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Physical Review A

Dipole-dipole interaction in a photonic crystal nanocavity

Yong-Gang Huang, Gengyan Chen, Chongjun Jin, W. M. Liu, Xuehua Wang

Published May 22, 2012• 24 citations
Publisher

Abstract

We put forward a general classical approach to obtain the quantum dipole-dipole interaction (DDI) between two two-level ``atoms'' in arbitrary nanostructures, in which the transfer rate of the DDI is analytically expressed as the difference between the two classical dipoles' total radiation power and the sum of the two individual dipole's radiation powers. The radiation power can be calculated by the finite-difference time-domain method. We apply the theory to investigate the DDI in a photonic crystal nanocavity. It is found that strong DDI at a distance can be achieved under resonant conditions and with a high quality factor, and the attractive or repulsive properties of the DDI can be manipulated. Our results should be significant for solid-state quantum-information processing based on the DDI.

DOI
10.1103/physreva.85.053827

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New Journal of Physics•Aug 13, 2013•36 citations
We put forward a general classical approach to obtain the quantum dipole-dipole interaction (DDI) between two two-level ``atoms'' in arbitrary nanostructures, in which the transfer rate of the DDI is analytically expressed as the difference between the two classical dipoles' total radiation power and the sum of the two individual dipole's radiation powers. The radiation power can be calculated by the finite-difference time-domain method. We apply the theory to investigate the DDI in a photonic crystal nanocavity. It is found that strong DDI at a distance can be achieved under resonant conditions and with a high quality factor, and the attractive or repulsive properties of the DDI can be manipulated. Our results should be significant for solid-state quantum-information processing based on the DDI.
Dipole-dipole interaction between two two-level `atoms' in photonic crystal nanocavity is investigated based on finite-difference time domain algorithm. This method includes both real and virtual photon effects and can be applied for dipoles with different transition frequencies in both weak and strong coupling regimes. Numerical validations have been made for dipoles in vacuum and in an ideal planar microcavity. For dipoles located in photonic crystal nanocavity, it is found that the cooperative decay parameters and the dipole-dipole interaction potential strongly depend on the following four factors: the atomic position, the atomic transition frequency, the resonance frequency, and the cavity quality factor. Properly arranging the positions of the two atoms, we can acquire equal value of the cooperative decay parameters and the local coupling strength. Large cooperative decay parameters can be achieved when transition frequency is equal to the resonance frequency. For transition frequency varying in a domain of the cavity linewidth around the resonance frequency, dipole-dipole interaction potential changes continuously from attractive to repulsive case. Larger value and sharper change of cooperative parameters and dipole-dipole interaction can be obtained for higher quality factor. Our results provide some manipulative approaches for dipole-dipole interaction with potential application in various fields such as quantum computation and quantum information processing based on solid state nanocavity and quantum dot system.
Photon scattering properties in one-dimensional waveguide side coupled to a nanocavity embedded in two atoms with dipole-dipole interaction (DDI) are investigated theoretically. The analytical expressions of the transmission and reflection amplitudes are deduced by using the real-space Hamiltonian. A method to determine the coupling strength of DDI is proposed. Realization of single photon switching by modulation the DDI is investigated. The influence of dissipations on the performance of the single photon switching are exhibited. An asymmetric Fano-type resonance, which can be controlled by the DDI, appears in the transmission spectrum.
Abstract The dipole–dipole interaction (DDI) has been studied in photonic quantum wells are simulated from two photonic crystals say A and B. An ensemble of nanoparticles is doped within the quantum well layer. Nanoparticles are interacting with each other via DDI. The absorption spectrum has been calculated by using the time dependent Schrodinger equation method. A probe field is applied to measure the absorption spectrum. Numerical simulations for the absorption coefficient have been performed. It has been found that in the absence of DDI the spectrum has two peaks and a minimum at zero detuning. However, in the presence of the large DDI coupling both peaks disappear and a large minimum appears. This means that the positions and heights of peaks can be changed due to DDI interaction. This study can be used to make new types of optical devices. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The effect of the dipole-dipole interaction (DDI) on absorption processes has been investigated in photonic nanowires. They are manufactured by embedding a photonic crystal into another crystal. The embedded crystal is doped with an ensemble of three-level quantum dots. A probe field is applied to monitor the absorption coefficient. A control field is applied to induce dipole moments in quantum dots. Owing to these fields dipoles are induced in quantum dots, and they interact with each other via the DDI. Quantum dots also interact with bound photon states of the nanowire via the electron-bound photon interaction. It is found that the system can be switched from a transparent state to an absorbing state through the DDI. The switching mechanism can be controlled by changing the location of a resonant energy in the quantum dots.
Ultra-high-quality factor photonic crystal nanocavities are attracting much attention because they can confine light into an ultra-small region and enable strong interaction between light and matter. One important step toward the realization of quantum information processing with cavity quantum electrodynamics approaches is a robust method that transfers photons among such cavities. We propose and theoretically investigate a scheme to transfer photons between strongly coupled, distant photonic crystal nanocavities by an adiabatic change in the cavity characteristics in the time domain. Adding one intermediate nanocavity for control allows efficient light transfer between objective nanocavities. Because our scheme utilizes adiabatic transfer, its operation is robust for both the control parameters and the control timing.
Using the electromagnetic response function of an electric dipole located within a dielectric geometry, we derive the mathematical equivalence between the classical response and quantum mechanical resonant dipole–dipole interaction between two quantum objects (atoms, quantum dots, etc). Cooperative spontaneous emission likewise emerges from this equivalence. We introduce a practical numerical technique using finite difference time domain for calculating both dipole–dipole interaction and collective spontaneous emission in confined dielectric structures, where strong light–matter coupling might arise. This method is capable of obtaining resonant dipole–dipole interaction over a wide range of frequencies in a single run. Our method recaptures the results of quantum mechanical second order perturbation theory for weak light–matter coupling. In strong coupling situations such as near a photonic band edge, second order Rayleigh–Schrödinger perturbation theory leads to divergences, and instead Brillouin–Wigner perturbation theory is required. This is equivalent to the use of a variational wavefunction to describe the exciton transfer between initial and final states. We introduce a system of coupled classical oscillators, that describes resonant dipole–dipole interaction and vacuum Rabi splitting in the strong-coupling regime, and that provides an effective numerical scheme based on the finite difference time domain method. This includes the effects of quantum entanglement and the correlation of quantum fluctuations. We discuss the crossover to Forster energy transfer when quantum correlations between the dipoles are damped by strong environmental interactions.