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Physical Review A

Analytical treatment of quantum jumps in a system of two interacting two-level atoms

Q. V. Lawande, B. N. Jagatap, S. V. Lawande

Published Oct 1, 1990• 11 citations
Publisher

Abstract

We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel's Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.

DOI
10.1103/physreva.42.4343

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IEEE Journal of Quantum Electronics•Jul 1, 1988•45 citations
We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel's Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.
We consider the effect of dipole-dipole interaction on the quantum jumps in a system of two three-level atoms in a ssV configuration interacting with coherent fields. We show that the intensity-intensity correlation for the strong transition shows additional fluctuations for some interatomic separations between the atoms signifying three levels of fluorescence. It is argued that the intermediate level of fluorescence arises from the coupling between the symmetric and antisymmetric states caused by the dipole-dipole interaction.
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.
We analyze the macroscopic quantum jumps (sudden interruptions in the fluorescence on a macroscopic time scale) that are produced when a pair of two-level atoms separated by a distance d is irradiated by a strong laser having wavelength ${\ensuremath{\lambda}}_{0}$, with ${\ensuremath{\lambda}}_{0}$\ensuremath{\gg}d. Included in the analysis is the dipole-dipole coupling of the atoms, the ac Stark effect, and the role played by a term that is present in the atom-laser field interaction Hamiltonian when k\ensuremath{\cdot}d\ensuremath{\ne}0 (k is the wave vector of the laser field and d is the vector connecting the two atoms). Our treatment is based on frequency-resolved delay functions, an extension of a concept developed by Reynaud, Dalibard, and Cohen-Tannoudji [IEEE J. Quantum Electron. 24, 1395 (1988)], which is shown to be useful to study frequency-resolved photon statistics. As examples, we study the statistics of the fluorescence produced by the two-atom system as well as those in the components of the fluorescent triplet produced by a single two-level atom.
The excitation spectrum arising from photon density-density correlations has been considered in a system of two interacting identical atoms. The two-level atoms are pumped near resonance by a strong electromagnetic field while they interact through their dipole-dipole interaction and radiate to each other as well. In such a system the photon density-density correlations arise from the interference spectrum due to the beating of the frequency of the pump field and the atomic transition frequency, as well as from the spectrum induced by the dipole-dipole and radiative interactions between the atoms. The spectral function of this system has been calculated in the limit of high photon densities. It consists of four terms describing four bands which are similar to those appearing in the two-atom resonance fluorescence spectrum for the symmetric modes when the central peak is missing. The collective behavior as well as the dynamics of the system are discussed in detail. By using the spectral function, an expression for the photon density-density correlation function at different times has been derived where thermal effects have been also included.
The statistics of spontaneous photon emission times in single atom resonance fluorescence are investigated through the radiative cascade of the dressed atom. The delay function which gives the distribution of the delays between two successive emissions is calculated for a coherent as well as an incoherent laser excitation. For a two-level atom, various signals that reflect the fluorescence intensity (average value, photon counting, fluctuation spectrum, etc.) are reviewed by this method. For a three-level atom, this approach is applied to the analysis of the recently observed phenomenon of intermittent fluorescence and quantum jumps.>