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Journal of the Optical Society of America B

Propagation of the twin-beam state from the near field to the far field

Justinas Galinis, Ondřej Haderka

Published Oct 24, 2017• 2 citations
Publisher

Abstract

The evolution of the twin-beam state propagating in free space is investigated theoretically using the Schmidt decomposition method. The influence of the spatially chirped pump beam on the twin beams is discussed. We use a theoretical model to analyze and discuss the experimental results of the twin-beam properties in the transition from the near-field to the far-field regime published by Haderka et al. [Sci. Rep.5, 14365 (2015)SRWSDA2045-232210.1038/srep14365]. Evolution of both radial and azimuthal cross-correlations from the near field to the far field is investigated, discussing the influence of the pump spatial spectrum and the phase matching conditions.

DOI
10.1364/josab.34.002406

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Quantum correlations in the spatial domain hold great promise for applications in quantum imaging, quantum cryptography and quantum information processing, owing to the infinite dimensionality of the associated Hilbert space. Here, we present a theoretical investigation, complemented by experimental measurements, of the propagation dynamics of the spatial quantum correlations in bright structured twin beams generated via a four-wave mixing process in a double-ΛΛΛ configuration in atomic vapor. We derive an analytical expression describing the evolution of the spatial quantum correlation distribution from the near field to the far field. To qualitatively support the theoretical predictions, we perform experiments measuring intensity-difference noise between different spatial subregions of the twin beams as they propagate from the near field to the far field. The presence of quantum correlations is manifested as squeezing in the intensity difference noise measurement. With a Gaussian pump, we observe localized correlations in the near field and localized anti-correlations in the far field. In contrast, with a structured Laguerre-Gaussian pump, there is a transition from localized correlations in the near field to delocalized correlations in the far field. The present results offer valuable insights into the fundamental behavior of spatial quantum correlations and open possibilities for potential applications in quantum information, quantum imaging and sensing.
Strong correlations between the signal and idler beams imprinted during their generation dominantly determine the properties of twin beams. They are also responsible for the waves in intensity coherence observed in the wave-vector space of a twin beam propagating in a nonlinear crystal in the regime with pump depletion. These waves start to develop at certain twin-beam intensities and move from the signal- and idler-beam centers towards their tails. They manifest themselves via the change of coherence volume monitored in the far field by the measurement of local modified g‾(2){\overline{g}}^{(2)}g​(2) function, which acts as a sensitive and stable tool for investigating field intensity coherence.
Abstract Properties of intense twin beams generated in parametric down-conversion in periodically poled LiNbO3 crystals and their chirped variants by intense pump fields are analyzed along the model of intense parametric down-conversion that allows for pump depletion and uses the dual spatio-spectral Schmidt modes. Spectral and spatial intensity auto- and cross-correlation functions are determined as they depend on the pump power. Temporal correlations in intense twin beams at the fs time scale are investigated using the Hong-Ou-Mandel interferometer and the process of sum-frequency generation.
Spatiospectral properties of twin beams at their transition from low to high intensities are analyzed in parametric and paraxial approximations using decomposition into paired spatial and spectral modes. Intensity auto- and cross-correlation functions are determined and compared in the spectral and temporal domains as well as the transverse wave-vector and crystal output planes. Whereas the spectral, temporal, and transverse wave-vector coherence increases with the increasing pump intensity, coherence in the crystal output plane is almost independent of the pump intensity owing to the mode structure in this plane. The corresponding auto- and cross-correlation functions approach each other for larger pump intensities. The entanglement dimensionality of a twin beam is determined with a comparison of several approaches.