Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach - art. no. 125326

We obtain the finite-temperature unconditional master equation of the densi ty 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 throu gh the PC device, we use the so-called quantum trajectory method to derive the zero-temperature conditional master equation. We first treat the electr on tunneling through the PC barrier as a classical stochastic point process (a quantum-jump model). Then we show explicitly that our results can be ex tended to the quantum-diffusive limit when the average electron tunneling r ate 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 Schrodinger equations for its conditioned state vector if and only if the information carried away f rom the CQD system by the PC reservoirs can be recovered by the perfect det ection of the measurements.