High-sensitivity microwave vector detection at extremely low-power levels for low-dimensional electron systems

We present a high-sensitivity microwave vector detection system for studying the low-dimensional electron system embedded in the gaps of a coplanar waveguide at low temperatures. Using this system, we have achieved 0.005% and 0.001\textdegree resolutions in amplitude and phase variations, respectively, at 10 GHz in a magnetotransport measurement on a quantum-wire array with an average signal power less than $-$75 dBm into the sample at 0.3 K. From the measured phase variation, we can distinguish a very tiny change in the induced dipole moment of each quantum wire.