Non-equilibrium theory of charge qubit decoherence in the quantum point contact measurement

A non-equilibrium theory describing the charge qubit dynamics measured by a quantum point contact is developed based on Schwinger-Keldysh's approach. Using the real-time diagram technique, we derive the master equation to all orders in perturbation expansions. The non-Markovian processes in the qubit dynamics is naturally taken into account. The qubit decoherence, in particular, the influence of the tunneling-electron fluctuation in the quantum point contact with a longer time correlation, is studied in the framework. We consider the Lorentzian-type spectral density to characterize the channel mixture of the electron tunneling processes induced by the measurement and determine the correlation time scale of the tunneling-electron fluctuation. The result shows that as the quantum point contact is casted with a narrower profile of the spectral density, tunneling electrons can propagate with a longer time correlation and lead to the non-Markovian processes of the qubit dynamics. The qubit electron in the charge qubit will be driven coherently. The quantum point contact measurement with the minimum deviation of the electron tunneling processes prevents the qubit state from the decoherence.