Superconducting waveguides are a promising platform for ultralow-loss transmission in the millimeter-wave to terahertz band under cryogenic conditions, with potential applications in astronomical instrumentation and emerging quantum technologies. We develop a framework, based on microscopic superconductivity theory, to evaluate the power-flow attenuation constant $α$ of superconducting rectangular waveguides in the $100~\mathrm{GHz}$--THz range, applicable to arbitrary electronic mean free paths $\ell$ from the dirty limit $\ell\llξ_0$ to the clean limit $\ell\ggξ_0$. We also derive an analytical expression for two-level-system (TLS)-induced attenuation $α_{\rm TLS}$ in thin native oxide layers within the standard TLS model. Using this framework, we perform numerical evaluations of $α$ for representative materials over standard waveguide sizes from WR15 to WR1. In the high-frequency regime $f \gtrsim 0.5 Δ/h$, low attenuation favors the clean regime $\ell\gtrsimξ_0$, indicating that high-purity materials can achieve very low attenuation below their gap frequency. For the TLS contribution, using parameter values representative of native Nb oxides, we find that $α_{\rm TLS}$ can become relevant at sufficiently low temperatures $T/T_c\lesssim 0.1$-0.2, where quasiparticle dissipation is exponentially suppressed. Finally, we extend the discussion to the strong-excitation regime using a recently developed nonlinear-response theory within the Keldysh--Usadel framework of nonequilibrium superconductivity and show that nonlinear dissipation produces a Higgs-mode peak in $α$ near $f\simeq Δ/h$ via a Kerr-type nonlinearity of the dissipative conductivity. This peak provides a distinct hallmark of the Higgs mode that has been largely overlooked so far.
The millimeter-submillimeter region bridges the microwave and infrared regimes and remains a challenging yet important part of the spectrum [1][2][3][4][5][6][7][8][9][10][11]. Superconducting waveguides in this band are attracting growing attention across multiple frontiers of science and technology.
In quantum technologies, recent efforts to push superconducting quantum hardware toward higher operating frequencies [2,3] seek to relax refrigeration requirements by reducing thermal occupation, which can enable operation at elevated temperatures. In this context, lowloss interconnects extending from the microwave into the millimeter-wave regime, and potentially toward the subterahertz range, are expected to become increasingly important. As system scaling increases routing distances, distributed attenuation becomes a key figure of merit.
In astronomical instrumentation operating in the 100 GHz to THz range [1,4,5], key observational windows include the cosmic microwave background (CMB) [6], molecular rotational lines and dust continuum emission [7,8]. Millimeter-and submillimeterwave bands are also being explored for technosignature searches in the search for extraterrestrial intelligence (SETI) [9][10][11]. In such cryogenic front ends, the delivered signal power can be extremely small, which places stringent constraints on transmission loss along waveguide runs. * kubotaka@post.kek.jp Normal-conducting waveguides have long been central to millimeter-and submillimeter-wave systems [4,5], offering relatively low attenuation [12] owing to their hollow metallic geometry. As the frequency is pushed toward the terahertz regime, however, conductor loss increases and low-loss propagation becomes a key bottleneck. One promising route to mitigating such attenuation is the use of superconducting waveguides (Fig. 1). Kurpiers et al. [13] measured attenuation in commercially available microwave-frequency waveguides at cryogenic temperatures. More recently, Nakajima et al. [14] fabricated a rectangular waveguide from bulk niobium and demonstrated an attenuation of 5 × 10 -4 dB/cm at a frequency of f ≃ 100 GHz and at a temperature of T ≃ 4-5 K, which is substantially smaller than that of comparable normal-metal waveguides. These results highlight the potential of superconducting waveguides for ultralow-loss transmission at millimeter-wave frequencies and, potentially, toward the terahertz regime.
For weakly lossy waveguides, provided the operating point is sufficiently above cutoff and sufficiently below the superconducting transition temperature T c , the attenuation can be obtained to first order by treating the wall surface impedance as a perturbation to the fields of the corresponding lossless waveguide solution [15,16]. In this regime, attenuation dominated by thermally excited quasiparticles is directly related to the superconducting surface resistance R s . The central theoretical task therefore reduces to calculating R s . Despite this conceptual simplicity, a systematic theoretical treatment of attenuation (α) in superconducting waveguides has received relatively limited attention. Only a small number of studies (see, e.g., Ref. [16] and references therein) have ad-dressed attenuation from the perspective of microscopic superconductivity theory. Moreover, existing treatments rely on the dirty-limit Mattis-Bardeen formalism for the linear-response complex conductivity, although practical materials are not necessarily in that limit.
This gap in the literature is not limited to the treatment of superconducting conductor loss. At sufficiently low temperatures, quasiparticle-induced dissipation becomes exponentially small, and dielectric loss associated with tunneling two-level systems (TLS) [17][18][19] in the thin native oxide layer covering the superconducting surface can begin to dominate. To our knowledge, the corresponding TLS-induced attenuation in superconducting waveguides has not yet been evaluated in a systematic manner. Such an assessment is likely to become increasingly important if superconducting waveguides are deployed at very low temperatures, for example in the millikelvin regime.
In this paper, we evaluate the attenuation constant α of superconducting waveguides, with a deliberate focus on rectangular geometry. The motivation is that, in astronomical instrumentation, waveguides are increasingly required to provide not only low-loss transmission but also circuit functionality such as filtering, channelization, and multiplexing [4,5]. In the millimeter-and submillimeter-wave bands, such functional waveguide circuits are routinely realized as compact CNC-milled metal blocks based on rectangular-waveguide technology, which offers mature design methodologies and straightforward mechanical integration. In quantum hardware, similar requirements are not yet as widely established, but they are likely to emerge as operating frequencies move into the millimeter-wave regime and system scaling increases ro
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