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Physical Review A

Coincidence counts and stimulated emission resulting from weak pulsed-field–atom interactions

P. R. Berman, A. Kuzmich

Published Mar 16, 2020• 1 citation
Publisher

Abstract

The interaction of a single-photon pulse of radiation with an atom or an ensemble of atoms is studied using a source-field approach. The atom-field interaction is weak insofar as it can be treated in lowest, nonvanishing order of perturbation theory. The output field intensity and second-order correlation function of the field are calculated. It is shown that, even when any modification of the atomic dynamics produced by the incident field is neglected, as a function of the time delay $\ensuremath{\tau}$ between the incident field pulse and the field radiated by the atom(s), there is a ``bump'' in the time-integrated second-order correlation at $\ensuremath{\tau}=0$. The increase in coincidence counts for $\ensuremath{\tau}=0$ can be interpreted in terms of Hanbury Brown and Twiss--type interference. By looking at the field intensity, we show that the bump has no direct relation with stimulated emission---it occurs even when the input field is attenuated. In recent down conversion experiments, an increase in coincidence counts has been attributed to stimulated emission---we comment on the validity of such an interpretation in light of our results.

DOI
10.1103/physreva.101.033824

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The interaction of a single-photon pulse of radiation with an atom or an ensemble of atoms is studied using a source-field approach. The atom-field interaction is weak insofar as it can be treated in lowest, nonvanishing order of perturbation theory. The output field intensity and second-order correlation function of the field are calculated. It is shown that, even when any modification of the atomic dynamics produced by the incident field is neglected, as a function of the time delay \ensuremathτ\ensuremath{\tau}\ensuremathτ between the incident field pulse and the field radiated by the atom(s), there is a ``bump'' in the time-integrated second-order correlation at \ensuremathτ=0\ensuremath{\tau}=0\ensuremathτ=0. The increase in coincidence counts for \ensuremathτ=0\ensuremath{\tau}=0\ensuremathτ=0 can be interpreted in terms of Hanbury Brown and Twiss--type interference. By looking at the field intensity, we show that the bump has no direct relation with stimulated emission---it occurs even when the input field is attenuated. In recent down conversion experiments, an increase in coincidence counts has been attributed to stimulated emission---we comment on the validity of such an interpretation in light of our results.
Hanbury Brown-Twiss interference and stimulated emission, two fundamental processes in atomic physics, have been studied in a wide range of applications in science and technology. We study interference effects that occur when a weak probe is sent through a gas of two-level atoms that are prepared in a singly excited collective (Dicke or "superatom") state and for atoms prepared in a factorized state. We measure the time-integrated second-order correlation function g^{(2)} of the output field as a function of the delay τ between the input probe field and radiation emitted by the atoms and find that, for the Dicke state, g^{(2)} is twice as large for τ=0 as it is for γ_{e}τ≫1 (γ_{e} is an excited state decay rate), while for the product state, this ratio is equal to 3/2. The results agree with those of a theoretical model in which any effects related to stimulated emission are totally neglected-the coincidence counts measured in our experiment arise from Hanbury Brown-Twiss interference between the input field and the field radiated by the atoms.
Recently, the question of the origin of correlations in thermal light has again been debated. The alternative viewpoints suggest that (i) stimulated emission causes the correlations implied by Bose-Einstein statistics and exemplified by the Hanbury Brown-Twiss effect, or (ii) stimulated emission coherently amplifies any initial field, with no change in the nature of photon statistics, apart from the addition of, and interference with, spontaneous-emission noise. It is shown that two essentially different physical models have been considered previously, with many results being only approximate. For these models we obtain the evolution of the photon statistics by deriving exactly the generating function for the diagonal elements of the field density matrix and the quantum characteristic function. The source of Bose-Einstein correlations is seen to be merely the interference in the superposition of random independent fields from a chaotic source, spontaneous emission being one example. Extending the investigation to a nonlinear model, we show that, although there is no longer coherent amplification, it is still not correct to infer that this interaction, which produces the amplification, also leads to Bose-Einstein statistics.
When a coherent field is combined with the phase-matched output of an atomic ensemble, the second-order correlation function of the total field can exhibit superbunching or antibunching. Homodyning the reference field with the atomic emission can amplify the nonclassical characteristics of the atomic emission. A theoretical description of these phenomena is presented. It is pointed out that, even if the number of excitations in the ensemble is much less than unity, truncating a factorized state to have at most two excitations can lead to errors in calculating the second-order correlation function. We also include the effects of dephasing produced by Rydberg-Rydberg interactions and show how they modify the bunching and antibunching that occur in the absence of atom-atom interactions. It is shown that the particle separation probability distribution and the joint particle separation probability distribution play critical roles in determining the effects of dephasing.
We present a time-dependent quantum calculations of the first order and second order photon correlation functions for the scattering of a single-photon pulse on a two-level atom (qubit) embedded in a one-dimensional open waveguide. Within Markov approximation we find the analytic expression for the quantum operator of positive frequency electric field. We restricted Hilbert space of initial states by the states with one and two excitations and show that the photon probability amplitudes are given by the off-diagonal matrix elements of the electric field operator between these states. For two-excitation initial state where the atom is excited and there exists a single photon in a waveguide we calculate the second order correlation function which describes the measurements by two detectors at two different space-time points. The second order correlation function exhibits the interference term showing that the measurements of two detectors are correlated. This interference is similar to that found in the Hanbury Brown and Twiss correlation experiment with two indistinguishable photons.