  We consider the continuous measurement of a double quantum dot by a weakly
coupled detector (tunnel point contact nearby). While the conventional approach
describes the gradual system decoherence due to the measurement, we study the
situation when the detector output is explicitly recorded that leads to the
opposite effect: gradual purification of the double-dot density matrix.
Nonlinear Langevin equation is derived for the random evolution of the density
matrix which is reflected and caused by the stochastic detector output. Gradual
collapse, gradual purification, and quantum Zeno effect are naturally described
by the equation. We also discuss the possible experiments to confirm the
theory.
