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Bulletin of the Russian Academy of Sciences Physics

Steady-state fluorescence intensity of two identical atoms with dipole-dipole interaction

Денис Кузнецов, M. G. Gladush, Vl. K. Rerikh

Published Jun 1, 2012• 1 citation
Publisher

Abstract

The dependence of steady-state fluorescence of a diatomic system on the frequency of a laser field is investigated. The steady-state fluorescence intensity can be presented in special geometry as the sum of two parts. The first part is described using an independent two-level system. The second is related to the two-photon excitation process and is described using a three-level system. The respective analytical expressions are obtained for the line profiles, their width, and intensity at the maxima.

DOI
10.3103/s1062873812060202

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The dependence of steady-state fluorescence of a diatomic system on the frequency of a laser field is investigated. The steady-state fluorescence intensity can be presented in special geometry as the sum of two parts. The first part is described using an independent two-level system. The second is related to the two-photon excitation process and is described using a three-level system. The respective analytical expressions are obtained for the line profiles, their width, and intensity at the maxima.
It is shown that when a monochromatic laser couples a single atomic ground level to two closely spaced excited levels the system can be driven into a state in which quantum interference prevents any fluorescence from the excited levels, regardless of the intensity of the exciting field. This steady-state interference occurs only at a particular excitation frequency which depends on the separation of the excited states and the relative size of the two transition dipole matrix elements. The results are derived from the density matrix equations of motion. It is shown that a correct description of the effect requires the inclusion of generalised Einstein A coefficients which are usually neglected in phenomenological damping theories. A dressed-state analysis is introduced to simplify the generalisation to atoms having more complex manifolds of excited states. Analogous interferences in multiphoton absorption and ionisation are also discussed briefly.
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.
This investigation describes the interaction of a three level atom with two laser fields. One of the transitions from the ground state is in resonance with twice the frequency of the first laser and the other transition from the ground state is in resonance with the second laser. The Green's function formalism is used to derive expressions from which the induced two photon and one photon excitation spectra are computed. Also, approximate expressions are derived for the excitation spectra in the appropriate frequency regions. These results agree well with the numerical computations based upon the precise expressions. The interference between the two transitions produce some splittings; these splittings depend upon the Rabi frequency of the one photon transition. The intensities of the weak peaks depend upon the ratio of the Rabi frequency of the two photon transition to the frequency of the first laser. Some features of the excitation spectra are interpreted in terms of previous knowledge about the behavior of two level atoms in strong laser fields.
Several general expressions for the atomic fluorescence radiance excited by a laser source are presented for both two-level and three-level systems. The laser has been approximated to a spectral continuum since its bandwidth is assumed to be much larger than the absorption profile. Two types of three-level systems are considered: (1) systems where two excited states are close together, both coupled radiatively with the ground state (Na, K, Cs, etc.); and (2) systems where one level is close to the ground state, both being radiatively connected with a third excited state (T1, In, Ga, etc.). Expressions are given for both linear and saturating conditions, and the use of such expressions for absolute species measurement is discussed. In our treatment, we have made the assumption that the rate equations approach is valid.
The spectrum of resonance fluorescence and the second-order correlation function are calculated for a system of two identical two-level cooperative systems interacting via the dipole-dipole interaction. The results are valid for arbitrary incident-field strengths and for atomic separations much less than the resonant wavelength. The intensity of the sidebands at the Rabi frequency is diminished by the dipole interaction, whereas that of the sidebands at twice the Rabi frequency is enhanced. Both the cooperative behavior and the dipole-dipole interaction act to diminish the photon antibunching, as shown by the second-order correlation function.