Photon number resolving detectors play a central role in quantum optics. A key challenge in resolving the number of absorbed photons in the microwave frequency range is finding a suitable material that provides not only an appropriate band structure for absorbing low-energy photons but also a means of detecting a discrete photoelectron excitation. To this end, we propose to measure the temperature gain after absorbing a photon using superconducting cadmium arsenide (${\mathrm{Cd}}_3{\mathrm{As}}_2$) with a topological semimetallic surface state as the detector. The surface electrons absorb the incoming photons and then transfer the excess energy via heat to the superconducting bulk's phonon modes. The temperature gain can be determined by measuring the change in the zero-bias bulk resistivity, which does not significantly affect the lattice dynamics. Moreover, the obtained temperature gain scales discretely with the number of absorbed photons, enabling a photon-number resolving function. Here, we will calculate the temperature increase as a function of the number and frequency of photons absorbed. We will also derive the timescale for the heat transfer process from the surface electrons to the bulk phonons. We will specifically show that the transfer processes are fast enough to ignore heat dissipation loss.

中文翻译：

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利用超导砷化镉的拓扑表面态的微波光子数解析探测器

光子数解析探测器在量子光学中起着核心作用。解决在微波频率范围内吸收的光子数的关键挑战是找到一种合适的材料，该材料不仅提供用于吸收低能光子的合适的能带结构，而且提供一种检测离散光电子激发的方法。为此，我们建议使用超导砷化镉（${\mathrm{光盘}}_3{\mathrm{作为}}_{\mathrm{2个}}$）以拓扑半金属表面状态作为检测器。表面电子吸收入射的光子，然后通过热量将多余的能量转移到超导主体的声子模式。可以通过测量零偏体电阻率的变化来确定温度增益，该变化不会显着影响晶格动力学。此外，所获得的温度增益随吸收的光子数而离散地缩放，从而实现光子数解析功能。在这里，我们将根据吸收的光子的数量和频率来计算温度的升高。我们还将得出从表面电子到体声子的传热过程的时间尺度。我们将具体表明，传输过程足够快，可以忽略散热损失。