Dynamics of a double quantum dot charge qubit measured by a quantum point contact

Quantum measurement always disturbs the quantum system being measured, which is known as measurement-induced backaction. We consider a specific model, a double quantum dot charge qubit measured by a nearby quantum point contact. We explore the evolution by deriving a master equation. The advantages of this master equation are (i) it has the Lindblad form and the non-Markovian effects are embodied in the time-dependent coefficients, (ii) the tunnelling and decay effect can be clearly understood in the master equation, and (iii) it can be further easily controlled by manipulate the Hamiltonian.