Improved Modeling of Quasi-Static Thermal and Optical Response of Lumped-Element Aluminum Manganese KIDs

TL;DR

The paper addresses the challenge of accurately modeling the quasi-static thermal and optical response of lumped-element AlMn KIDs for broadband submillimeter observations. It replaces analytic Mattis–Bardeen approximations with a fully numerical evaluation of the MB integrals for the complex conductivity and the quasi-particle density $n_{ ext{qp}}$, linking these to the fractional resonance-frequency shift $rac{ ext{d}f_{ ext{res}}}{f_0}$. The authors show that the numerical MB model provides substantially better fits to dark data and removes degeneracies between the kinetic-inductance fraction $oldsymbol{ ext{alpha}}$ and the superconducting gap $ riangle_0$, while a gap-broadening term does not improve fits. Optical-loading data for AlMn yield qualitative agreement but do not tightly constrain the optical efficiency $ ext{eta}_{ ext{opt}}$ due to the devices’ limited response and the cooler operating regime; the work nonetheless validates a robust modeling approach that will inform future use of AlMn KIDs in NEW-MUSIC across multiple bands.

Abstract

We report on the optical characterization of the AlMn kinetic inductance detectors (KIDs) in development for use in the Next-generation Extended Wavelength-MUltiband Sub/millimeter Inductance Camera (NEW-MUSIC) on the Leighton Chajnantor Telescope (LCT). NEW-MUSIC will cover 80-420 GHz, split into six spectral bands, with polarimetry. This broad spectral coverage will enable study of a range of scientific topics such as the accretion and feedback in galaxies and galaxy cluster evolution via the Sunyaev-Zeldovich effect, the transient synchrotron emission from the explosive deaths of massive stars and other time-domain phenomena, and dusty sources from low to high redshift (with polarization). Al KIDs have already been demonstrated for bands 2-5. AlMn KIDs will be used for the 90~GHz band, as Al's pair-breaking energy is too high. However, AlMn has only barely been explored as a KID material. To this end, we first improved the modeling techniques used for Al KIDs within BCS theory by eliminating the use of analytical approximations for the expressions of the complex conductivity and found these changes reduced fit parameter degeneracy in the analysis of AlMn. Then, we tested the addition of a gap smearing parameter, a standard extension to BCS theory in use for high kinetic inductance materials, and found it did not improve the fits.

Figures (3)

• Figure 1: Measured $\delta f_\text{res}/f_0$ data points (black and red dotted curves) taken with no optical loading for a single AlMn KID resonator. The fitted model to the data using a fully numerical implementation of Mattis-Bardeen theory is shown as the dashed black line and the analytical implementation is shown as the dashed red line.
• Figure 2: Recovered values for $\alpha$ and $\Delta_0$ for all AlMn resonators from fits employing analytic approximations of Mattis-Bardeen theory (Eqs. \ref{['eq:sigma1']} and \ref{['eq:sigma2']}) in purple and from fully numerical fits in green. The degeneracy between these two parameters vanishes when the numerical technique is used.
• Figure 3: Typical $\delta f_\text{res}/f_0$ data sets used to fit for optical efficiency. Black, blue, and red data points and lines correspond to dark, cold, and hot data and fits. The plot on the left shows this for an AlMn resonator and on the right is for an Al resonator. The zoomed-in portion of the plots shows the response in the low temperature range where optically generated quasi-particles should dominate over thermally generated quasi-particles. The response level in this regime, in particular, the magnitude of the difference between the hot and cold curves, corresponds to the optical efficiency.