We investigate production of three-photon states in cascaded parametric down-conversion (PDC). The analysis includes preparation of Greenberger-Horne-Zeilinger polarization-entangled states in cascaded type-II and type-I PDC in the framework of considering the dual-grid structure that involves two periodically poled crystals. Considering cascaded optical parametric oscillator (OPO) driven by a sequence of laser pulses with Gaussian time-dependent envelopes, we investigate quantum statistical properties of high intensity mode generated in intracavity three-photon splitting. Calculating the normalized third-order correlation function below-and at the generation threshold, we demonstrate that in the pulsed regime, depending on the duration of pulses and the time-interval separations between them, the degree of three-photon-number correlation essentially exceed the analogous one for the case of continuous pumping.
The formation of 2D and 3D photonic lattices by Bessel standing wave and combined interferometric-mask techniques
is performed with the use of cw 532 nm laser beam in photorefractive lithium niobate crystal doped with Fe and Fe, Cu
impurity ions. The non-uniform intensity distribution of the beams is imparted into the irradiating photorefractive
medium via electro-optic effect thus creating micro- and nano-scale 2D and 3D refractive index gratings with new
symmetries and properties. Non-diffracting Bessel standing wave technique provides the recording of high contrast 2D
photonic lattices which is the combination of annular and planar gratings with the period of ~9 μm in radial direction
and half-wavelength period of 266 nm in azimuthal direction. The created by combined interferometric-mask technique
3D photonic lattices can be represented as numerous mask-generated 2D quasi-periodic structures located in each antinode
of the standing wave. The formed 3D gratings have ~ 30 μm period in radial and azimuthal directions and 266 nm
in axial direction. The 2D and 3D gratings were interrogated by diffraction of low intensity Gaussian probe beams from
the recorded structures, as well as by direct observation by phase microscope.
We investigate production of three-photon and four-photon states in cascaded parametric processes of photon splitting
and summing in χ (2)nonlinear media, under action of pump field. Generation of photon triplets using simultaneously phase
matched three-photon processes: ω0↔ω1+ω2 , ω2↔ω1+ω1 , is considered in dual-grating layered structure that involves
nonlinear and linear segments. The production of heralded two-photon entangled states from three-photon states is analyzed
for this configuration by using the method of conditional detection of auxiliary photons. Cascaded four-photon downconversion
based on simultaneously phase matched three-photon processes: ω0↔ω2 +ω2 , ω2↔ω1+ω1 is arranged for
phase-reversed configuration. The effects of correlation between photons in both three-photon and four-photon states is
analyzed in the regimes of amplification of corresponding modes at the frequency of three-photon downconversion
ω1 = ω0/3 and the frequency of four-photon down-conversion ω1 = ω0/4respectively for both cascaded systems.
Recently, superconducting artificial atom has been justified experimentally as an ideal element for various
applications including circuit quantum electrodynamics realizing strong-coupling limit. Some of the proposed
systems in this area are usually described in terms of the quantum anharmonic oscillator and display quantum
dynamics in macroscopic level, giant nonlinearity as well as very strong coupling with external field and strong
coupling with an environment. In this report, we investigate the quantum properties of an artificial atom as a
model of multilevel anharmonic oscillator in the framework of photon number distributions as well as the Wigner
functions. We concentrate on the regimes of strong driving and giant nonlinearity that allow us to consider
artificial atom on the level of few excitation numbers.
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