeneracy, allowing precise extraction of $p_z$ and tunneling matrix element.
• TLS-resonator ac coupling is measured to determine the vacuum fluctuation field via quantum electrodynamics.
• The vacuum fluctuation field from TLS-resonator coupling is compared with that calculated from the electric field volume, validating consistency.

Experimental results

Research questions

• RQ1 What is the distribution of electric dipole moments $p_z$ among individual TLSs in a thick insulating film?
• RQ2 How precisely can the tunneling matrix element and $p_z$ be measured for individual TLSs using a resonant microwave probe?
• RQ3 To what extent does the vacuum fluctuation field measured via TLS-resonator coupling agree with that derived from the electric field volume?
• RQ4 Are multiple distinct TLS dipole types present in silicon nitride, and what are their characteristic $p_z$ values?

Key findings

• Sixty individual two-level systems (TLSs) were measured in a silicon nitride film using DWR spectroscopy, with distinct dipole types observed at $p_z = 3.3$ and $8.3$ Debye.
• The hyperbolic energy dependence of TLSs confirmed double-well degeneracy, enabling precise determination of $p_z$ and tunneling matrix elements for each TLS.
• The vacuum fluctuation field measured via quantum electrodynamical coupling between TLS and resonator was found to be only 16% smaller than the value calculated from the electric field volume.
• The microscopic loss tangent measured from individual TLSs is consistent with ensemble-averaged macroscopic data, validating the method's reliability.