Poly- and single-crystalline diamond nitrogen-induced TLS losses estimation with superconducting lumped elements micro-resonators

TL;DR

The work addresses measuring ultra-low dielectric losses in diamond substrates for quantum sensing and high-power applications. It employs high-Q superconducting lumped-element resonators analyzed within the TLS framework, using the relation $1/Q_L = 1/Q_i + 1/Q_C$ to separate intrinsic losses and extract the TLS loss tangent. By comparing poly-crystalline and several single-crystal diamond samples with complementary Raman spectroscopy, the study links nitrogen-related defects to increased TLS losses and shows boundary defects can dominate total losses, especially at joint regions. The results demonstrate TLS losses on the order of $10^{-6}$ for high-quality single-crystal diamonds, with implications for diamond-based quantum devices and high-power microwave windows.

Abstract

Research on diamond has intensified due to its exceptional thermal, optical, and mechanical properties, making it a key material in quantum technologies and high-power applications. Diamonds with engineered nitrogen-vacancy (NV) centers represent a very sensitive platform for quantum sensing, while high-optical quality diamond windows represent a fundamental safety component inside Electron Cyclotron Resonance Heating (ECRH) systems in nuclear fusion reactors. A major challenge is the development of ultra-low-loss, high-optical-quality single-crystal diamond substrates to meet growing demands for quantum coherence and power handling. Traditionally, dielectric losses ($\tan δ$) in diamonds are evaluated using Fabry-Perot microwave resonators, in which the resonance quality factors Q of the cavity with and without the sample are compared. These devices are limited to resolutions around 10$^{-5}$ by the need to keep the resonator dimensions within a reasonable range. In contrast, superconducting thin-film micro-strip resonators, with Q factors exceeding 10$^6$, are stated to provide higher sensitivity for assessing ultra-low-loss materials. This study examines four diamond samples grown through different processes, analyzing their dielectric losses at extreme low temperatures (sub-Kelvin) within the Two-Level System (TLS) framework. Complementary Raman spectroscopy measurements allowed us not only to associate higher nitrogen content with increased losses, but also to investigate how the different growth process influence the way these defects are incorporated in the crystal lattice.

Figures (4)

• Figure 1: a) example of $f_r$ vs T measurement performed in the ultra-low temperature range on one of the samples. Warmer colors indicate higher acquisistion temperatures b) the fractional resonance frequency shift associated with the measurement set shown in Fig. 1a. The dotted red line identifies the fitting curve that is used to extract the value of the losses c) resonator internal quality factor vs number of photons injected, for on-chip powers ranging from -45 to -115 dBm (10 dBm steps) and a calculated single photon energy around -150 dBm. Visible is the onset of $Q_i$ saturation above 3.5E9 ($\approx$ -55 dBm) photons present in the resonator
• Figure 2: a) optical microscope image of one of the lumped elements resonators used in this work. Visible are the meandering inductor, the IDC and a section of the feed-line b) schematic representation of the acquisition setups used in the dilution refrigerator c) An example of the circle-fits correction routines employed in this work
• Figure 3: a) values of $\tan \delta^0_{TLS}$ for the four samples, extrapolated from the fractional resonance frequency shift and b) lowest measured values of the total loss tangent $\tan \delta$
• Figure 4: Raman measurements of the diamond samples performed with a) green (532 nm) and b) red (633 nm) excitations. BND refers to measurements performed focusing the laser light directly on the boundary between two tiles of the J-Clone.