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Journal of the Physical Society of Japan

Second-Order Correlation Function of Two-Photon Fluorescence of a Two-Level Atom in a Squeezed Vacuum

Xun‐Li Feng, Jingtao Zhang, Zhizhan Xu

Published Sep 1, 2000• 0 citations
Publisher

Abstract

The photon statistics of the two-photon fluorescence of a two-level atom in a squeezed vacuum is investigated by using the second-order correlation function g (2) ( t ). Based on its analytical solution, g (2) ( t ) is found to be an oscillatory function of time when the average photon number of the squeezed vacuum light field is above a threshold. The origin of the oscillatory behavior of g (2) ( t ), which generally results from the external driving field for resonance fluorescence, is the driving effect of the squeezed vacuum light field on the atom. It is also found that the oscillatory behavior of g (2) ( t ) can provide a measurement of the ac Stark effect.

DOI
10.1143/jpsj.69.2873

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Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak-field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. Heisenberg equations of motion are solved in the steady-state and analytic expressions for the fluorescent-light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed, and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation, the second-order intensity correlation function does not factorize. This and other differences are discussed, and curves are presented to illustrate the behavior of various quantities. We also present results for thermal excitation of the atom.
By using the two photon Bloch equation and quantum regression theorem, the second order correlation function of two photon fluorescence of a two level atom in a broad band squeezed vacuum is obtained. From this, the bunching and the antibunching effects of two photon fluorescence are investigated. We find that the second order correlation function is dependent on the squeezing parameter (|M|) of the squeezed vacuum. There is a critical value (Γ/4g) for |M|,above which the second order correlation function oscillates around 1. This indicates that the two photon fluorescence can exhibit both antibunching and bunching effects. Below the critical value, the second order correlation function does not oscillate and the two photon fluorescence exhibits the antibunching effect only.
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We study the statistical properties of fluorescence from a coherently driven two-level atom placed in a broadband squeezed vacuum. The photon statistics are studied in terms of waiting time distribution or the delay function that describes the probability of emission of the very next photon following an emission of a photon initially. In an intense field limit, we analytically obtain the delay function for total emission and examine its phase-dependent behavior in a squeezed vacuum. We further analytically calculate the delay functions for the Mollow sidebands and use them to discuss the time correlation and successive emission of photons belonging to the left and right sidebands.