- [] Nonlinear aspects of quantum plasma physics
- Nonlinear aspects of quantum plasma physics
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- Nonlinear Waves: Classical and Quantum Aspects

This procedure allows us to infer the relative phases between wavefunction elements up to the phases of signal and idler beams from the output of waveguide 1 Figure 3b. The predicted wavefunction phases are shown in Figure 3c. Supplementary Information , which precisely characterizes the degree of spatial entanglement and cannot be obtained with only photon correlations.

Measurement of the relative phases between wavefunction elements by SFG. Signal and idler beams are split and recombined with a network of fibre couplers and injected into the three waveguides with a fibre V-groove array.

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An electro-optic phase modulator is used to generate an interference pattern between the sum-frequency fields generated from the combinations of signal and idler beams in waveguides 2—3 and waveguides SFG and signal-idler beams are collected in free-space at the output of waveguide 1 with a lens of 0. A wavelength-division multiplexer not shown in the figure is used to separate signal and idler wavelengths.

Solid red line is the theoretical fit see Supplementary Information for details. Waveguide 1 is the fixed reference for all the phase measurements.

See Supplementary Information for a calculation of the error bars. The SFG characterization method proposed here provides a practical path for characterization and development of monolithically integrated networks that for devices similar to ours can be four orders of magnitude faster than the equivalent quantum measurements and with two orders of magnitude greater accuracy Supplementary Information. In the future it will be of interest to explore how the SFG analogy can be applied to larger photon number states generated through SPDC.

All the beams were collected in free-space at the output of the waveguides with a lens with 0. SFG and signal-idler wavelengths were separated with a dichroic mirror.

SFG power from the output of waveguide 1 and signal-idler powers from the outputs of all three waveguides were then measured with two standard power meters. The measured powers were corrected for Fresnel losses at the chip interface and used to calculate the SFG conversion efficiency at the output of the array. SFG conversion efficiencies for the single channel inputs were measured by combining signal and idler beams with a fibre coupler. The measurement process was automated with Labview.

The three outputs were collected with a fibre V-groove array, and photon coincidences between each pair of waveguides were measured with two gated InGaAs avalanche photodiodes and a time-tagging module. Photon coincidences from the single channels were measured by splitting signal-idler photons with a fibre coupler. Absolute photon pair generation rates were calculated by discretization of equation 2 through the relation.

## [] Nonlinear aspects of quantum plasma physics

The pump power P p was measured during the SPDC characterization from the first output of the fibre array. Relative squared amplitudes of the wavefunction elements were calculated as.

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At each step we assigned to the two correlation matrices a random value calculated from a normal distribution with a sigma given by the error in the measurements. Average value and error in the fidelity were finally calculated from the simulated distribution. For SFG-power measurements second-harmonic generation SHG contributions were first measured by inputting signal and idler beams into each channel individually. The procedure was repeated and automated with Labview.

FL wrote the manuscript with contributions from all authors.

## Nonlinear aspects of quantum plasma physics

On-chip generation of heralded photon-number states. Sci Rep ; 6 : Generation of nonclassical biphoton states through cascaded quantum walks on a nonlinear chip. Phys Rev X ; 4 : On-chip quantum interference between silicon photon-pair sources. Nat Photonics ; 8 : — Path-entangled photon sources on nonlinear chips.

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Rev Phys ; 2 : 19— Towards quantum supremacy with lossy scattershot boson sampling. New J Phys ; 18 : Reference-frame- independent quantum-key-distribution server with a telecom tether for an on-chip client. Phys Rev Lett ; : Complete characterization of quantum-optical processes.

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## Nonlinear Waves: Classical and Quantum Aspects

Measurement of qubits. Phys Rev A ; 64 : High-resolution spectral characterization of two photon states via classical measurements. Laser Photon Rev ; 8 : L76—L Fast and highly resolved capture of the joint spectral density of photon pairs. Optica ; 1 : — Bi-photon spectral correlation measurements from a silicon nanowire in the quantum and classical regimes.

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Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential. Notre catalogue. Livres Education. Konotop, Fatkhulla Abdullaev - Springer Livres. Produit indisponible. Description Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices including quantum and nonlinear lattices , and nonlinear optics and photonics.

Livres Education Solid-state physics.