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Physical Review A

Resonant fluorescence of a bichromatically driven three-level atom with the electron shelving effect

Jingyang Li, Yaping Yang

Published Nov 13, 2024• 1 citation
Publisher

Abstract

The electron shelving effect significantly improves the control accuracy of medium energy level transitions, enabling high-sensitivity fluorescence signal detection in precision spectroscopy and quantum metrology and thus allowing a more precise investigation of the microstructure and dynamical behavior of the medium. Here, we investigate theoretically the fluorescence properties of bichromatically driven three-level atoms with electron shelving effect under strong coupling conditions. The physical process by which the electron shelving effect leads to the appearance of two types of peaks in the central peaks of multiple Mollow triplets is explored. This phenomenon is attributed to the different orientations of electric dipole moments in fluorescence emission process caused by a nonresonant weak field. Due to the disappearance of the central broad peak of the central Mollow triplet caused by the quantum interference, the pure sharp peak survives completely induced by the electron shelving effect. The physical picture of the two-mode squeezing effect in out-of-phase quadrature noise spectra originating from the asymmetrical fluorescence operators induced by the nonresonant weak field is revealed. Moreover, the frequency range and degree of two-mode squeezing can be improved by appropriately increasing the Rabi frequency of the weak field. These results not only are helpful for realizing the electron shelving effect experiment in polychromatic strong-coupling systems but also provide a scheme for developing nonclassical spectroscopy and quantum precision measurement based on the electron shelving effect.

DOI
10.1103/physreva.110.053708

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The electron shelving effect significantly improves the control accuracy of medium energy level transitions, enabling high-sensitivity fluorescence signal detection in precision spectroscopy and quantum metrology and thus allowing a more precise investigation of the microstructure and dynamical behavior of the medium. Here, we investigate theoretically the fluorescence properties of bichromatically driven three-level atoms with electron shelving effect under strong coupling conditions. The physical process by which the electron shelving effect leads to the appearance of two types of peaks in the central peaks of multiple Mollow triplets is explored. This phenomenon is attributed to the different orientations of electric dipole moments in fluorescence emission process caused by a nonresonant weak field. Due to the disappearance of the central broad peak of the central Mollow triplet caused by the quantum interference, the pure sharp peak survives completely induced by the electron shelving effect. The physical picture of the two-mode squeezing effect in out-of-phase quadrature noise spectra originating from the asymmetrical fluorescence operators induced by the nonresonant weak field is revealed. Moreover, the frequency range and degree of two-mode squeezing can be improved by appropriately increasing the Rabi frequency of the weak field. These results not only are helpful for realizing the electron shelving effect experiment in polychromatic strong-coupling systems but also provide a scheme for developing nonclassical spectroscopy and quantum precision measurement based on the electron shelving effect.
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.
The quadrature squeezing spectra in the resonance fluorescence of a V-type three-level atom driven by a coherent field and coupled to a single-mode cavity is investigated. For weak excitation, the fluorescence field exhibit squeezing in the out-of-phase quadrature. The coupling between the atom and the cavity mode can greatly enhance the squeezing centred at the laser frequency. More importantly, for strong excitation, under the effect of the cavity-atom coupling, the in-phase quadrature of fluorescence can exhibit two-mode squeezing at the two inner sideband frequencies. By working in the dressed-state representation and hiring secular approximation, we give an analytical explanation for the effect. The result shows, under appropriate conditions, the squeezing can be greatly enhanced by appropriately tuning the cavity resonant frequency.
We focus on the influence of multiphoton effect on the fluorescence spectrum and photon statistics of the bichromatically driven two-level atomic system. The influence of the multiphoton effect of the weaker driving field on the system and spontaneous emission are revealed by Schrieffer-Wolff perturbation theory, respectively. The physical origin of the multiphoton process affecting the fluorescence spectral asymmetry characteristics is fully investigated by studying the population distribution and the dressed atomic transition weight. Further, the suppression condition of the central peak of the central band is investigated. The photon statistical properties of the system are revealed by studying the frequency-resolved correlations between different sidepeaks and the central peak and sidepeak, respectively. In particular, the physical picture of the asymmetry of the two-photon correlation signal that is affected by the multiphoton process of the weaker driving field affecting the timing detection is fully revealed by the two methods of correlation moment and conditional quantum state, respectively. These results of ours provide a theoretical approach for studying multiphoton processes in multichromatically driven quantum systems, as well as for developing quantum simulation techniques such as spin locking.
The incoherent part of the Mollow spectrum for resonance fluorescence has a subnatural linewidth in the weak-field limit. We show that this is due to squeezing of the fluctuations in the induced atomic dipole. The reduced linewidth persists for driving field intensities of approximately 12% of the saturation intensity, where Rabi sidebands begin to appear. We find a similar linewidth narrowing in the transmitted and fluorescent spectra for a single atom in a weakly driven resonant cavity. In this system single-quantum frequency splitting can produce a two-peaked spectrum. Both peaks have a narrowed linewidth. The spectrum of the transmitted light shows a second nonclassical effect that is due to squeezing. A spectral hole may appear at line center, giving a two-peaked spectrum even when there is no frequency splitting.
Summary form only given. The problem of an atom driven by a strong laser was first investigated theoretically in 1969 by B.R. Mollow. He discovered that the resonance fluorescence spectrum has a three-peaked structure with the central peak being more pronounced than the two side peaks. The common Mollow triplet fluorescence pattern can be altered in many ways, by making adjustments to the system. The system can be placed in a squeezed vacuum, the atom can be placed in a cavity, or a bichromatic field can be used instead of a monochromatic laser. These alterations all have an effect on the resulting resonance fluorescence and probe absorption spectra. Other interesting modifications occur when the atom interacts with a stochastic field as well as a laser. The previous approaches were numerical. Here we also obtain analytic solutions (in certain limits) which provide additional insight.
We investigate the spectrum of resonance fluorescence of laser-driven three-level systems in the V or $\ensuremath{\Lambda}$ configuration where one transition is metastable. If the laser driving the weak transition has a sufficiently small Rabi frequency we find an extremely narrow structure in the resonance fluorescence spectrum of the strong transition. Analytical expressions approximating the spectrum are given and the properties of the spectrum are discussed. With the help of a simplified model of resonance fluorescence emitted on the strong transition we are able to show that the origin of the narrow peak can be traced back to electron shelving, i.e., to the existence of light and dark periods in the resonance fluorescence emitted on the strong transition.