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arXiv:1307.2792 · Physical Review B

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

Momchil Minkov, Vincenzo Savona

Published Aug 19, 2013• 11 citations
arXivHTMLPDF

Abstract

We theoretically investigate the magnitude and range of the photon-mediated interaction between two quantum dots embedded in a photonic crystal waveguide, including fabrication disorder both in the crystal and in the dot positioning. We find that disorder-induced light localization has a drastic effect on the excitation transfer rate---as compared to an ideal structure---and that this rate varies widely among different disorder configurations. Nevertheless, we also find that significant rates of $50\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{eV}$ at a range of $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ can be achieved in realistic systems.

DOI
10.1103/physrevb.88.081303

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We theoretically investigate the magnitude and range of the photon-mediated interaction between two quantum dots embedded in a photonic crystal waveguide, including fabrication disorder both in the crystal and in the dot positioning. We find that disorder-induced light localization has a drastic effect on the excitation transfer rate---as compared to an ideal structure---and that this rate varies widely among different disorder configurations. Nevertheless, we also find that significant rates of 50\ensuremathμeV50\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{eV}50\ensuremathμeV at a range of 10\ensuremathμm10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}10\ensuremathμm can be achieved in realistic systems.
We have theoretically studied the excitation transfer between distant quantum dots in a photonic crystal waveguide. Due to Anderson localization of disordered position and size of the photonic crystal holes was found to have a highly nontrivial effect on the interaction. We have simulated realistic systems with different magnitudes of the disorder and showed that while localization indeed has a profound effect on both range and magnitude of the dot-dot excitation transfer rate at several |im distance. The average excitation transfer rate was found to be larger than 10μev at distance on the order of 10μm. The transfer time to this corresponded was on the order of 10 ps, close to the single qubit operation time and much shorter than the decoherence time measured. The obtained results were found in good agreement with previous results.
We show that two spatially separated semiconductor quantum dots under resonant and continuous-wave excitation can be strongly entangled in the steady state, thanks to their radiative coupling by mutual interaction through the normal modes of a photonic crystal dimer. We employ a quantum master equation formalism to quantify the steady-state entanglement by calculating the system negativity. Calculations are specified to consider realistic semiconductor nanostructure parameters for the photonic crystal dimer--quantum dots coupled system, determined by a guided-mode expansion solution of Maxwell equations. Negativity values of the order of 0.1 (2020%20 of the maximum value) are shown for interdot distances that are larger than the resonant wavelength of the system. It is shown that the amount of entanglement is almost independent of the interdot distance, as long as the normal mode splitting of the photonic dimer is larger than their linewidths, which becomes the only requirement to achieve a local and individual qubit addressing. Considering inhomogeneously broadened quantum dots, we find that the steady-state entanglement is preserved as long as the detuning between the two quantum dot resonances is small when compared to their decay rates. The steady-state entanglement is shown to be robust against the effects of pure dephasing of the quantum dot transitions. We finally study the entanglement dynamics for a configuration in which one of the two quantum dots is initially excited and find that the transient negativity can be enhanced by more than a factor of two with respect to the steady-state value. These results are promising for practical applications of entangled states at short time scales.
We investigate the disorder-limited propagation of photons in photonic crystal waveguides in the slow-light regime. We use analysis of Fabry-Perot resonances to map the mode dispersion and extract the photon localization length. Propagation lengths are deduced to be limited to less than 20 μm for group index >50. Anderson-localized modes are observed at high group indices, when the localization lengths are shorter than the waveguide lengths, consistent with the Fabry-Perot analysis. The results have consequences for integrated quantum-dot single-photon circuits which rely on slow-light effects to enhance emission rates.
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