ENCODING and decoding images FOCUS continuous-wave pump laser with hundreds of mW intensity, the probability of generating a double-pair is negligible and the output state is well described by a two-photon state of the form
| ψ
> ≈ C 0 | 0
> + C 1∑Ψ kl a † k a † l | 0 k, l
>,( 1) where C 0 and C 1 are normalization coefficients( C 0 >> C 1), a † k is the creation operator of a photon in the mode k of the electromagnetic field( spatial, spectral, and polarization) and Ψ kl is the two-photon wavefunction.
The properties of Ψ kl – and thus those of the quantum correlations of the photons emitted by the source – are entirely determined by the characteristics of the pump laser and the crystal used. On the one hand, engineering the crystal parameters allows modification of the phasematching conditions( Figs. 1b and c), thereby changing the properties of the state. This is the case, for
Figure 1. a, Illustration of the spontaneous parametric down conversion( SPDC) process. b, Momentum and c energy conservation in SPDC.
example, when using periodically poled crystals [ 7 ]. On the other hand, one can also modify the properties of the pump laser, such as its wavelength or spatial structure. This latter approach, known as pump shaping, is particularly attractive since it allows for adaptive and dynamic control of the two-photon state. Over the past years, many research teams have started using it to optimize their states for specific applications [ 8 ]. In this article, we describe an approach that exploits this idea to tailor the spatial correlations between photon pairs in the form of arbitrary objects.
ENCODING AND DECODING IMAGES A key feature of SPDC is the transfer of the pump beam first-order spatial coherence to the down-converted photon pairs’ second-order coherence. Our approach, illustrated in Figure 2a, leverages this property by placing an object and a thin nonlinear crystal at the front and back focal planes of a lens. In such a configuration, the crystal is effectively illuminated with a pump that has the shape of the transverse spatial Fourier transform of the object. Due to momentum conservation( Fig. 1b), the structure of the photon pairs spatial correlations
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