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arXiv:0906.4734

Controlling the transverse correlation in QPM parametric down-conversion

Olavo Cosme, A. Delgado, G. Lima, Carlos Henrique Monken, Sebastião Pádua

Published Jun 25, 2009• 0 citations
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Abstract

In this work we study the transverse spatial correlation of the pair of photons generated via the process of spontaneous parametric frequency down-conversion, in periodically poled non-linear crystals illuminated by a pulsed laser beam. It is well known that the two-photon state generated in quasi-phase matching (QPM) configurations depends explicitly on the characteristics of the pump beam, on the crystal modulated non-linearity, and on the detection geometry. This has allowed the development of several techniques for controlling the biphoton spectral and spatial properties. Here we discuss another technique for implementing the spatial entanglement modification in QPM gratings. We show, theoretically and experimentally, that in nearly collinear geometries, the spatial shape modulation of the pump beam allows for the control of the biphoton transverse spatial correlation.

DOI
10.48550/arxiv.0906.4734

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In this work we study the transverse spatial correlation of the pair of photons generated via the process of spontaneous parametric frequency down-conversion, in periodically poled non-linear crystals illuminated by a pulsed laser beam. It is well known that the two-photon state generated in quasi-phase matching (QPM) configurations depends explicitly on the characteristics of the pump beam, on the crystal modulated non-linearity, and on the detection geometry. This has allowed the development of several techniques for controlling the biphoton spectral and spatial properties. Here we discuss another technique for implementing the spatial entanglement modification in QPM gratings. We show, theoretically and experimentally, that in nearly collinear geometries, the spatial shape modulation of the pump beam allows for the control of the biphoton transverse spatial correlation.
The two-photon state generated by spontaneous parametric down-conversion (SPDC) exhibit spatial entanglement embedded in the corresponding mode function. The control of the spatial characteristics of the generated two-photon state is an issue of paramount importance. For example, the spatial entanglement of the two down converted photons forms the basis of quantum imaging, and entanglement in orbital angular momentum has opened a new scenario for implementing multidimensional Hilbert spaces. We put forward several techniques to engineer the spatial structure of entangled two-photon states generated in SPDC. The first strategy we consider for spatial control of the quantum state makes use of the direct manipulation of the pump beam. This technique makes feasible to prepare arbitrary engineered entangled states in any d-dimensional Hilbert space. The second strategy is based on the proper preparation of the down-converting crystal itself, namely quantum state manipulation by quasi-phase-matching (QPM) engineering. We use properly designed transversely varying QPM gratings in nonlinear crystals.
Here we investigate the all-optical control of spectral correlations in spontaneous parametric down-conversion. We show that when photon pairs are projected onto high-order spatial modes, the spatial structure of the pump field defines the phase-matching function of the nonlinear interaction. Thus, by structuring the pump field in both space and spectrum, the biphoton spectral correlations are fully controlled. Considering a standard periodically-poled crystal as the nonlinear medium, we show that the Gouy phase matching method proposed here can generate both spectrally uncorrelated and high-dimensional spectrally entangled photon pairs, similarly to what is achieved with aperiodically-poled crystals. Furthermore, we show that our method can generate a wider class of quantum states if the pump field is a spatiotemporal wavepacket, that is, if its spatial and spectral structures are correlated.
The spectral properties of entangled photon pairs generated via quasi-phased matching in spontaneous parametric down-conversion are proposed and demonstrated experimentally.A general mathematical model for evaluating the spectral properties is developed to obtain the spectrum shape and range of down-converted photons.The model takes into account the effects of phase mismatching due to non-ideal pumping and the relationship between crystal periodic modulation function and the incidence angle of the pump beam.The spectrum curve shape is determined by the discrete Fourier transform of a Gaussian pump beam and the integration of parametric down-conversion generated by an individual plane wave.An experiment is carried out with a PPLN non-linear crystal and dispersing optics, which shows a good consistency in their spectral ranges and shapes with our model predictions within the spectrum of 600-633 nm.This therefore illustrates that both the simulation model and the experimental process are reasonable.This novel method has potential applications in high-accuracy calibration in the wide spectrum using correlated photons.
We propose the generation of two-channel time-energy entangled twin photons based on two simultaneous first-order quasi-phase-matched (QPM) spontaneous parametric down-conversion processes in a periodically poled lithium niobate (PPLN) with a monochromatic pump. The theoretical model for the generation of the entangled photons is established, and the analytical solution is obtained in a lossless crystal with an undepleted pump assumption. The generated condition of entangled photons is achieved in terms of the QPM grating period and the pump wavelength. It is shown that two channels of entangled twin photons with different wavelengths can be created by suitably choosing the PPLN grating period once the pump wavelength is fixed, which provides the potential to introduce the wavelength division multiplexed technique into quantum information systems.
The results of quantum analysis of the light generated by consecutive and simultaneous quasi-phase-matched (QPM) wave interactions in periodically poled nonlinear crystals (PPNCs) are presented. In the case of the consecutive interactions of waves with multiple frequencies ω, 2ω and 3ω, the parametric amplification at low-frequency pumping is investigated. Generation of the quadrature-squeezed light at frequencies ω and 3ω in the 2ω frequency pumping field, the photon statistics and correlation as well as the entanglement properties for photons produced at different frequencies are studied. In the case of simultaneous QPM spontaneous parametric down-conversion processes in single PPNC, the main attention is paid to obtaining the polarization-entangled states at the collinear geometry of the wave interaction.