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Physical Review A

Precision measurement of phase-dependent resonance fluorescence spectra

H. Z. Zhao, Zhou Lu, A. M. Bacon, L. J. Wang, John E. Thomas

Published Feb 1, 1998• 23 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.57.1427

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The role of quantum jumps in the squeezing of resonance fluorescence from short-lived and long-lived atoms

Samir Bali

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.

Journal of Optics B Quantum and Semiclassical Optics•Jul 28, 2004•3 citations
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∘\else\textdegree\fi)(0\ifmmode^\circ\else\textdegree\fi{})(0\ifmmode∘\else\textdegree\fi) and out of phase (90\ifmmode∘\else\textdegree\fi)(90\ifmmode^\circ\else\textdegree\fi{})(90\ifmmode∘\else\textdegree\fi) with a resonant driving field, as well as \ifmmode±\else\textpm\fi45\ifmmode∘\else\textdegree\fi\ifmmode\pm\else\textpm\fi{}45\ifmmode^\circ\else\textdegree\fi{}\ifmmode±\else\textpm\fi45\ifmmode∘\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∘\else\textdegree\fi45\ifmmode^\circ\else\textdegree\fi{}45\ifmmode∘\else\textdegree\fi and \ensuremath−45\ifmmode∘\else\textdegree\fi\ensuremath{-}45\ifmmode^\circ\else\textdegree\fi{}\ensuremath−45\ifmmode∘\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.
We measure phase-dependent optical noise spectra for a simple system: long-lived coherently driven two-level atoms in an atomic beam. Very different noise spectra are measured for radiation which is in phase and out of phase with the driving field. The spectra and corresponding analysis afford clear insights into the roles played by three distinct sources of atomic noise. The measured noise spectra are in good agreement in magnitude and shape with results of a quantum treatment using no free parameters.
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 observe squeezing in the phase-dependent fluorescence spectra of two-level atoms that are coherently driven by a near-resonant laser field in free space. In contrast to previous predictions that emphasized the in- and out-of-phase quadratures, we find that maximum squeezing occurs for homodyne detection at a phase near $\ifmmode\pm\else\textpm\fi{}{45}^{\ensuremath{\circ}}$ relative to the exciting field. A new physical picture of phase-dependent noise is developed that incorporates quantum collapses into a Bloch vector model and yields a very simple form for the complete squeezing spectrum.
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.