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Journal of Physics A Mathematical and General

On the characterization of quantum jumps in a coherently-driven Raman system

Q. V. Lawande, Amitabh Joshi, S. V. Lawande

Published Oct 21, 1995• 0 citations
Publisher

Abstract

We examine the characteristics of quantum jumps in a Raman ( Lambda ) system driven by two coherent fields in terms of the joint probability for successive arrivals of photons. In particular, we derive the general expression for P(1, T 1 ; 0, T 2 ; 1, T 3 ), the probability that a photon is counted in the interval (t,t+T 1 ) and (t+T 1 +T 2 , t+T 1 +T 2 +T 3 ) with no photon in the intermediate interval (t+T 1 , t+T 1 +T 2 ) and discuss its behaviour.

DOI
10.1088/0305-4470/28/20/019

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We examine the characteristics of quantum jumps in a Raman ( Lambda ) system driven by two coherent fields in terms of the joint probability for successive arrivals of photons. In particular, we derive the general expression for P(1, T 1 ; 0, T 2 ; 1, T 3 ), the probability that a photon is counted in the interval (t,t+T 1 ) and (t+T 1 +T 2 , t+T 1 +T 2 +T 3 ) with no photon in the intermediate interval (t+T 1 , t+T 1 +T 2 ) and discuss its behaviour.
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We present a microscopic model for the so-called quantum jumps in three-level atoms with one transition between two levels being strongly driven and the third level being metastable. Our model is based on calculating the elementary probability density P(0,t)(t1, … , t n ) which gives the probability density that exactly n photons are emitted at times t1, … , t n by the atom in the time interval (0, t) on the strong transition. This enables us to calculate the conditional probabilities c ˜ ( τ ) that given a photon has emitted at τ = 0 the next photon emission occurs at time τ. This quantity is shown to be the sum of two exponentials which for sufficient differetial in the time scales describe the periods of light and darkness. Using this conditional probability it is possible to numerically simulate the individual photon emissions.
We consider a three-level atomic system driven strongly on one transition and weakly on the other. The excited state on the weak transition is assumed to be metastable. We give an analysis of the fluorescence from the strong transition in terms of the elementary probability density p[0{p}_{[0}p[0​,t)(t1{\mathrm{t}}_{1}t1​,t2{t}_{2}t2​,..., tn{t}_{n}tn​) which gives us the probability density that exactly n photons are emitted at times t1{t}_{1}t1​,t2{t}_{2}t2​,...,tn{t}_{n}tn​ by the atom in the time interval [0,t). We show that p[0{p}_{[0}p[0​,t) essentially factorizes into products of conditional densities c\ifmmode \tilde{}\else \~{}\fi{}(\ensuremath{\tau}) that, given a photon is emitted at time zero, the next photon emission occurs at time \ensuremath{\tau}. This enables a simulation of the individual photon emissions to be given which shows directly the existence of prolonged dark windows in the fluorescence corresponding to the shelving of the electron in the metastable state or ``quantum jumps.''