Abstract
The content of this chapter is mainly based on the publication “Quantum entanglement of high angular momenta” (Fickler et al., Science 338:640, 2012, [1]). The chapter will describe a novel way of entangling two photons in the transverse spatial degree of freedom (DOF) in a very efficient, clean and flexible way. Moreover, it allows the entanglement of very higher-order modes, which carry a large amount of orbital angular momentum (OAM) quanta. To verify the generated entanglement of high OAM, a novel technique was developed to test the non-classicality of the state only by looking at its intensity structure. Both, the novel way to entangle two photons in the transverse spatial DOF and the new method for verifying entanglement, led to the demonstration of entanglement of the highest quantum number that has been experimentally shown till date.
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- 1.
As it was shown earlier, the photon state can be considered to be a vector polarization state with transverse spatially varying polarization. See Sect. 2.2.5 for more information.
- 2.
A measurement of the actual pump and down conversion wavelength identified both values to be 405.5 nm and 811 nm (at 30 \(^\circ \)C crystal temperature). However, in all later descriptions the wavelengths will be labeled with “405 nm” for the pump and “810 nm” for the down converted photon pairs.
- 3.
One should be careful with the term “macroscopic”. There is no generally accepted definition about when an object or a property connected to it, can be considered macroscopic. A possible and loose definition can be found in the paper of Leggett [10].
- 4.
The scope of the experiment in [17] is a different one. There, the focus was to increase the dimensionality of entanglement.
- 5.
In an earlier investigation [1] an erroneous witness was introduced and used to show entanglement. Here, we show that only for the highest OAM quanta, namely the state
, a direct evaluation of an entanglement witness is not tenable anymore. However, it is still possible to demonstrate that the measurements cannot be described by a separable state, hence the claims from [1] remain the same. - 6.
The accidental coincidences are calculated according to \(\textit{accs}=S_1*S_2*\tau \), where \(S_i\) labels the singles behind both slit-wheels \(i=1,2\) and \(\tau \) stands for the coincidence window.
, a direct evaluation of an entanglement witness is not tenable anymore. However, it is still possible to demonstrate that the measurements cannot be described by a separable state, hence the claims from [References
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Fickler, R. (2016). Entanglement of High Angular Momenta. In: Quantum Entanglement of Complex Structures of Photons. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-22231-8_3
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DOI: https://doi.org/10.1007/978-3-319-22231-8_3
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