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Journal of Physics B Atomic and Molecular Physics

Resonance fluorescence of an atom in a standing-wave laser field

Emilio Fiordilino, Marvin H. Mittleman

Published Aug 14, 1984• 6 citations
Publisher

Abstract

The authors calculate the fluorescent spectrum of an atom driven by a standing-wave laser field which is exactly resonant with the atomic transition when the atom is at rest. The motion of the atom causes Doppler shifts which destroy the exact resonance and produces a spectrum which can have peaks at omega k = omega L +k.V+k L .vn where omega L is the laser frequency, k L .v is the Doppler shift and n is any integer.

DOI
10.1088/0022-3700/17/15/017

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The authors calculate the fluorescent spectrum of an atom driven by a standing-wave laser field which is exactly resonant with the atomic transition when the atom is at rest. The motion of the atom causes Doppler shifts which destroy the exact resonance and produces a spectrum which can have peaks at omega k = omega L +k.V+k L .vn where omega L is the laser frequency, k L .v is the Doppler shift and n is any integer.
A previous calculation of forces on atoms in external (dc) fields and in homogeneous traveling-wave laser fields is modified for the case of a standing-wave laser field. The case of intense laser fields, where the Rabi frequency is much greater than the natural decay rate of the atom, is described. A general result for any Doppler shift of the laser frequency due to the atomic motion is obtained. It is specialized to the two cases in which this shift is either much smaller or larger than the natural decay rate. In the first case, we get the same result as that of a previous calculation. The second case has not been discussed previously.
Dopplerons are the signature of the nonlinear response of moving atoms driven by a continuous standing-wave laser beam. They display maxima on the velocity-dependent atomic population difference at velocities nearly equal to ±(c/ω)[(δ(ω2 + 2Ω2)1/2/(2p + 1)], where Ω is the Rabi frequency associated with an individual beam field and δω is the detuning between the driving frequency and the center of the Doppler linewidth. Probing the device with a weak signal yields gain for Doppler broadenings of the magnitude of the detuning, exclusively on the atomic-resonance-frequency side, with a maximum shifted from the driving frequency by the generalized Rabi frequency associated with a standing wave, defined by (δω2 + 4Ω2)1/2. The existence of dopplerons is demonstrated by peaks occurring at frequencies shifted from the driving frequency by even harmonics of doppleron frequencies. The intensity of the peaks is shown to depend on the Doppler width, and the complexity of the gain curve is shown to increase as the pump intensity does.
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.
Resonance-fluorescence power spectrum of two-level atoms driven by a strong monochromatic laser field is discussed, taking into account effects due to the dipole-dipole interaction between the atoms. For two atoms confined to a region smaller than the wavelength of the driving field, we predict significant deviations of the power spectrum from the single-atom case. The two-atom spectrum is nonsymmetric, the wing peaks are shifted from their Rabi-frequency positions, and additional maxima may appear.
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.