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arXiv:1706.03027 · Journal of the Optical Society of America B

Large time-asymmetric quantum fluctuations in amplitude–intensity correlation measurements of V-type three-level atom resonance fluorescence

Luis Gutiérrez, H. M. Castro-Beltrán, R. Román-Ancheyta, Levente Horvath

Published Oct 4, 2017• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/josab.34.002301

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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.
We investigate steady-state squeezing in the phase quadratures of the resonance fluorescence emitted from a three-level V-type atom driven by two coherent fields and damping in common vacuum. Quantum fluctuation spectra of the optimum-phase quadratures are calculated. We find that the steady-state squeezing of the observed driven transition between the excited state and the ground state is strongly affected by the decay rate of the controlling transition, detuning and intensity of driven fields, and the phase quadrature of fluorescent light. When the decay rate of the controlling transition approaches zero, and the driving fields are not resonant simultaneously, the squeezing peak can be extra narrow and the squeezing can be deeply enhanced to exceed the degree of squeezing for the driven two-level atom. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters and also develop an analytic description in the limit of strong driving fields that leads to explicit lineshape and linewidth formulae.
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.