Radiative coupling of quantum dots in photonic crystal structures

Abstract

We derive a general formalism to model the polariton states resulting from the radiation-matter interaction between an arbitrary number of excitonic transitions in semiconductor quantum dots and photon modes in a photonic crystal structure in which the quantum dots are embedded. The Maxwell equations, including the linear nonlocal susceptibility of the exciton transitions in the quantum dots, are cast into an eigenvalue problem, which can be applied to any structure whose photon modes can be computed with reliable accuracy, and in addition naturally allows for disorder effects to be taken into account. We compute realistic photon modes using Bloch-mode expansion. As example systems, we study typical InGaAs quantum dots in a GaAs photonic crystal structures -- an $Ln$ cavity or a $W1$ waveguide. For a single dot, we reproduce known analytical results, while for the two dot case, we study the radiative excitation transfer mechanism and characterize its strength, the dependence on the detuning between quantum dot and photon modes, and the dependence on inter-dot distance. We find in particular that the inter-dot radiative coupling strength can reach $100\mu eV$ in a short cavity, and its decay with distance in longer cavities and waveguides is determined by the group velocity of the exchanged photons and their radiative lifetime. We also show that, for an $Ln$ cavity of increasing length, the radiative excitation transfer mechanism is subject to a crossover from a regime where a single photon mode is dominating, to a multi-mode regime -- occurring around $n$ = 150 for the system under study.

arXiv comment17 pages, 12 figures

References in corpus (49)

• Quantum Computation with Quantum Dots
• The Quantum Internet
• Quantum nature of a strongly-coupled single quantum dot-cavity system
• Coupling Superconducting Qubits via a Cavity Bus
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Exciton photon strong-coupling regime for a single quantum dot in a microcavity
• Coherent generation of nonclassical light on a chip via photon-induced tunneling and blockade
• Coherent quantum state storage and transfer between two phase qubits via a resonant cavity
• Ultrafast all-optical switching by single photons
• Strongly correlated photons on a chip
• Direct Observation of Controlled Coupling in an Individual Quantum Dot Molecule
• Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED
• Cavity Quantum Electrodynamics with Anderson-localized Modes
• Experimental realization of highly-efficient broadband coupling of single quantum dots to a photonic crystal waveguide
• Ultrafast optical rotations of electron spins in quantum dots
• Experimental observation of strong photon localization in disordered photonic crystal waveguides
• Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method
• Optical RKKY Interaction between Charged Semiconductor Quantum Dots
• Generation and transfer of single photons on a photonic crystal chip
• Optical control of one and two hole spins in interacting quantum dots
• A Waveguide-Coupled On-Chip Single Photon Source
• Coherent optical control of the spin of a single hole in a quantum dot
• Photon statistics from coupled quantum dots
• Mutual Coupling of two Semiconductor Quantum Dots via an Optical Nanocavity Mode
• GaAs photonic crystal cavity with ultra-high Q: microwatt nonlinearity at 1.55 $\mu$m
• Few emitters in a cavity: From cooperative emission to individualization
• Conditional operation of a spin qubit
• A site-controlled quantum dot system offering both high uniformity and spectral purity
• On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide
• Long-range radiative interaction between semiconductor quantum dots
• Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system
• Electromagnetic modes of a disordered photonic crystal
• Optically induced rotation of a quantum dot exciton spin
• Spin-Forster transfer in optically excited quantum dots
• Spin and energy transfer in nanocrystals without transport of charge
• Extraction of the beta-factor for single quantum dots coupled to a photonic crystal waveguide
• Complete control of a matter qubit using a single picosecond laser pulse
• Continuous-wave versus time-resolved measurements of Purcell-factors for quantum dots in semiconductor microcavities
• Long-range spin-qubit interaction mediated by microcavity polaritons
• Dynamics of Coupled Qubits Interacting with an Off-Resonant Cavity
• High fidelity optical preparation and coherent Larmor precession of a single hole in an InGaAs quantum dot molecule
• Cavity versus dot emission in strongly coupled quantum dots-cavity systems
• The linear spectrum of a quantum dot coupled to a nano-cavity
• Photonic-Crystal Waveguides with Disorder: Measurement of a Band-Edge Tail in the Density of States
• Emission characteristics of quantum dots in planar microcavities
• Broadband Purcell enhanced emission dynamics of quantum dots in linear photonic crystal waveguides
• Light-mass Bragg cavity polaritons in planar quantum dot lattices
• Effect of hole-shape irregularities on photonic crystal waveguides
• Ultralong-range radiative excitation transfer between quantum dots in a planar microcavity

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• Haldane Quantum Hall Effect for Light in a Dynamically Modulated Array of Resonators
• Extended range of dipole-dipole interactions in periodically structured photonic media
• Statistics of Anderson-localized modes in disordered photonic crystal slab waveguides
• Harvesting, coupling and control of single exciton coherences in photonic waveguide antennas
• Entanglement dynamics and Mollow nonuplets between two coupled quantum dots in a nanowire photonic crystal system
• Theory and experiments of coherent photon coupling in semiconductor nanowire waveguides with quantum dot molecules
• Steady-state entanglement between distant quantum dots in photonic crystal dimers
• Long-distance radiative coupling between quantum dots in photonic crystal dimers
• Photoluminescence of a quantum-dot molecule
• Long-distance radiative excitation transfer between quantum dots in disordered photonic crystal waveguides
• Strong and long-range radiative interaction between resonant transitions