Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Express

Macroscopic entanglement and violation of Bell’s inequalities between two spatially separated quantum dots in a planar photonic crystal system

P. Yao, Stephen Hughes

Published Jun 24, 2009• 73 citations
Publisher

Abstract

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.

DOI
10.1364/oe.17.011505

Related papers

Macroscopic entanglement between two spatially separated quantum-dot excitons in a planar photonic crystal

Peijun Yao, Stephen Hughes

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.

Conference on Lasers and Electro-Optics•Jan 1, 2009•0 citations

Violation of Bell’s inequality for two coupled quantum dots confined in a cavity

Amitabh Joshi, Blake Anderson, Min Xiao

A system of two coupled quantum dots entangled through their interaction with a cavity mode, including F\"orster and exciton-phonon interactions, exhibits violation of Bell's inequality at certain interaction times of these dots with the field mode. The effects of relative positions of these dots in the cavity and exciton-phonon and F\"orster interaction strengths on the violation of Bell's inequality are discussed.

Physical Review B•Mar 5, 2007•6 citations

Entanglement dynamics and Mollow nonuplets between two coupled quantum dots in a nanowire photonic-crystal system

Gerasimos Angelatos, Stephen Hughes

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.

arXiv:1411.4628•Physical Review A•May 20, 2015•24 citations

Generation of entangled photon pairs from a single quantum dot embedded in a planar photonic-crystal cavity

Pradyumna K. Pathak, Stephen Hughes

We present a formal theory of single quantum dot coupling to a planar photonic crystal that supports quasidegenerate cavity modes and use this theory to describe and optimize entangled-photon pair generation via the biexciton-exciton cascade. In the generated photon pairs, either both photons are spontaneously emitted from the dot or one photon is emitted from the biexciton spontaneously while the other is emitted via the leaky cavity mode. In the strong-coupling regime, the generated photon pairs can be maximally entangled in qualitative agreement with the dressed-state predictions of Johne et al. [Phys. Rev. Lett. 100, 240404 (2008)]. We derive useful analytical formulas for the spectrum of the emitted photon pairs in the presence of exciton and biexciton broadening, which is necessary to connect to realistic experiments and demonstrate the important differences with the approximate dressed-state approach. We also present a method for calculating and optimizing the entanglement between the emitted photons, which can account for postsample spectral filtering. Pronounced entanglement values of greater than 80% are demonstrated using experimentally achievable parameters even without spectral filtering.

arXiv:0812.2474•Physical Review B•May 18, 2009•35 citations

Single-photon nonlinearity of a semiconductor quantum dot in a cavity

D. Sanvitto, Fabrice P. Laussy, Frank Bello +6 more

A single atom in a cavity is the model system of cavity quantum electrodynamics (CQED). The strong coupling regime between the atom and cavity-confined photon corresponds to the reversible exchange of energy between the two modes, and underpins a wide range of CQED phenomena with applications in quantum information science, including for example as quantum logic gates and as sources of entangled states. An important advance was achieved recently when strong coupling between excitons and cavity photons was reported for the first time for localized quantum dots (QDs) in micron-size solid state cavities. This has significance in terms of scalability and integration with other optical devices, and could lead to the emergence of "quantum optics on a chip" technology. However the results presented so far for quantum dots are in the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi splitting); they are not a true QED effect and can equally well be described by classical physics as the coupling between two oscillators. In this paper, we present evidence for a purely quantum phenomenon for the QD/cavity photon system, namely the increase in splitting of the levels when the mean number of photons in the cavity is increased. This corresponds to non-linearities on the single-photon scale: the presence of a single excitation in the cavity changes the level structure, affecting the emission energies for a second photon. Such results are a first step in demonstrating the promise of quantum dots for CQED applications.

arXiv:cond-mat/0612034•Dec 1, 2006•0 citations

Entanglement for excitons in two quantum dots placed in two separate single-mode cavities

Gao‐xiang Li, Hua-Tang Tan, Shao‐ping Wu +1 more

The dynamical behavior of entanglement for excitons in two quantum dots placed in two separately single-mode optical cavities driven by an external broadband two-mode squeezed vacuum is studied in the low exciton density regime. It is found that if the field in the two separate cavities is initially prepared in a pure two-mode squeezed vacuum state, the excitons in the two quantum dots can evolve into a pure entangled state only when the dissipation of the cavities and exciton modes is negligible. When the effect of the dissipation is included, the excitons will be in a two-mode Gaussian entangled mixed state whose properties are decided by the externally driven field and the initial field. The dependence of the entanglement property of the excitons in the two quantum dots on the squeezing properties of the fields in the two cavities is also discussed.

Physical Review A•Sep 29, 2004•16 citations
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 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.
We present a formal theory of single quantum dot coupling to a planar photonic crystal that supports quasidegenerate cavity modes and use this theory to describe and optimize entangled-photon pair generation via the biexciton-exciton cascade. In the generated photon pairs, either both photons are spontaneously emitted from the dot or one photon is emitted from the biexciton spontaneously while the other is emitted via the leaky cavity mode. In the strong-coupling regime, the generated photon pairs can be maximally entangled in qualitative agreement with the dressed-state predictions of Johne et al. [Phys. Rev. Lett. 100, 240404 (2008)]. We derive useful analytical formulas for the spectrum of the emitted photon pairs in the presence of exciton and biexciton broadening, which is necessary to connect to realistic experiments and demonstrate the important differences with the approximate dressed-state approach. We also present a method for calculating and optimizing the entanglement between the emitted photons, which can account for postsample spectral filtering. Pronounced entanglement values of greater than 80% are demonstrated using experimentally achievable parameters even without spectral filtering.
A single atom in a cavity is the model system of cavity quantum electrodynamics (CQED). The strong coupling regime between the atom and cavity-confined photon corresponds to the reversible exchange of energy between the two modes, and underpins a wide range of CQED phenomena with applications in quantum information science, including for example as quantum logic gates and as sources of entangled states. An important advance was achieved recently when strong coupling between excitons and cavity photons was reported for the first time for localized quantum dots (QDs) in micron-size solid state cavities. This has significance in terms of scalability and integration with other optical devices, and could lead to the emergence of "quantum optics on a chip" technology. However the results presented so far for quantum dots are in the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi splitting); they are not a true QED effect and can equally well be described by classical physics as the coupling between two oscillators. In this paper, we present evidence for a purely quantum phenomenon for the QD/cavity photon system, namely the increase in splitting of the levels when the mean number of photons in the cavity is increased. This corresponds to non-linearities on the single-photon scale: the presence of a single excitation in the cavity changes the level structure, affecting the emission energies for a second photon. Such results are a first step in demonstrating the promise of quantum dots for CQED applications.
The dynamical behavior of entanglement for excitons in two quantum dots placed in two separately single-mode optical cavities driven by an external broadband two-mode squeezed vacuum is studied in the low exciton density regime. It is found that if the field in the two separate cavities is initially prepared in a pure two-mode squeezed vacuum state, the excitons in the two quantum dots can evolve into a pure entangled state only when the dissipation of the cavities and exciton modes is negligible. When the effect of the dissipation is included, the excitons will be in a two-mode Gaussian entangled mixed state whose properties are decided by the externally driven field and the initial field. The dependence of the entanglement property of the excitons in the two quantum dots on the squeezing properties of the fields in the two cavities is also discussed.