Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach

Details Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach

2000-06-22

arxiv.org/abs/cond-mat/0006333v3

Phys. Rev. B 63, 125326 (2001)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

14 pages, 1 figures, RevTex, onecolumn, to appear in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.63.125326

We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD) 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\"{o}dinger 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.

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