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We describe a stochastic evolution of a quantum system interacting with a light prepared in a continuous-mode two-photon state. The problem of a conditional evolution of the quantum system, depending on the results of the measurement of the output field, is formulated and solved making use of the model of repeated interactions. We define the discrete in-time interaction between the quantum system and its environment being the electromagnetic field approximated by a chain of harmonic oscillators. We determine analytical formulae for quantum trajectories associated with one-dimensional and two-dimensional counting processes, corresponding respectively to unidirectional or bidirectional input field prepared in the two-photon state. Moreover, we determine the formulae for the exclusive probability densities of photon counts that allow us to completely characterize the photon statistics of the output field. Finally, we show how to apply the quantum trajectories to obtain the formula for the probability of the two-photon absorption for a three-level atom in a ladder configuration. The paper also includes a discussion on the optimal two-photon state that maximizes the two-photon absorption probability. |
