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

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 LaguerreGaussian 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 phase and amplitude differences at the positions of the emitters. As a reults 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 a general directional property of the emitted field that when the phase differences at the positions of the emitters equal an even multiple of π/4, the system behaves as a two-sided antenna. When the phase difference equals an odd multiple of π/4, the system behaves as an 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 uni-directional antenna radiating along the interatomic axis.

Markovian Quantum Antenna Theory

“…Therefore, there is an absolute limit on the number of coupling phenomena one may wish to consider if the system has a finite number of dimensions. 15 IV. QUANTUM ANTENNA DIRECTIVITY We now put together all of the ingredients of the basic quantum model of the QDA system developed above in order to explore the possibility of analyzing a concrete radiating quantum dot array excited by external classical field.…”

“…Both of these conditions on the evolution of ρ(t), namely trace-preserving and complete positivity, are required for the consistency of quantum mechanics. For the technical definition of a completely positive operator, see[35],[37],[41] 15. For a treatment of bounded GKSL operators in infinite-dimensional spaces, see[40].…”

Markovian Quantum Antenna Theory

“…Therefore, there is an absolute limit on the number of coupling phenomena one may wish to consider if the system has a finite number of dimensions. 15 IV. QUANTUM ANTENNA DIRECTIVITY We now put together all of the ingredients of the basic quantum model of the QDA system developed above in order to explore the possibility of analyzing a concrete radiating quantum dot array excited by external classical field.…”

Quantum Antennas

“…For example, using Laguerre–Gaussian or Bessel beams for a pump, one can achieve highly tunable directional emission. [ 70 ]…”

“…In Section 2, we have already remarked the possibility of shaping intensity and higher‐order correlations of the field, emitted by the antenna, by designing the initial states, geometry, and driving of the antenna. [ 66,70,83,84 ] In particular, the correlations of the emitted field can be widely varied by changing the initial state of the antenna, and the desired spatial distribution of the correlations can be achieved by designing the antenna state. [ 66 ] Creating the initial timed Dicke states of the antenna, one is able to achieve highly directional emission of a single photon.…”