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Physical Review A

Photon correlation in an ion-trap system

Matthias Jakob, Gagik Yu. Kryuchkyan

Published Mar 1, 1999• 14 citations
Publisher

Abstract

The photon correlation phenomenon in the resonance fluorescence of a harmonically trapped two-level ion is investigated including effects which result from the quantized motion. An analytical result is obtained for the second-order correlation function which involves the initial population distribution of the trap states. Collapses and revivals occur in the photon correlation function as a consequence of the discrete dependence of the Rabi frequencies on the vibrational excitation number.

DOI
10.1103/physreva.59.2111

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The photon correlation phenomenon in the resonance fluorescence of a harmonically trapped two-level ion is investigated including effects which result from the quantized motion. An analytical result is obtained for the second-order correlation function which involves the initial population distribution of the trap states. Collapses and revivals occur in the photon correlation function as a consequence of the discrete dependence of the Rabi frequencies on the vibrational excitation number.
For a single trapped ion, second-order time correlations of fluorescence photons are measured in a self-homodyne configuration by beating the fluorescence with itself. At the nanosecond timescale, the correlations are governed by electronic excitation and decay of the ion and anti-bunching in the resonance fluorescence is observed and quantitatively reproduced. On the other hand, at the microsecond timescale the motion of the ion determines the correlations: secular motional modes, their amplitude and relative coherence are measured. Besides precisely monitoring the trap frequencies, our observations also quantify the temporal stability of the trapping potential.
In the present communication we consider a time dependent ion-field interaction. Here we discuss the interaction between a single trapped ion and two fields taking into account the coupling parameter to be time dependent and allowing for amplitude modulation of the laser field radiating the trapped ion. At exact resonances the analytic solution for the Heisenberg equations of motion is obtained. We examine the effect of the velocity and the acceleration on the Rabi oscillations by studying the second order correlation function. The phenomenon of squeezing for single and two fields cases is considered. The cross correlation between the fields is discussed.
The spectrum of resonance fluorescence and the second-order correlation function are calculated for a system of two identical two-level cooperative systems interacting via the dipole-dipole interaction. The results are valid for arbitrary incident-field strengths and for atomic separations much less than the resonant wavelength. The intensity of the sidebands at the Rabi frequency is diminished by the dipole interaction, whereas that of the sidebands at twice the Rabi frequency is enhanced. Both the cooperative behavior and the dipole-dipole interaction act to diminish the photon antibunching, as shown by the second-order correlation function.
In order to study the influence of nonlinear parameters on the cross-correlation function of two vibrational modes of the trapped ions along mutually orthogonal directions,the exact solution of the nonlinear double-photon JaynesCummings model which describes the interaction between a single two-dimension three-level trapped ion and two classical standing wave lasers was obtained by theoretical analysis and numerical computation. The cross-correlation function of two vibrational modes of the trapped ion was analyzed numerically. The results show that the anticorrelation effect is strengthened at first and then weakened with the increasing of the Lamb-Dicke parameters when initial average quantum number is small. But the correlated effect is always strengthened with the increase of the Lamb-Dicke parameters. The anticorrelation effect will be weakened and then disappear with the increasing of initial average quantum number. The initial average quantum number and Lamb-Dicke parameters characterized by nonlinear effects have obvious influence on cross correlation.