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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Quantum phase properties of impeded second-harmonic generation

Vlasta Peřinová, A. Lukš, J. Křepelka

Published Apr 1, 1998• 2 citations
Publisher

Abstract

Using the statistical characteristics of the photon number, quantum phase and field quadratures, based on the preferred phase, we have demonstrated a Kerr-like behaviour for the cascaded second-order nonlinearities and have studied thoroughly the oscillations superimposed on the Kerr-like trend for an input coherent state. We have performed a global study over the entire quantum period in an idealized model of the trend of this process based on the lossless Kerr progression.

DOI
10.1088/1355-5111/10/2/011

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Using the statistical characteristics of the photon number, quantum phase and field quadratures, based on the preferred phase, we have demonstrated a Kerr-like behaviour for the cascaded second-order nonlinearities and have studied thoroughly the oscillations superimposed on the Kerr-like trend for an input coherent state. We have performed a global study over the entire quantum period in an idealized model of the trend of this process based on the lossless Kerr progression.
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Abstract We demonstrate theoretically cascaded fourth and second harmonics generation in a periodically oriented nonlinear crystal with a half-order of the periodical orientation. We consider a cascaded process in which four photons of the fundamental harmonic are initially converted into an intermediate photon of the fourth harmonic, which parametrically decays at the second stage into two photons of the second harmonic. We show that fractional phase matching can be achieved by using an asymmetric periodically poled grating. To describe the propagation and transformation of light inside a nonlinear crystal, the quantum spatial Heisenberg equations have been applied, using which the average numbers of photons of the fourth and second harmonics have been calculated as functions of the nonlinear crystal length.
In the first part of this thesis, we investigate the propagation of quantum fluctuations in a nonlinear interferometer comprising under conditions of harmonic generation by computer simulations. This investigation assumes idealized conditions such as lossless and uniform nonlinear media, an ideal cavity and ideal photodetectors. After linearizing wave equations for harmonic generation with a coherent state input, we obtain equations for one dimensional spatial propagation of the mean field and quantum fluctuations for initial conditions set by arbitrary interferometer phase. We discover that fluctuations are de-squeezed in the X and Y quadratures as the interferometer phase is tuned. However, we discover that there is are quadratures P-Q obtained by rotating the X-Y quadratures for which squeezing is improved by factors of 10^9. We present a practical idea to implement rotation of X quadrature fluctuations to the Q quadrature by using an ideal empty optical cavity. Signal-to-Noise ratio of the nonlinear interferometer was calculated and compared with that of a linear interferometer with coherent state input. We calculated a maximum performance improvement of a factor of 60 for a normalized propagation length ζ0 = 3 under ideal conditions. In the second part of this thesis, we investigate experimentalarrangements to transfer atomic coherence from light to cesium atoms. We discuss the experimental arrangement to generate coherence under conditions of electromagnetically induced transparency (EIT). We measure a continuous wave EIT width of 7.18 MHz and present results for pulsed arrangements.
We study the statistical properties of squeezed Kerr states generated by squeezing, with a two-photon parametric process, the output of a Kerr medium whose input is coherent light. The squeezing has the effect of allowing the photon statistics to depend on the Kerr nonlinearity. Without the squeezing the statistics are Poissonian, but after squeezing they may be either sub-Poissonian or super-Poissonian. We also study the Q-function quasiprobability distribution for these states and related distributions associated with the quantum-mechanical phase. Finally, we show that quadrature squeezing can be enhanced and that squeezing and sub-Poissonian statistics can coexist.