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We describe an electrothermal model for the turn-on dynamics of superconducting nanowire singlephoton detectors (SNSPDs). By extracting a scaling law from a well-known electrothermal model of SNSPDs, we show that the rise-time of the readout signal encodes the photon number as well as the length of the nanowire with scaling trise ∝ /n. We show that these results hold regardless of the exact form of the thermal effects. This explains how SNSPDs have inherent photon-number resolving capability. We experimentally verify the photon number dependence by collecting waveforms for different photon number, rescaling them according to our predicted relation, and performing statistical analysis that shows that there is no statistical significance between the rescaled curves. Additionally, we use our predicted dependence of rise time on detector length to provide further insight to previous theoretical work by other authors. By assuming a specific thermal model, we predict that rise time will scale with bias current, trise ∝ 1/I b . We fit this model to experimental data and find that trise ∝ 1/(n 0.52±0.03 I 0.63±0.02 b ), which suggests further work is needed to better understand the bias current dependence. This work gives new insights into the non-equilibrium dynamics of thin superconducting films exposed to electromagnetic radiation.

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A crucial step toward enabling real-world applications for quantum sensing devices such as Rydberg atom electric field sensors is reducing their size, weight, power, and cost (SWaP-C) requirements without significantly reducing performance. Laser frequency stabilization is a key part of many quantum sensing devices and, when used for exciting non-ground state atomic transitions, is currently limited to techniques that require either large SWaP-C optical cavities and electronics or use significant optical power solely for frequency stabilization. Here, we describe a laser frequency stabilization technique for exciting non-ground state atomic transitions that solves these challenges and requires only a small amount of additional electronics. We describe the operation, capabilities, and limitations of this frequency stabilization technique and quantitatively characterize its performance. We show experimentally that Rydberg electric field sensors using this technique are capable of data collection while sacrificing only 0.1% of available bandwidth for frequency stabilization of noise up to 900 Hz.

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