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The kinetic inductance detector (KID) is an exciting new device that promises high-sensitivity, large-format, submillimetre to x-ray imaging arrays for astrophysics. KIDs comprise a superconducting thin-film microwave resonator capacitively coupled to a probe transmission line. By exciting the electrical resonance with a microwave probe signal, the transmission phase of the resonator can be monitored, allowing the deposition of energy or power to be detected. We describe the fabrication and low-temperature testing, down to 26 mK, of a number of devices, and confirm the basic principles of operation. The KIDs were fabricated on r-plane sapphire using superconducting niobium and aluminium as the resonator material, and tantalum as the x-ray absorber. KID quality factors of up to Q = (741 ± 15) × 10 3 were measured for niobium at 1 K, and quasiparticle effective recombination times of τ * R = 30 µs after x-ray absorption. Al/Ta quasiparticle traps were combined with resonators to make complete detectors. These devices were operated at 26 mK with quality factors of up Q = (187.7 ± 3.5) × 10 3 and a phase-shift responsivity of ∂θ/∂N qp = (5.06 ± 0.23) × 10 −6 degrees per quasiparticle. Devices were characterized both at thermal equilibrium and as x-ray detectors. A range of different x-ray pulse types was observed. Low phase-noise readout measurements on Al/Ta KIDs gave a minimum NEP = 1.27 × 10 −16 W Hz −1/2 at a readout frequency of 550 Hz and NEP = 4.60 × 10 −17 W Hz −1/2 at 95 Hz, for effective recombination times τ * R = 100 µs and τ * R = 350 µs respectively. This work demonstrates that high-sensitivity detectors are possible, encouraging further development and research into KIDs.

We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s): The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polynomial matrix. The entire procedure can be implemented using only orthogonal transformations of constant matrices and results to a minimal basis with orthonormal coe¢ cients.

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