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Physical Review A

Resonance fluorescence from two identical atoms in a standing-wave field

Georg Lenz, Pierre Meystre

Published Oct 1, 1993• 44 citations
Publisher

Abstract

We investigate the resonance fluorescence spectrum from two identical atoms driven by a strong standing-wave field. We find interesting modifications of the Mollow spectrum, caused by interferences between the two atoms, and in particular a succession of ``dark'' and ``bright'' states as one of the atoms is moved to successive nodes of the field. Large enough separation between the atoms leads to their decorrelation and the disappearance of these interferences, the atoms acting then as independent radiators. From a technical viewpoint, we also illustrate how the use of superoperators in Liouville space keeps the discussion transparent and provides a convenient tool for numerical calculations.

DOI
10.1103/physreva.48.3365

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Resonance fluorescence from two identical atoms in a standing wave

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We have investigated the resonance fluorescence spectrum from two identical atoms driven by a strong standing wave field. We found interesting modifications of the Mollow spectrum, caused by interferences between the two atoms, and in particular a succession of dark and bright states as one of the atoms is moved to successive nodes of the field. Large enough separation between the atoms leads to the disappearance of these interferences, and the atoms act then as independent radiators, the fluorescence spectrum becoming then independent of the interatomic distance. From the point of view advocated by E. Wolf,1 one can interpret these modifications as caused by source correlations. For instance, we obtain new sidebands which are altered as the separation between atoms is modified. When these sidebands eventually cross, the fluorescence spectrum displays interesting properties such as “dark” and “bright” states. These investigations lay the foundations for a discussion of the influence of particle statistics on spectral properties of atoms cooled and trapped in optical molasses. The next step in this direction will include the effects of translational motion on these spectra.2 This program will eventually lead to a full-fledged field theoretical description of the spectral and translational correlation properties of an ensemble of cooled and trapped atoms.

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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.

Quantum Electronics and Laser Science Conference•Jan 1, 2000•0 citations
We investigate the resonance fluorescence spectrum from two identical atoms driven by a strong standing-wave field. We find interesting modifications of the Mollow spectrum, caused by interferences between the two atoms, and in particular a succession of dark'' and bright'' states as one of the atoms is moved to successive nodes of the field. Large enough separation between the atoms leads to their decorrelation and the disappearance of these interferences, the atoms acting then as independent radiators. From a technical viewpoint, we also illustrate how the use of superoperators in Liouville space keeps the discussion transparent and provides a convenient tool for numerical calculations.
We have investigated the resonance fluorescence spectrum from two identical atoms driven by a strong standing wave field. We found interesting modifications of the Mollow spectrum, caused by interferences between the two atoms, and in particular a succession of dark and bright states as one of the atoms is moved to successive nodes of the field. Large enough separation between the atoms leads to the disappearance of these interferences, and the atoms act then as independent radiators, the fluorescence spectrum becoming then independent of the interatomic distance. From the point of view advocated by E. Wolf,1 one can interpret these modifications as caused by source correlations. For instance, we obtain new sidebands which are altered as the separation between atoms is modified. When these sidebands eventually cross, the fluorescence spectrum displays interesting properties such as “dark” and “bright” states. These investigations lay the foundations for a discussion of the influence of particle statistics on spectral properties of atoms cooled and trapped in optical molasses. The next step in this direction will include the effects of translational motion on these spectra.2 This program will eventually lead to a full-fledged field theoretical description of the spectral and translational correlation properties of an ensemble of cooled and trapped atoms.
Resonance fluorescence of two two-level atoms driven by a coherent laser field propagating parallel to the interatomic axis is examined, taking into account the dipole-dipole interaction. We show that the number of peaks in the fluorescence intensity depends on the direction of observation with respect to the interatomic axis and on whether the system is driven by a standing-wave or a running-wave laser field. When the system is driven by the standing-wave field the fluorescence intensity shows two peaks and a dip for an observation direction perpendicular to the interatomic axis and three peaks in the direction parallel to it. When the system is driven by the running-wave field only two peaks are observed for the perpendicular direction. We explain these features in terms of the collective states of the system and show that the directional effect can be attributed to the fact that the antisymmetric state of the system does not radiate in the direction perpendicular to the interatomic axis. Photon statistics also demonstrate the directional effect for the standing-wave field. Frequency regimes are found where sub-Poissonian photon statistics occur. Depending on the direction of the observation, a state close to a Fock state can occur for one or two frequencies of the driving field, corresponding to zero-photon-number fluctuations or maximum sub-Poissonian behavior. The fluorescence spectrum is found to depend on the direction of observation and the interatomic separation. For small interatomic separations and a standing-wave driving field the spectrum exhibits seven lines for the perpendicular direction and 13 lines in the direction parallel to the interatomic axis. For the running-wave field the spectrum shows 13 lines independent of the direction of observation. Moreover, we show that for particular interatomic separations dark regimes appear in the spectrum. We discuss the effect of the dipole-dipole interaction on the dark states and explain the spectral features in terms of the dressed-atom model. We also consider the absorption spectrum of a weak probe beam illuminating the two-atom system. We show that apart from a weak dispersion structure, the spectrum shows large peaks as one of the atoms is moved to successive nodes of the field.
The influence of the standing wave amplitude on the resonance fluorescence of a three-level system of radiators is discussed. Great attention is devoted to the peculiarities of dressed states in the standing wave and the exchange integrals between two atoms situated in the anti-nodes or the nodes. The correlation functions of emitted photons at two dressed frequencies were obtained. It is shown that in the case when the distance between two atoms is smaller than the wavelength of the field, the emitted photons are strongly correlated. As was observed, for large values of laser field intensity, the control of spontaneous emission is possible at two frequencies as well as the atom–atom interaction process. The dependence of the fluorescent light spectrum as a function of the position of two atoms dressed in the standing wave is investigated.
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.