Quantum metrology of low frequency electromagnetic modes with frequency upconverters

We present the RF Quantum Upconverter (RQU) and describe its application to quantum metrology of electromagnetic modes between dc and the Very High Frequency band (VHF) ($\lesssim$300MHz). The RQU uses a Josephson interferometer made up of superconducting loops and Josephson junctions to implement a parametric interaction between a low-frequency electromagnetic mode (between dc and VHF) and a mode in the microwave C Band ($\sim$ 5GHz), analogous to the radiation pressure interaction between electromagnetic and mechanical modes in cavity optomechanics. We analyze RQU performance with quantum amplifier theory, and show that the RQU can operate as a quantum-limited op-amp in this frequency range. It can also use non-classical measurement protocols equivalent to those used in cavity optomechanics, including back-action evading (BAE) measurements, sideband cooling, and two-mode squeezing. These protocols enable experiments using dc--VHF electromagnetic modes as quantum sensors with sensitivity better than the Standard Quantum Limit (SQL). We demonstrate signal upconversion from low frequencies to microwave C band using an RQU and show a phase-sensitive gain (extinction ratio) of $46.9$\;dB, which is a necessary step towards the realization of full BAE.