We introduce a formalism for describing the quantum dynamics between two spatially-separated quantum dots on-chip, and apply this formalism to demonstrate pronounced entanglement between two quantum-dot excitons separated by distances of 300 µm and more.
We present and apply a medium-dependent quantum optics formalism for describing the exciton dynamics of two spatially-separated quantum dots on-chip, in the regime of coupled-cavity quantum electrodynamics. With each dot placed in a spatially-separated cavity and coupled through a periodic waveguide channel, the quantum dot excitons behave as a composite entangled pair, exhibiting pronounced entanglement over distances of 300 microm and more. The computed light spectra above the two cavities show clear signatures of pronounced photon coupling including increased vacuum Rabi splitting and cavity-induced transmission and absorption. The macroscopic entanglement is confirmed by investigating the Bell inequality, which is shown to be violated for hundreds of picoseconds.
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 (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.
The modified spontaneous emission dynamics of two photon-coupled quantum dots in a planar-photonic crystal are theoretically investigated. Based on a photon Green function technique for quantizing the electromagnetic fields in arbitrary surroundings, pronounced vacuum Rabi oscillations and dipole-dipole interactions are self-consistently incorporated and are shown to result in a high degree of quantum-bit entanglement. Quantum dots with different optical dipole moments are also found to yield a very rich display of quantum dynamics and offer several advantages over coupling identical atoms.
We introduce a nanowire-based photonic-crystal waveguide system capable of controllably mediating the photon coupling between two quantum dots which are macroscopically separated. Using a rigorous Green-function-based master equation approach, our two-dot system is shown to provide a wide range of interesting quantum transport regimes. In particular, we demonstrate the formation of long-lived entangled states and study the resonance fluorescence spectrum which contains clear signatures of the coupled quantum dot pair. Depending upon the operating frequency, one can obtain a modified Mollow triplet spectrum or a Mollow nonuplet, namely, a spectrum with nine spectral peaks. These multiple peaks are explained in the context of photon-exchange-mediated dressed states. Results are robust with respect to scattering loss, and spatial filtering via propagation allows for each quantum dot's emission to be observed individually.
The dynamics of the entanglement for coherent excitonic states in the system of two, coupled, large semiconductor quantum dots ${(R/a}_{B}\ensuremath{\gg}1)$ mediated by a single-mode cavity field is investigated. Maximally entangled coherent excitonic states can be generated by cavity field initially prepared in odd coherent state. The entanglement of the excitonic coherent states between two dots reaches maximum when no photon is present in the cavity. The effects of the zero-temperature environment on the entanglement of excitonic coherent state are also studied using the concurrence for two subsystems of the excitons.