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arXiv:1506.07318 · Physical Review A

Radiation pattern of two identical emitters driven by a Laguerre-Gaussian beam: An atom nanoantenna

V. E. Lembessis, A. Lyras, Anwar Al Rsheed, Omar Marzook Al-Dossary, Z. Ficek

Published Aug 27, 2015• 10 citations
arXivHTMLPDF

Abstract

We study the directional properties of a radiation field emitted by a geometrically small system composed of two identical two-level emitters located at short distances and driven by an optical vortex beam, a Laguerre-Gaussian beam which possesses a structured phase and amplitude. We find that the system may operate as a nanoantenna for controlled and tunable directional emission. Polar diagrams of the radiation intensity are presented showing that a constant phase or amplitude difference at the positions of the emitters plays an essential role in the directivity of the emission. We find that the radiation patterns may differ dramatically for different phases and amplitude differences at the positions of the emitters. As a result the system may operate as a two- or one-sided nanoantenna. In particular, a two-sided highly focused directional emission can be achieved when the emitters experience the same amplitude and a constant phase difference of the driving field. We find the general directional property of the emitted field that when the phase differences at the positions of the emitters equal an even multiple of $\ensuremath{\pi}/4$, the system behaves as a two-sided antenna. When the phase difference equals an odd multiple of $\ensuremath{\pi}/4$, the system behaves as a one-sided antenna. The case when the emitters experience the same phase but different amplitudes of the driving field is also considered and it is found that the effect of different amplitudes is to cause the system to behave as a unidirectional antenna radiating along the interatomic axis.

DOI
10.1103/physreva.92.023850

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We study the directional properties of a radiation field emitted by a geometrically small system composed of two identical two-level emitters located at short distances and driven by an optical vortex beam, a Laguerre-Gaussian beam which possesses a structured phase and amplitude. We find that the system may operate as a nanoantenna for controlled and tunable directional emission. Polar diagrams of the radiation intensity are presented showing that a constant phase or amplitude difference at the positions of the emitters plays an essential role in the directivity of the emission. We find that the radiation patterns may differ dramatically for different phases and amplitude differences at the positions of the emitters. As a result the system may operate as a two- or one-sided nanoantenna. In particular, a two-sided highly focused directional emission can be achieved when the emitters experience the same amplitude and a constant phase difference of the driving field. We find the general directional property of the emitted field that when the phase differences at the positions of the emitters equal an even multiple of \ensuremathπ/4\ensuremath{\pi}/4\ensuremathπ/4, the system behaves as a two-sided antenna. When the phase difference equals an odd multiple of \ensuremathπ/4\ensuremath{\pi}/4\ensuremathπ/4, the system behaves as a one-sided antenna. The case when the emitters experience the same phase but different amplitudes of the driving field is also considered and it is found that the effect of different amplitudes is to cause the system to behave as a unidirectional antenna radiating along the interatomic axis.
In recent years, the radiative properties of atomic systems have been a hot topic in the research fields of quantum optics and quantum information. With the continuous development of nanophotonics, quantum antennas have become an important model for studying atomic radiation. In order to investigate these phenomena in depth, we investigate a system composed of two two-level atoms, and study the two-photon emission phenomenon of diatomic system under conditions of driving directional tunable laser field, interatomic dipole-dipole interaction, and spontaneous emission coherence. In this study, we diagonalize the atomic Hamiltonian to obtain the eigenvalues and entangled states of the system (symmetric and asymmetric states of two atoms), and use the rotating wave approximation to rotate the system into the laser frame. The evolution of the system is characterized mainly by the evolution of symmetric and asymmetric state, as well as the evolution of coherent terms. In our studies it is found that for identical atoms, certain laser directions and geometric configurations can exclusively drive the superradiant and subradiant states of atoms, which can enhance the first-order interference effect of the atoms and markedly increase the probability of two-photon emission in a specific detection direction. When the superradiant state of the atom is solely driven, there will be no coupling between the superradiant state and subradiant state, resulting in a correlation function angular distribution that is symmetric along the direction perpendicular to atomic axis. Further adjusting the laser direction causes the atomic interference patterns to shift, and the system will exhibit two-photon emission characteristics on one side or both sides. For nonidentical atomic systems, due to detuning between the two atoms, the laser cannot drive the superradiant state or subradiant state individually, and the influence of changing the laser direction on the coupling strength diminishes with the increase of detuning between the atoms. When the laser is in resonance with one of the atoms, due to the atomic interactions, the other atom can achieve the strongest coherent effect without resonating with the laser. This research reveals that atomic detuning is crucial for the correlation values and angular distribution of the correlation function. By adjusting the atomic detuning and laser direction, the system can display highly directed one-sided two-photon emission characteristics. However, different dissipation rates will lead the probability of two-photon emission to decrease. Our studies can achieve highly directional two-photon emission on one side or both sides, which provides a theoretical basis for studying the two-photon emission of nanoantennas.
We determine how a system composed of two nonidentical two-level atoms with different resonance frequencies and different damping rates could work as a nanoantenna for controlled mode switching and light routing. We calculate the angular distribution of the emitted field detected in a far-field zone of the system including the direct interatomic interactions and arbitrary linear dimensions of the system. The calculation is carried out in terms of the symmetric and antisymmetric modes of the two-atom system. We find that as long as the atoms are identical, the emission cannot be switched between the symmetric and antisymmetric modes. The switching may occur when the atoms are nonidentical and the emission can then be routed to different modes by changing the relative ratio of the atomic frequencies, or damping rates, or by a proper tuning of the laser frequency to the atomic resonance frequencies. It is shown that in the case of atoms of different resonance frequencies but equal damping rates, the light routing is independent of the frequency of the driving laser field. It depends only on the sign of the detuning between the atomic resonance frequencies. In the case of atoms of different damping rates, the emission can be switched between different modes by changing the laser frequency from the blue to red detuned from the atomic resonance. The effect of the interatomic interactions is also considered, and it is found that in the case of unequal resonance frequencies of the atoms, the interactions slightly modify the visibility of the intensity pattern. The case of unequal damping rates of the atoms is affected rather more drastically, the light routing becoming asymmetric under the dipole-dipole interaction with the enhanced intensities of the modes turned towards the atom of smaller damping rate.
We study the collective decay dynamics of two or three quantum emitters coupled to a one-dimensional chiral waveguide. We find that both the asymmetry of emission intensity and the propagation phases play crucial roles in determining radiation behavior. Under suitable parameters, we show that the multiple emitters exhibit tunable radiance in the two-emitter case, such as one emitter exhibits superradiance while the other exhibits subradiance. Furthermore in the three-emitter case, the emitter can experience successive changes of radiation states. Our results highlight how chiral and anisotropic waveguide properties can be used to engineer controllable quantum light-matter interactions, with potential applications implemented in unidirectional quantum devices, and help explore more complex multibody radiation effects in waveguide quantum electrodynamics platforms.
We examine angular distribution of the probability of correlated fluorescence photon emission from a linear chain of identical equidistant two-level atoms. We selectively excite one of the atoms by a resonant laser field. The atoms are coupled to each other via the dipole-dipole interaction and collective spontaneous emission. Our attention is focused on the simultaneous observation of correlated pairs of photons. It is found that the interference between the emitting atoms can result in a highly directional emission of photon pairs. These pairs of photons exhibit strong correlations and their emission is highly concentrated into specific directions. We demonstrate the crucial role of the selective coherent excitation in such a geometrical configuration. Shifting the driving field from an atom located at one end of the chain to the other causes the radiation pattern to flip to the opposite half of the detection plane. Furthermore, we find that atomic systems in which only an atom situated at a particular position within the linear chain is driven by a laser field can radiate correlated twin photons in directions along which the radiation of single photons is significantly reduced. Alternatively, superbunching in the emitted photon statistics preferentially occurs in directions of negligible or vanishing single-photon emission. The effect of superbunching strengthens as more emitters are added to the chain. Depending on the number of atoms and the position of the driven atom within the chain, the strongly correlated pairs of photons can be emitted into few well-defined directions.
We investigate the collective spontaneous emission in a system of two identical quantum dots (QDs) strongly coupled through the dipole-dipole ($d\ensuremath{-}d$) interaction. The QDs are modeled as two-level quantum objects, while the $d\ensuremath{-}d$ interaction is described as the exchange of a virtual photon through the photonic reservoir. The master equation approach is used in the analysis. The main attention is focused on antenna characteristics of the two-QD system---the radiation intensity dependence on the meridian and azimuthal angles of observation. We show that the radiation pattern of such a system is nonstationary and its temporal behavior depends on the initial quantum state. In particular, for entangled initial states the radiative pattern exhibits oscillations on the frequency which corresponds to the $d\ensuremath{-}d$ interaction energy. We also analyze spectral properties of the directional diagram. The comparison of radiation patterns is carried out for two QDs and two classical dipoles. The concept of quantum nanoantenna is proposed based on collective spontaneous emission in QD ensembles.
We describe the design of an artificial `free space' 1D-atom for quantum optics, where we implement an effective two-level atom in a 3D optical environment with a chiral light-atom interface, i.e. absorption and spontaneous emission of light is essentially unidirectional. This is achieved by coupling the atom of interest in a laser-assisted process to a `few-atom' array of emitters with subwavelength spacing, which acts as a phased-array optical antenna. We develop a general quantum optical model based on Wigner-Weisskopf theory, and quantify the directionality of spontaneous emission in terms of a Purcell β\betaβ-factor for a given Gaussian (paraxial) mode of the radiation field, predicting values rapidly approaching unity for `few-atom' antennas in bi- and multilayer configurations. Our setup has for neutral atoms a natural implementation with laser-assisted Rydberg interactions, and we present a study of directionality of emission from a string of trapped ions with superwavelength spacing.