Calculation of quantum-dot blinking using the Gillespie Monte Carlo algorithm

We calculate the stochastic photoluminescence intensity of a single colloidal quantum dot in order to calculate the blinking behaviour of the optical emission. The combination of the long-lived dark state with a lifetime of the order of seconds together with the radiative recombination lifetimes in the nanosecond regime make the stochastic model of the system incredibly computer intensive. The stochastic behaviour of the single quantum dot using a system of rate equations for the probabilities of occupancy of the confined energy levels is calculated. A standard Monte Carlo algorithm is modified by introducing a time step that is dependent on the transitions possible in the state that the system occupies. The model is verified by comparison with the calculation using the standard algorithm and from the calculated probability densities. The improvement in computational time of this algorithm over the standard Monte Carlo method is also determined.