Long-range radiative interaction between semiconductor quantum dots

Abstract

We develop a Maxwell-Schrödinger formalism in order to describe the radiative interaction mechanism between semiconductor quantum dots. We solve the Maxwell equations for the electromagnetic field coupled to the polarization field of a quantum dot ensemble through a linear non-local susceptibility and compute the polariton resonances of the system. The radiative coupling, mediated by both radiative and surface photon modes, causes the emergence of collective modes whose lifetimes are longer or shorter compared to the ones of non-interacting dots. The magnitude of the coupling and the collective mode energies depend on the detuning and on the mutual quantum dot distance. The spatial range of this coupling mechanism is of the order of the wavelength. This coupling should therefore be accounted for when considering quantum dots as building blocks of integrated systems for quantum information processing.

Linear spectrum of a quantum dot coupled to a nanocavity

“…Under this assumption, the steps leading to a set of coupled mode equations are formally the same as in our previous works. 6,7 In particular Maxwell equations are cast into an integral Dyson equation. 28 We denote with ⑀ = ⑀͑r͒ the spatially dependent dielectric constant that characterizes the resonant photonic structure.…”

“…We have previously shown that simple analytical expressions hold in the case of a QD in a homogeneous medium 6 or in a planar microcavity. 7 In the general case, a compact analytical expression cannot be found.…”

“…As an example, the electromagnetic field can vehiculate an excitation transfer between two distant QDs with nonoverlapping electronic states. [6][7][8] If the QD is embedded in a high-quality cavity, the three-dimensional confinement of electromagnetic field can lead to observation of the strong coupling between one QD and the resonant mode of the electromagnetic field. [9][10][11][12][13] This system, however, cannot be seen as a perfect parallel to the atom-cavity coupling in cavity quantum electrodynamics ͑CQED͒.…”

Collective spontaneous emission in coupled quantum dots: Physical mechanism of quantum nanoantenna

“…If the separation between the emitters, exemplified, e.g., by quantum dots (QDs), is small, there is a probability that the excitation can be transferred via charge tunneling [9][10][11][12][13] or long-range radiative interaction. 14 If the interemitter distance is a little bit longer, they are coupled by a near-field quasielectrostatic dipole-dipole (d-d) interaction, mostly referred to as the Förster energy transfer. [15][16][17] It should be noted that in actual experimental conditions, one of the mechanisms prevails over the others, allowing one to study them separately.…”

Long-distance radiative excitation transfer between quantum dots in disordered photonic crystal waveguides

“…25 At longer distance, the interaction was theoretically shown to be finite but weak (as compared to typical radiative loss and decoherence rates) in three-dimensional (bulk) 26 and twodimensional 27 spatially homogeneous dielectric environments. The ideal compromise between interaction strength and range is thus expected in a one-dimensional environment like a PHC waveguide, and indeed, the possibility for entangled states between distant QDs coupled to such a structure has been demonstrated, 28 and the characteristic interaction distance was estimated 29 to be given by r 12 = 2v g /γ , where v g is the group velocity at the exciton resonant frequency, while γ is the loss rate of the waveguide modes.…”