Lett Sample Clauses

Lett. The most popular variety of quantum entanglement involves the polarization degree of freedom of two photons; in this case we deal obviously with two (polarization) modes per photon [7, 8, 23]. Recently, there has been a lot of interest in spatial entanglement of two photons; in this case the number of modes per photon can be much larger than two so that entanglement is correspondingly (in fact, exponentially) richer [89–91, 99–103]. This in- terest is motivated, fundamentally, by the desire to understand the nature of quantum en- tanglement in a high-dimensional Xxxxxxx space. From the point of view of applications the high-dimensional case is important since it holds promise for implementing high-dimensional alphabets for quantum information, e.g. for quantum key distribution [104]. A popular ba- sis for the spatial modes is the basis in which the modes are distinguished on account of their orbital angular momentum (OAM) [100–102]. An issue of much discussion in high- dimensional entanglement, OAM or otherwise, is how many modes are involved, beyond the statement that this number is (much) larger than 2 [39, 99–102, 105]. In this chapter we demonstrate a practical method to quantify the number of OAM spatial modes involved in biphoton entanglement; in our experiment this number has been varied in a controlled way from 1 to 8. This result has been achieved by using a special two-photon interferometer. Our two-photon interferometer contains an image rotator in one of its arms (see Fig. 9.1). Similar interferometers with built-in rotation have only been tested at the one-photon level, where the rotation has been linked to a topological (Berry) phase [106]. A one-photon in- terferometer with an image reversal has been shown to act as a sorter between even and odd spatial modes [107, 108]. We will instead consider two-photon interference in an interferom- eter with built-in rotation. In two-photon interference experiments, two photons are combined on a beamsplitter, before being detected. These experiments, which have been pioneered by Xxxx, Ou and Xxxxxx (HOM) [27], demonstrate an effective bunching between the photons in each pair, but only if the optical beams have good spatial and temporal overlap. More recent versions of these “HOM” experiments study the generation of spatial anti-bunching [90], and the effect of a modified pump profile (TEM01 versus TEM00) on the interference pattern (bunching versus anti-bunching) [89, 91]. The key question that we will...
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