Vacuum-dressed superconductivity in NbN observed in a high-$Q$ terahertz cavity

TL;DR

These results demonstrate that quantum vacuum fluctuations in a high-$Q$ terahertz cavity can modify the superconducting state of NbN films, as reflected in cavity-dressed optical conductivity and a reduced superfluid density. By combining terahertz time-domain spectroscopy with transfer-matrix modeling and a Zimmermann-based description of optical conductivity, the study reveals cavity-induced changes without external driving. First-principles calculations with QED–DFT and Eliashberg theory show a mechanism of electron-density redistribution with only minor changes to the superconducting gap and negligible Tc shift, consistent with the experiments. Overall, the work establishes a platform for cavity materials engineering and ground-state manipulation via vacuum--matter coupling in superconductors at terahertz frequencies.

Abstract

Emerging theoretical frameworks suggest that physical properties of matter can be altered within an optical cavity by harnessing quantum vacuum electromagnetic fluctuations, even in the total absence of external driving fields. Among the most intriguing predictions is the potential to noninvasively manipulate superconductivity. Here, we experimentally observe modified superconductivity in niobium nitride (NbN) thin films within high-quality-factor ($Q$) terahertz cavities. Using terahertz time-domain spectroscopy, we characterize the NbN response both in free space and within a high-$Q$ photonic-crystal cavity. Our analysis reveals significant cavity-induced modifications to the optical conductivity. A theoretical model indicates that these changes originate from a substantial ($\sim13\,\%$) reduction in the superfluid density and a minor ($\sim2\,\%$) reduction in the superconducting gap, driven by cavity vacuum fluctuations. These results demonstrate a platform for engineering ground states via vacuum--matter coupling, opening frontiers in cavity materials science.

Figures (13)

• Figure 1: Probing cavity-modified superconductivity in NbN. (a) Conceptual illustration of the vacuum--matter coupling-induced change in the real part of the optical conductivity, $\sigma_1(\omega)$, of a NbN film inside a high-$Q$ one-dimensional photonic-crystal cavity (1D-PCC). In free space, $\sigma_1$ is zero below the superconducting optical gap $2\Delta$. Within the 1D-PCC, the confined quantum vacuum fluctuations "dress" the superconducting ground state, making $\sigma_1$ finite below the gap. (b) Optical conductivity $\sigma = \sigma_1 + i\sigma_2$ of a 10-nm NbN film measured in free space at $14$ K in the normal state. (c) $\sigma$ of the NbN film in free space at $4$ K in the superconducting state. The real part shows the opening of the superconducting gap, while the imaginary part exhibits the $1/\omega$ inductive response characteristic of a superfluid. Symbols represent experimental data and solid lines represent fits using the Zimmermann model. (d) Transmittance of the bare 1D-PCC at $6\,\mathrm{K}$. Experimental data (black dots) are in excellent agreement with the transfer-matrix method simulation (red line). Gold shaded regions indicate the photonic band gaps containing high-$Q$ defect modes (peaks I, II, III, IV, and V), while gray regions represent the pass bands. The thicknesses of the silicon layers #1, #2, and #3 are $94$, $348$, and $97$$\upmu$m, respectively. The spacing between silicon layers #1 and #2 (#2 and #3) is $77$$\upmu$m ($76$$\upmu$m).
• Figure 2: Temperature dependence of the NbN-cavity transmittance spectra. (a) Comparison between simulated (red solid lines) and experimental (black solid dots) transmittance of the NbN-cavity integration at various temperatures from $4.0$ to $14.0$ K. The transmittance curves are vertically offset for clarity. The vertical dotted lines track the temperature-dependent optical gap, $2\Delta(T)$. The regions of interest -- the photonic band gaps where high-$Q$ defect modes reside -- are highlighted in gold, and the gray regions indicate the pass bands. (b) High-resolution experiment-simulation comparison of the cavity modes at $T=4.0\,\mathrm{K}$. The amplitude discrepancies of peaks I, II, and III (shaded regions) are larger than the combined uncertainties of the experimental measurement and the TMM simulation. The inset shows the temperature dependence of the amplitude for peak II, illustrating the discrepancy between simulation and experiment that emerges exclusively in the superconducting state.
• Figure 3: Modified complex optical conductivity of the NbN film embedded in the 1D-PCC at $4\,\mathrm{K}$. The extraction is based on matching the cavity mode transmittance via the TMM simulations and the experiment. In the TMM simulations, we used the Zimmermann modeling parameters (effective temperature and superconducting gap) to fit the experimental transmittance spectra. (a) Detailed amplitude comparison of experimental data (black circles), TMM simulations using free-space conductivity (red line), and TMM fits using the cavity-dressed conductivity (blue line) for cavity modes I, II, and III. The high $Q$-factors of these modes provide the sensitivity required to resolve the discrepancy between free-space and in-cavity responses. (b) Extracted real ($\sigma_1$, left) and imaginary ($\sigma_2$, right) parts of the modified complex conductivity of the NbN film. The black circles represent the experimentally measured conductivity of NbN in free space, and the blue solid line represents the cavity-dressed conductivity with the fitted parameters ($T_{\text{eff}}$ and $\Delta_{\text{in-cav}}$). The vertical dotted lines indicate the superconducting optical gap $2\Delta$ of NbN in free space at $4\,\mathrm{K}$.
• Figure S4: The electrical resistance of a NbN film in free space, normalized by the resistance at $300$ K. The inset zooms in at the temperature region near $T_\mathrm{c}$.
• Figure S5: The experimental and fitted optical conductivity of NbN film in free space at various temperatures. Same as Fig. 1d of the main text, but at different temperatures. Each curve of $\sigma_1$ ($\sigma_2$) is vertically offset by 2000 S/cm (5000 S/cm) for clarity.