Single shot spin readout using a cryogenic high-electron-mobility transistor amplifier at sub-Kelvin temperatures

We use a cryogenic high-electron-mobility transistor circuit to amplify the current from a single electron transistor, allowing for demonstration of single shot readout of an electron spin on a single P donor in Si with 100 kHz bandwidth and a signal to noise ratio of ∼9. In order to reduce the impact of cable capacitance, the amplifier is located adjacent to the Si sample, at the mixing chamber stage of a dilution refrigerator. For a current gain of ∼2.7×103, the power dissipation of the amplifier is 13 μW, the bandwidth is ∼1.3 MHz, and for frequencies above 300 kHz the current noise referred to input is ≤70 fA/Hz. With this amplification scheme, we are able to observe coherent oscillations of a P donor electron spin in isotopically enriched 28Si with 96% visibility.