FFTS readout for large arrays of Microwave Kinetic Inductance Detectors

Microwave Kinetic Inductance Detectors (MKIDs) have great potential for large very sensitive detector arrays for use in, for example, sub-mm imaging. Being intrinsically readout in the frequency domain, they are particularly suited for frequency domain multiplexing allowing $\sim$1000s of devices to be readout with one pair of coaxial cables. However, this moves the complexity of the detector from the cryogenics to the warm electronics. We present here the concept and experimental demonstration of the use of Fast Fourier Transform Spectrometer (FFTS) readout, showing no deterioration of the noise performance compared to low noise analog mixing while allowing high multiplexing ratios.

💡 Research Summary

The paper presents a novel readout architecture for large arrays of Microwave Kinetic Inductance Detectors (MKIDs) based on a digital Fast Fourier Transform Spectrometer (FFTS). MKIDs are superconducting resonators whose resonance frequency and quality factor shift in response to absorbed photons, allowing each detector to be probed by a single microwave tone. Traditional readout schemes rely on analog mixing, which can handle only one tone at a time and thus do not scale to the thousands of detectors required for modern sub‑mm and far‑infrared astronomy.

The authors propose to generate a set of probe tones in the intermediate frequency (IF) band (0.1–300 MHz) using a 12‑bit arbitrary waveform generator (AWG) with a 1 GS/s DAC. These tones are up‑converted to the radio‑frequency (RF) band (4–4.3 GHz) with a single‑sideband mixer driven by a low‑phase‑noise local oscillator (LO) at 4 GHz (SG1). The RF comb passes through a cryogenic MKID chip (operating at 100 mK), where each tone experiences a phase and amplitude modulation determined by the corresponding resonator’s response. After amplification by a 4 K low‑noise amplifier (Tₙ≈4 K), the signal is down‑converted using the same LO, returning to the original IF frequencies. A final amplification stage brings the signal to the full scale of an 8‑bit, 2 GS/s ADC on the FFTS board.

The FFTS continuously performs an 8192‑point complex FFT on the digitized data, producing a power spectrum with 8192 bins of 122 kHz width. By arranging the probe tones so that each occupies a distinct bin, the system effectively implements 8192 digital down‑converters in parallel, allowing simultaneous monitoring of thousands of detectors. The authors demonstrate the concept with eight MKIDs (Q≈1.5×10⁵) and compare the FFTS readout to a conventional IQ‑mixer readout. Both methods yield identical noise performance, limited by the cryogenic amplifier rather than the readout electronics.

Key experimental results include:

1. Optical response – An LED illumination step produces the expected stepwise change in the transmission |S₂₁|² for each MKID, confirming that the FFTS can track resonance shifts in real time.
2. Noise spectra – When probing 8 kHz off resonance, both FFTS and IQ readouts show excess frequency noise that rolls off at ≈15 kHz, matching the resonator bandwidth (δf = f₀/(2Q)). At 1 MHz off resonance the noise becomes white and reaches the system floor, indicating that the FFTS does not add additional noise.
3. NEP estimation – From the 8 kHz off‑resonance noise and a measured quasiparticle lifetime (~1 ms), a dark Noise Equivalent Power of ~1×10⁻¹⁷ W/√Hz at 20 Hz is inferred.

Scalability analysis shows that the 8192 FFT bins theoretically support up to ~4000 MKIDs with a single coaxial pair. However, as the number of tones (n) grows, the peak voltage at each stage scales as P_peak ≈ P·n·C (C≈25 for random phases), raising concerns about ADC clipping and intermodulation distortion. Consequently, the required Effective Number of Bits (ENOB) for the ADC depends on the total gain budget. For a 1000‑pixel array with Q=5×10⁴ and –85 dBm per tone, about 9 ENOB would be needed to keep ADC noise below the cryogenic amplifier noise; for phase or |S₂₁|² readout, where detector noise dominates, ~7 ENOB suffices.

The current implementation outputs only the power transmission |S₂₁|², but the FFTS internally retains complex data, enabling future extraction of both phase and amplitude (complex S₂₁) without hardware changes. This would improve linearity (phase readout) and sensitivity for low‑background applications.

In conclusion, the FFTS‑based readout provides a practical path to multiplexing hundreds to thousands of MKIDs with minimal degradation of noise performance. It already supports >100 pixels for ground‑based mm/sub‑mm astronomy and can be extended to meet the stringent NEP requirements (<2×10⁻¹⁹ W/√Hz) of future space missions such as SPICA. The work demonstrates that digital FFT spectroscopy, originally developed for heterodyne back‑ends, can be repurposed as a highly scalable, low‑noise MKID readout platform.