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Bulletin of the American Physical Society

Non-Markovian dynamics of a solid-state charge qubit measured by a quantum point contact

Chung-Chin Jian, Po‐Wen Chen, Hsi‐Sheng Goan

Published Feb 28, 2012• 0 citations
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We investigate the non-Markovian characteristics in continuous measurement of a charge qubit by a quantum point contact. The backflow of information from the reservoir to the system in the non-Markovian domain gives rise to strikingly different qubit relaxation and dephasing in comparison with the Markovian case. The intriguing non-Markovian dynamics is found to have a direct impact on the output noise feature of the detector. Unambiguously, we observe that the non-Markovian memory effect results in an enhancement of the signal-to-noise ratio, which can even exceed the upper limit of “4,” leading thus to the violation of the Korotkov-Averin bound in quantum measurement. Our study thus may open new possibilities to improve detector's measurement efficiency in a direct and transparent way.
A nonequilibrium theory describing the charge qubit dynamics measured by a quantum point contact is developed based on Schwinger-Keldysh's approach. Using the real-time diagrammatic 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 correlation time comparing to the time scale of the qubit dynamics, 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 propagate in a longer correlation time scale and lead to the non-Markovian processes of the qubit dynamics. The qubit electron in the charge qubit can be driven coherently. The quantum point contact measurement with the minimum deviation of the electron-tunneling processes prevents the qubit state from the decoherence.
In this article, we report the recent progress on decoherence dynamics of electrons in quantum dot quantum computing systems using the exact master equation we derived recently based on the Feynman–Vernon influence functional approach. The exact master equation is valid for general nanostructure systems coupled to multi-reservoirs with arbitrary spectral densities, temperatures and biases. We take the double quantum dot charge qubit system as a specific example, and discuss in details the decoherence dynamics of the charge qubit under coherence controls. The decoherence dynamics risen from the entanglement between the system and the environment is mainly non-Markovian. We further discuss the decoherence of the double-dot charge qubit induced by quantum point contact (QPC) measurement where the master equation is re-derived using the Keldysh non-equilibrium Green function technique due to the non-linear coupling between the charge qubit and the QPC. The non-Markovian decoherence dynamics in the measurement processes is extensively discussed as well.