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arXiv:2102.07908 · Journal of Physics B Atomic Molecular and Optical Physics

Phase-dependent fluctuations of resonance fluorescence near the coherent population trapping condition

O de los Santos-Sánchez, H M Castro-Beltrán

Published Feb 15, 2021• 3 citations
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Abstract

Abstract We study phase-dependent fluctuations of the resonance fluorescence of a single Λ-type three-level atom in the regime near coherent population trapping, i.e. alongside the two-photon detuning condition. To this end, we employ the method of conditional homodyne detection (CHD) which considers squeezing in the weak driving regime, and extends to non-Gaussian fluctuations for saturating and strong fields. In this framework, and using estimated parameter settings of the resonance fluorescence of a single trapped 138 Ba + ion, the light scattered from the probe transitions is found to manifest a non-classical character and conspicuous asymmetric third-order fluctuations in the amplitude-intensity correlation of CHD.

DOI
10.1088/1361-6455/abe67f

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quant-pharXiv:2512.21740•Dec 26, 2025•0 citations
Abstract We study phase-dependent fluctuations of the resonance fluorescence of a single Λ-type three-level atom in the regime near coherent population trapping, i.e. alongside the two-photon detuning condition. To this end, we employ the method of conditional homodyne detection (CHD) which considers squeezing in the weak driving regime, and extends to non-Gaussian fluctuations for saturating and strong fields. In this framework, and using estimated parameter settings of the resonance fluorescence of a single trapped 138 Ba + ion, the light scattered from the probe transitions is found to manifest a non-classical character and conspicuous asymmetric third-order fluctuations in the amplitude-intensity correlation of CHD.
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.
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.
Conditional homodyne detection (CHD) allows a fresh view of the nonclassicality of optical fields. A balanced homodyne detector replaces a photodetector in the Hanbury-Brown-Twiss setup of photon correlations, thus measuring a quadrature (amplitude) of the field on the cue of a photon detection. In CHD, both quadratures of a quantum field violate classical inequalities even if photon correlations look classical. We calculate the amplitude-intensity correlations for the resonance fluorescence of a two-level atom and a three-level atom in the V configuration, notable producers of quantum effects (antibunching, squeezing, and sub-Poissonian statistics). In the V atom, where we consider that the ground state is coupled strongly (weakly) to a short (long) lived state, the strong transition resembles the two-level atom features, albeit with larger oscillations and a slower decay. However, the autocorrelation of the fluorescence of the weak transition is clearly asymmetric around a zero delay, indicating the breakdown of detailed balance, and violating the inequalities by orders of magnitude due to the low photon flux. Cross correlations of strong and weak channels also display antibunching and the loss of bounds.
In this paper, we show theoretically that the fields scattered by a bichromatically driven V-type three-level atom exhibit large and asymmetric amplitude–intensity correlations. These features result from the different fluctuations of the amplitude and intensity field operators and the competition among transitions. The amplitude–intensity correlations of resonance fluorescence, with its large third-order fluctuations, describe phase-dependent nonclassical features of the emitted field in addition to the second-order measure related to squeezing. We also calculate spectra and variances of these correlations and intensity–intensity correlations, which provide a wealth of supporting information.
Properties of a Three-Level ΛΛΛ-Type Atom Driven by Coherent and Stochastic Fields
We present a theoretical investigation of a three-level ΛΛΛ-type atom driven by a strong coherent laser and a weak stochastic field exhibiting amplitude and phase fluctuations. The stochastic field is modeled as a complex Gaussian-Markovian random process with finite bandwidth to describe realistic laser noise. Using the Born-Markov and rotating-wave approximations, we derive a Lindblad-form master equation that incorporates spontaneous emission and noise-induced terms, and we solve for the steady-state regime. We examine level populations in both the bare and dressed bases and compute the incoherent resonance-fluorescence spectrum. Our analysis shows that the stochastic drive is not merely a source of decoherence but a versatile control parameter. By detuning the stochastic-field central frequency relative to the coherent drive (especially for narrow bandwidths), we observe pronounced changes in emission characteristics, including selective enhancement or suppression, and reshaping of the multi-peaked fluorescence spectrum when the detuning matches the generalized Rabi frequency. Numerical results reveal nontrivial steady-state modifications distinct from purely coherent driving, enabling precise control of populations and suggesting applications in quantum control, quantum technologies, spectroscopy, and noise-assisted manipulation of atomic systems.