Single Molecule Photon Statistics from a Sequence of Laser Pulses

TL;DR

This paper derives photon emission statistics for a sequence of laser pulses in quantum optics using the optical Bloch equation and quantum trajectories, providing new insights into coherence contributions and classification of photon emission probabilities.

Contribution

It introduces a path-based method to calculate photon statistics from laser pulse sequences, emphasizing coherence effects and simplifying the analysis of photon emission probabilities.

Findings

Derived general expressions for photon emission probabilities Pn(t).

Analyzed the case of two square laser pulses and their photon emission probabilities.

Discussed bounds and limiting cases for photon emission probabilities.

Abstract

There are many ways of calculating photon statistics in quantum optics in general and single molecule spectroscopy in particular such as the generating function method, the quantum jump approach or time ordering methods. In this paper starting with the optical Bloch equation, within the paths interpretation of Zoller, Marte and Walls we obtain the photon statistics from a sequence of laser pulses expressed by means of quantum trajectories. We find general expressions for Pn(t) - the probability of emitting n photons up to time t, discuss several consequences and show that the interpretation of the quantum trajectories (i) emphasizes contribution to the photon statistics of the coherence paths accumulated in the delay interval between the pulses and (ii) allows simple classification of the terms negligible under certain physical constraints . Applying this method to the concrete example of two square laser pulses we find the probabilities of emitting 0,1 and 2 photons, examine several limiting cases and investigate the upper and lower bounds of P0(t), P1(t) and P2(t) for a sequence of two strong pulses in the limit of long measurement times. Implication to single molecule non-linear spectroscopy and theory of pairs of photons on demand are discussed briefly.