Spatial Characterization Of Two-Photon States - GAP-Optique
Spatial Characterization Of Two-Photon States - GAP-Optique
Spatial Characterization Of Two-Photon States - GAP-Optique
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Introduction<br />
The role of photons in quantum physics and technology is growing [1, 2, 17].<br />
Frequently, those applications are based on two dimensional systems, such as<br />
the two orthogonal polarization states of a photon, losing all information in<br />
other degrees of freedom. These applications only use a portion of the total<br />
quantum state of the light.<br />
The polarization itself is related to a broader degree of freedom. The angular<br />
momentum of the photons contains a spin contribution associated with<br />
the polarization, as well as an orbital contribution associated with the spatial<br />
distribution of the light (its intensity and phase). In general, the spin and<br />
the orbital angular momentum cannot be considered separately. However, in<br />
the paraxial regime both contributions are independent [18]. In this regime it<br />
is possible to exploit the possibilities offered by the infinite dimensions of the<br />
orbital angular momentum (oam) of the light.<br />
Currently available technology offers different possibilities to work with<br />
oam. Computer generated holograms are widely used in classical and quantum<br />
optics for generating and detecting different oam states [19, 20]. The efficiency<br />
of these processes has increased with the design of spatial light modulators<br />
capable of real time hologram generation [21].<br />
<strong>Of</strong> special interest is the generation of paired photons entangled in oam.<br />
Entanglement is a quantum feature with no analogue in classical physics. Spontaneous<br />
parametric down-conversion (spdc) is a reliable source for the generation<br />
of pairs of photons entangled in different degrees of freedom, including<br />
oam [22]. The existence of correlations in the oam of pairs of photons generated<br />
in spdc was proven experimentally by Mair and coworkers in 2001. Other<br />
nonlinear processes can be used to generate pairs of photons with correlations<br />
in their oam content. In reference [23], the authors show the generation of<br />
spatially entangled pairs of photons by the excitation of Raman transitions in<br />
cold atomic ensembles.<br />
Several studies illustrate the potential offered by higher-dimensional quantum<br />
systems. For instance, reference [24] reports a Bell inequality violation<br />
by a two-photon three-dimensional system, confirming the existence of oam<br />
entanglement in the system. Reference [25] introduced a quantum coin tossing<br />
protocol based on oam states. In reference [26], the authors present a quantum<br />
key distribution scheme using entangled qutrits, which are encoded into<br />
the oam of pairs of photons generated in spdc. And, in reference [12], the<br />
authors report the generation of hyperentangled quantum states by using the<br />
combination of the degrees of freedom of polarization, time-energy and oam.<br />
All the previously mentioned applications are based on specific oam correlations<br />
between the photons. However, there has been some controversy about<br />
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