Output spectrum of a measuring device at arbitrary voltage and temperature

TL;DR

This paper calculates the noise spectrum of a quantum point contact used for qubit measurement across arbitrary voltages and temperatures, revealing asymmetries and peak behaviors dependent on voltage and temperature conditions.

Contribution

It generalizes previous high-voltage results to arbitrary voltages and temperatures, providing new insights into the spectral features of quantum measurement devices.

Findings

At $V \,\sim\, B$, the spectrum becomes asymmetric in frequency.

The coherent peaks at $\,\pm B$ can be up to 8 times higher than background.

For $V < B$ and T=0, coherent peaks are absent.

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 $\omega=\pm B$ 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.