Quasiparticle Generation-Recombination Noise in the Limit of Low Detector Volume

We have measured the quasiparticle generation-recombination (GR) noise in aluminium lumped element kinetic inductors with a wide range of detector volumes at various temperatures. The basic detector consists of meandering inductor and interdigitated capacitor fingers. The inductor volume is varied from 2 to 153 {\mu}m^{3} by changing the inductor width and length to maintain a constant inductance. We started with measuring the power spectrum density (PSD) of the detectors frequency noise which is a function of GR noise and we clearly observed the spectrum roll off at 10 kHz which corresponds to the quasiparticle lifetime. Using data from a temperature sweep of the resonator frequency we convert the frequency fluctuation to quasiparticle fluctuation and observe its strong dependence on detector volume: detectors with smaller volume display less quasiparticle noise amplitude. Meanwhile we observe a saturated quasiparticle density at low temperature from all detectors as the quasiparticle life time {\tau}qp approaches a constant value at low temperature.