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Physical Review A

Interference pattern with a dark center from two atoms driven by a coherent laser field

Terry Rudolph, Z. Ficek

Published Jul 1, 1998• 15 citations
Publisher

Abstract

In a recent paper Meyer and Yeoman [Phys. Rev. Lett. 79, 2650 (1997)] have shown that the resonance fluorescence from two atoms placed in a cavity and driven by an incoherent field can produce an interference pattern with a dark center. We study the fluorescence from two coherently driven atoms in free space and show that this system can also produce an interference pattern with a dark center. This happens when the atoms are in nonequivalent positions in the driving field, i.e., the atoms experience different intensities and phases of the driving field. We discuss the role of the interatomic interactions in this process and find that the interference pattern with a dark center results from the participation of the antisymmetric state in the dynamics of the driven two-atom system.

DOI
10.1103/physreva.58.748

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Europhysics Letters (EPL)•Apr 15, 1998•2 citations
In a recent paper Meyer and Yeoman [Phys. Rev. Lett. 79, 2650 (1997)] have shown that the resonance fluorescence from two atoms placed in a cavity and driven by an incoherent field can produce an interference pattern with a dark center. We study the fluorescence from two coherently driven atoms in free space and show that this system can also produce an interference pattern with a dark center. This happens when the atoms are in nonequivalent positions in the driving field, i.e., the atoms experience different intensities and phases of the driving field. We discuss the role of the interatomic interactions in this process and find that the interference pattern with a dark center results from the participation of the antisymmetric state in the dynamics of the driven two-atom system.
We show that the resonance fluorescence from a symmetric system of two incoherently pumped atoms coupled to a cavity mode produces interference fringes that possess a minimum on the symmetry plane. This unique deviation from Young-type interferences can be explained intuitively by the process of stimulated emission and reabsorption, leading to a cavity-induced anticorrelation of the atomic dipoles. Detailed consideration of an optical pumping scheme reveals the surprising role of cavity damping. We propose an experiment utilizing a two-level system in In+{\mathrm{In}}^{+}In+.
In a recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)], polarization-sensitive measurements of the fluorescence from two four-level ions driven by a linearly polarized laser were made. Depending on the polarization chosen, different degrees of interference were observed. We carry out a theoretical and numerical study of this system, showing that the results can largely be understood by treating the atoms as independent radiators which are synchronized by the phase of the incident laser field. The interference and its loss may be described in terms of the difference between coherent and incoherent driving of the various atomic transitions in the steady state. In the numerical simulations, which are carried out using the Monte Carlo wave-function method, we remove the assumption that the atoms radiate independently and consider the photodetection process in detail. This allows us to see the total interference pattern build up from individual photodetections and also to see the effects of superfluorescence, which become important when the atomic separation is comparable to an optical wavelength. The results of the calculations are compared with the experiment. We also carry out simulations in the non-steady-state regime and discuss the relationship between the visibility of the interference pattern and which-path considerations.
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 study the quantum dynamics of an array of coherently driven two-level atoms coupled to an optical resonator. In the strong coupling regime the cavity field generated by atomic scattering interferes destructively with the pump on the atoms. In this configuration atomic excitation is suppressed even for strong driving fields, while the stationary intracavity field amplitude is almost independent of the atom number. The magnitude of this interference effect depends on the detuning between laser and cavity field and on the relative atomic positions and is strongest when the atoms are ordered in a wavelength spaced lattice placed at the antinodes of the cavity mode. In this case three dimensional intensity minima are created in the vicinity of each atom. We analyze the mechanical forces in the regime where the interference condition is fulfilled, and show that the atomic pattern is mechanically stable whenever the driving frequency is red detuned with respect to the cavity frequency, irrespective of the atomic transition frequency