Continuous Quantum Measurement with Independent Detector Cross Correlations

We investigate the advantages of using two independent, linear detectors for continuous quantum measurement. For single-shot measurement, the detection process may be quantum limited if the detectors are twins. For weak continuous measurement, cross correlations allow a violation of the Korotkov-Averin bound for the detector’s signal-to-noise ratio. The joint weak measurement of noncommuting observables is also investigated, and we find the cross correlation changes sign as a function of frequency, reflecting a crossover from incoherent relaxation to coherent, out of phase oscillations. Our results are applied to a double quantum-dot charge qubit, simultaneously measured by two quantum point contacts.

Figure 1

Cross-correlated quantum measurement setup: Two quantum point contacts are measuring the same double quantum-dot qubit. As the quantum measurement is taking place, the current outputs of both detectors can be averaged or cross correlated with each other.

Figure 2

(a) Time domain destruction of the quantum state by the weak measurement process for $ϵ=\Delta$. The elapsed time is parameterized by color, and $(x,y,z)$ denote coordinates on the Bloch sphere. (b) The measured cross correlator $S_{zx}(\omega )$ changes sign from positive at low frequency (describing incoherent relaxation) to negative at the qubit oscillation frequency (describing out of phase, coherent oscillations). (c),(d) The correlators $S_{xx}$, $S_{zz}$ have both a peak at zero frequency and at qubit oscillation frequency. We take $\Gamma ={\Gamma }_x={\Gamma }_z=0.07\Delta /\hslash$. $S_{ij}$ are plotted in units of ${\Gamma }^{-1}$.