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Publication# Multimode entanglement in coupled cavity arrays

Timothy Chi Hin Liew, Vincenzo Savona

*Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft, *2013

Journal paper

Journal paper

Abstract

We study a driven-dissipative array of coupled nonlinear optical resonators by numerically solving the von Neumann equation for the density matrix. We demonstrate that quantum correlated states of many photons can also be generated in the limit where the nonlinearity is much smaller than the losses, contrary to common expectations. Quantum correlations in this case arise from the interference between different pathways that the system can follow in the Hilbert space to reach its steady state under the effect of coherent driving fields. We characterize, in particular, two systems: a linear chain of three coupled cavities and an array of eight coupled cavities. We demonstrate the existence of a parameter range where the system emits photons with continuous-variable bipartite and quadripartite entanglement, in the case of the first and the second system, respectively. This entanglement is shown to survive realistic rates of pure dephasing and opens up a new perspective for the realization of quantum simulators or entangled photon sources without the challenging requirement of strong optical nonlinearities.

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A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its

Photon

A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic

Density matrix

In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of a

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A quantum dot is a semiconductor nanostructure that confines the motion of conduction band electrons and valence band holes in all three spatial directions, thus creating fully discrete energy levels. The confinement in the InAs/GaAs material system is generated by the bandgap difference for the two materials (∼ 0.4 eV for InAs, and ∼ 1.4 eV for GaAs) which provides a minimum of potential energy for both electrons and holes inside the InAs nanoparticle. The appearance of new nanoscale effects modifies the electro-optical properties of such a system which makes possible the improvement of existing device performance or even fascinating novel device applications. For the creation of coherent structures with very high purity and high density, as it is required for application in light emitting devices, self-assembling is a very important pathway. The quantum dot creation mostly relies on the relaxation of the strain accumulated during the growth of lattice mismatched materials, which happens in a non-equlibrium condition. This results in a statistical distribution of all the parameters characterizing the InAs nanocrystals as size, composition and strain, whose direct manifestation is the inhomogeneously broadened light emission deriving from quantum dot ensembles. At the dawning of the quantum dot development the broadening was considered as a limiting factor for application in semiconductor lasers. Today, it is considered favorably for all the applications where a broad gain spectrum is required as optical amplifiers, monolithic and external-cavity tunable lasers, and superluminescent diodes. The objective of this thesis is the application of InAs/GaAs self-assembled quantum dots to the active region of high power and broad-band superluminescent diodes emitting in the 1.3 μm wavelength region. Superluminescent diodes are edge-emitting semiconductor light sources based on the amplification of spontaneous emission along a waveguide where optical gain is achieved through current injection. They combine the high power and brightness of laser diodes with the low coherence of LEDs. The latter is a fundamental feature for the application in optical coherence tomography medical imaging, where the image resolution is related to the spectral bandwidth of the light source used. The achievement of bandwidths larger than 100 nm are demonstrated in this work through the optimization of molecular beam epitaxy growth conditions. This may be done optimizing the statistical size-dispersion of the dot ensemble, or through the use of different dot layers emitting at slightly different wavelengths. The large bandwidth emission is obtained also due to the peculiar energy structure of this material, for which a multi-state emission appears under particular injection conditions. As a term of comparison, best commercial single-chip superluminescent diodes for the imaging application at 1.3 μm show bandwidths around 60 nm. Moreover, the discrete nature of the energy levels in InAs quantum dots together with the implementation of a GaAs-based technology can be beneficial for the device temperature stability (the competing technology, based on InP, suffers from strong thermal degradation). The analysis and understanding of the device temperature characteristics will be detailed in the last chapter of the manuscript. Even though standard devices show an important temperature dependence, a better stability may be achieved through the use of p-doped active regions. In the last few years quantum dot devices have shown outstanding properties if compared to the competing quantum well technology. Low threshold currents, high temperature stability and low chirp in lasers, large bandwidths and low gain saturation in amplifiers have been demonstrated. However, in spite of the large interest among the scientific community, many of the microscopic processes at the origin of the electro-optical characteristics of this material are not completely understood yet. The physics of the quantum dot active material, will be modeled in this work through the use of systems of rate equations with different complexity depending on the system they are applied to. We will provide a mean-field rate equation model allowing to get insights about carrier dynamics in QD lasers. Also, we will develop two different traveling-wave rate equation models, one for the modeling of the L-I characteristics and the other for the modeling of the spectral characteristics of quantum dot superluminescent diodes. Considering the carrier and photon density distributions across the device cavity is essential in superluminescent diodes, where the high single pass gain results in large non-homogeneities of photon and carrier distributions. The work is motivated by an industrial cooperation with EXALOS AG, a leading company in the development, manufacturing, and sales of broadband superluminescent diodes.

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