Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach
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We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD's) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine how the CQD system state depends on the actual current through the PC device, we use the so-called quantum trajectory method to derive the zero-temperature conditional master equation. We first treat the electron tunneling through the PC barrier as a classical stochastic point process (a quantum-jump model). Then we show explicitly that our results can be extended to the quantum-diffusive limit when the average electron tunneling rate is very large compared to the extra change of the tunneling rate due to the presence of the electron in the dot closer to the PC. We find that in both quantum-jump and quantum-diffusive cases, the conditional dynamics of the CQD system can be described by the stochastic Schr椩nger equations for its conditioned state vector if and only if the information carried away from the CQD system by the PC reservoirs can be recovered by the perfect detection of the measurements.
Physical Review B: Condensed Matter and Materials Physics
© 2001 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.