Output spectrum of a measuring device at arbitrary voltage and temperature

Abstract

We calculate the noise spectrum of the electrical current in a quantum point contact which is used for continuous measurements of a two-level system (qubit). We generalize the previous results obtained for the regime of high transport voltages (when $V$ is much larger than the qubit's energy level splitting $B$ (we put $e=\hbar=1$)) to the case of arbitrary voltages and temperatures. When $V \sim B$ the background output spectrum is essentially asymmetric in frequency, i.e., it is no longer classical. Yet, the spectrum of the amplified signal, i.e., the two coherent peaks at $ω=\pm B$ is still symmetric. In the emission (negative frequency) part of the spectrum the coherent peak can be 8 times higher than the background pedestal. Alternatively, this ratio can be seen in the directly measureable {\it excess} noise. For $V < B$ and T=0 the coherent peaks do not appear at all. We relate these results to the properties of linear amplifiers.

7 pages, 5 figures, the results generalized for arbitrary angle between the magnetic field and the observed component of the spin, minor corrections and typos