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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Physical interpretation of phase-dependent resonance fluorescence

Samir Bali

Published May 16, 2003• 0 citations
Publisher

Abstract

Phase-sensitive detection of resonance fluorescence, i.e., allowing the light emitted from an atom which is undergoing Rabi oscillations in free space to interfere with a coherent local oscillator (LO) beam, has drawn considerable attention throughout the history of quantum optics. Recently, phase-sensitive squeezing spectra for single-atom resonance fluorescence were observed for the first time using strongly-driven long-lived atoms. A measurement of phase-sensitive intensity correlations for this system will be presented. Using physical arguments I will construct the phase-sensitive two-time intensity autocorrelation function, and elucidate the role played by quantum fluctuations in phase-dependent resonance fluorescence.

DOI
10.1117/12.492924

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Phase-sensitive detection of resonance fluorescence, i.e., allowing the light emitted from an atom which is undergoing Rabi oscillations in free space to interfere with a coherent local oscillator (LO) beam, has drawn considerable attention throughout the history of quantum optics. Recently, phase-sensitive squeezing spectra for single-atom resonance fluorescence were observed for the first time using strongly-driven long-lived atoms. A measurement of phase-sensitive intensity correlations for this system will be presented. Using physical arguments I will construct the phase-sensitive two-time intensity autocorrelation function, and elucidate the role played by quantum fluctuations in phase-dependent resonance fluorescence.
Phase-sensitive squeezing in the resonance fluorescence of two-level atoms, that are coherently driven by a near-resonant laser field in free space, was observed recently (Lu et al 1998 Phys. Rev .L ett. 81 3635). This was accomplished via homodyne detection at a phase near ±45 ◦ relative to the driving field for strong off-resonant excitation of ‘long-lived’ atoms (where th ea tomic lifetime far exceeded the laser–atom interaction time, meaning that relaxation effects could be ignored). On the other hand, traditional theoretical predictions of phase-sensitive squeezing in the resonance fluorescence from two-level atoms have emphasized in- and out-of-phase (i.e., 0 ◦ and 90 ◦ ) quadratures, and weak, on-resonant excitation of ‘short-lived’ atoms (where the observation time for laser–atom interaction fa re xceeded the natural atomic lifetime, meaning that relaxation effects dominate). Here, we calculate the probability of a delayed-coincidence detection in the interference field of a fluorescing dipole with a local oscillator (LO). We show that, despite the strikingly different conditions in which squeezing occurs in short- and long-lived atoms, squeezing in both cases can be shown to arise from a joint detection of two photons which are related by a quantum jump in the following way: the first photodetection precipitates a quantum jump of the atom to the ground state, and the second measures the mean amplitude of the fluorescent field subsequent to the quantum jump.
We measure squeezing spectra for phase-dependent fluorescence of coherently driven two-level atoms in free space. The measured spectra are in excellent agreement with our predictions for a single two-level atom. We find that maximum squeezing occurs for homodyne detection at a phase near ±45° relative to the exciting field, rather than in the in- or out-of-phase quadratures. A new physical picture of phase-dependent noise that incorporates quantum collapses into a Bloch vector model shows why this occurs.
We measure phase-dependent fluorescence spectra for an elementary system: long-lived coherently driven two-level atoms in an atomic beam. Phase-dependent fluorescence spectra measure quadrature noise in the atomic radiation field. These noise spectra are obtained using a homodyne detection scheme that suppresses excess noise by subtracting signals from two identically prepared atomic samples. Noise spectra are obtained for atomic radiation which is in phase $(0\ifmmode^\circ\else\textdegree\fi{})$ and out of phase $(90\ifmmode^\circ\else\textdegree\fi{})$ with a resonant driving field, as well as $\ifmmode\pm\else\textpm\fi{}45\ifmmode^\circ\else\textdegree\fi{}$ out of phase with an off-resonant driving field. The measured phase-dependent fluorescence spectra are much richer than ordinary fluorescence spectra, and exhibit many novel features. Particularly interesting are phase-dependent noise spectra for off-resonant excitation. These strikingly exhibit direct manifestations of time ordering, which appear as large differences between the measured $45\ifmmode^\circ\else\textdegree\fi{}$ and $\ensuremath{-}45\ifmmode^\circ\else\textdegree\fi{}$ quadrature noise spectra. The measured noise spectra are in excellent agreement in magnitude and shape with the results of a quantum treatment using no free parameters.
Electron shelving gives rise to bright and dark periods in the resonance fluorescence of a three-level atom. The spectral signature of such blinking is a very narrow inelastic peak on top of the two-level atom spectrum. Here, we investigate theoretically phase-dependent fluctuations (e.g., squeezing) of intermittent resonance fluorescence in the frameworks of balanced and conditional homodyne detection (BHD and CHD, respectively). In BHD, the squeezing is reduced significantly in size and Rabi frequency range compared to that for a two-level atom. The sharp peak is found only in the spectrum of the squeezed quadrature, splitting the negative broader squeezing peak for weak fields. CHD correlates the BHD signal with the detection of emitted photons. It is thus sensitive to third-order fluctuations of the field, produced by the atom-laser nonlinearity, that cause noticeable deviations from the second-order BHD results. For weak driving, the third-order spectrum is negative, enlarging the squeezing peak but also reducing the sharp peak. For strong driving, the spectrum is dominated by third-order fluctuations, with a large sharp peak and the sidebands becoming dispersive. Finally, the addition of third-order fluctuations makes the integrated spectra of both quadratures equal in magnitude in CHD, in contrast to those by BHD. A simple mathematical approach allows us to obtain very accurate analytical results in the shelving regime.