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Physical Review Letters

Squeezing and anomalous moments in resonance fluorescence

W. Vogel

Published Oct 28, 1991• 76 citations
Publisher

Abstract

A scheme for measuring squeezing in resonance fluorescence from a single trapped and cooled ion is proposed, which is based on the observation of photon pair correlations after beating the fluorescence with a local oscillator. In addition to squeezing, anomalous moments and sub-Poissoinian photon statistics of the fluorescence contribute to the nonclasical behavior of the light in homodyne detection.

DOI
10.1103/physrevlett.67.2450

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 10, 2011•0 citations
A scheme for measuring squeezing in resonance fluorescence from a single trapped and cooled ion is proposed, which is based on the observation of photon pair correlations after beating the fluorescence with a local oscillator. In addition to squeezing, anomalous moments and sub-Poissoinian photon statistics of the fluorescence contribute to the nonclasical behavior of the light in homodyne detection.
Squeezing in resonance fluorescence was predicted more than a decade ago,1 but it has not been observed until now. There are lwo problems in connection with such an experiment. First, in a homodyne measurement of the photon statistics the observable effect is limited by the detection and collection efficiencies and is therefore extremely small.2 Second, since the squeezing effect is phase sensitive, the atom must be localized very well. To overcome these problems, homodyne intensity-correlation measurements of the fluorescence from a trapped ion have been proposede.3
The photon-counting statistics of squeezed states in collective time-dependent resonance fluorescence is calculated for the homodyne detection technique. The secular approximation is applied to obtain analytical expressions for the photon-counting distribution produced by homodyning the fluorescent field and coherent radiation. Squeezing is shown to appear only in the transient regime of resonance fluorescence. The time location of squeezing is independent of the number of atoms, N, but squeezing increases with increasing N. Moreover, squeezing occurs only for a judicious choice of the phase of the local oscillator and occurs over long counting times T. The time interval T is strongly dependent on the initial atomic population. If initially all atoms are in their excited states, squeezing appears with a delay twice as long as that for initially nonexcited atoms.
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.
The three-dimensional localization of a single ion to the Lamb–Dicke limit in a radio-frequency trap has been combined with the technique of heterodyne detection to provide high-resolution spectroscopy of the fluorescent light of the ion. A coherent component with a linewidth of 0·7 Hz, corresponding to elastic scattering of the incident laser light, was observed in the heterodyne signal. The method may be extended to observe the narrow sidebands related to the secular motion in the trap, yielding information on the dynamics of the ion. Quantum properties of the fluorescent radiation can be detected by probing higher order field correlations. As an example we investigated the phenomenon of antibunching which appears as intensity anticorrelations of the emitted radiation. A measurement of intensity cross-correlations of the fluorescent light superimposed with a weak local oscillator is expected to permit the observation of squeezing in the resonance fluorescence of a single ion.
Using master equation and quantum Monte Carlo wavefunction approaches, we study the circumstances surrounding the emergence and degradation of the elusive squeezing of fluctuations in two-level atom resonance fluorescence. For its measurement we suggest conditional homodyne detection (CHD) [G.T. Foster, L.A. Orozco, H.M. Castro-Beltran, H.J. Carmichael, Phys. Rev. Lett. 85, pp. 3149-3152, 2000], which is nearly independent of detector efficiencies, which have harmed previous attemps. Squeezing in resonance fluorescence requires a weak laser, so the average interval between emitted photons is much longer than the regression time to the steady state; here, the spectrum of the out-of-phase quadrature is a negative peak. In CHD, moderate fields generate a non-zero third-order correlation in the dipole fluctuations that contaminates squeezing, making the noise non- Gaussian. If the probability to emit two and even three close photons is still small the additional contribution is also negative, helping to make the full spectrum a bit larger and easier to measure. Strong driving spreads the photoemission distribution, which destroys squeezing, and the third order fluctuations become responsible for the non-classicality of the fluorescence.