Hologram of a single photon

Abstract

The complete characterization of a quantum wavefunction of an unknown photon presents a challenging task whose difficulty lies particularly in the retrieval of its local phase variations. This is caused by the fundamental property of single photons i. e. their entirely indeterminate global phase following from the perfect rotational symmetry of their Wigner functions in the phase space [14], which precludes the application of interferometric techniques such as optical holography utilizing fixed phase relation between investigated and reference light. Therefore the characterization of photon's spatial structure has never benefited from the precision and a simplicity provided by the holography methods [12,13] but as yet has been tackled only using indirect tomographic techniques [15] or weak values measurements [2].In this paper, we experimentally show that the hologram of a single photon (HSP) encoding full information about its spatial structure given by the quantum wavefunction ψ(x) = x|ψ [2] can be recorded if the first-order interference of optical fields is replaced by the non-classical interference of spatially varying two-photon probability amplitudes. The idea of HSP, sketched in Fig. 1a, relies on overlapping the unknown photon |ψ u of an arbitrary local phase profile ϕ(x) = arg(ψ u (x)) with a reference photon |ψ r having the constant local phase profile on a beam splitter, both photons occupying similar spectral (temporal) modes. Afterwards we measure positions of photons which coincidentally left two distinct output ports of the beam splitter parametrized by x and x coordinates. Any feature distinguishing photons, such as local difference between their quantum wavefunctions ψ u (x) and ψ r (x) prevents them from ideal two-photon coalescence known as Hong-Ou-Mandel effect [16], thus the observation of spatially localized coincidences (x, x ) serves as a sensitive probe of the spatial structure of the unknown photon. As we visualize in Fig. 1b, such a coincidence event can originate either from transmission or reflection of both photons at the beam splitter. These two Figure 1. Quantum interference of two spatially structured photons. a, In analogy to classical holography we repeatedly overlap an unknown photon |ψu with a reference (known) photon |ψr with the constant local phase profile on a 50/50 beam splitter and we spatially localize coincidence events in x and x , measuring their joint probability distribution |Ψ(x, x )| 2 which is sensitive to any differences between the quantum wavefunctions of the photons ψu(x) and ψr(x) including the local variations of their phases. b, The spatially localized coincidence events (x, x ) originate from the nondestructive interference of probability amplitudes of two classically exclusive, but quantum-mechanically coexisting scenarios: (left) the unknown photon in x and the reference photon in x have passed through the beam splitter, (right) both photons localized conversely in x and x have been reflected from the beam splitter.

Imaging with quantum states of light

“…The authors had previously shown that the intensified CMOS camera they used was able to perform spatially resolved multiphoton counting [75]. This work led to subsequent demonstrations using a similar setup, such as the acquisition of holograms in a single photon regime [76], the demonstration of bi-photon mode engineering for quantum-enhanced interferometry [77], and the demonstration of a wave-vector multiplexed quantum memory for photons interacting with cold atoms [78].…”

Experimental quantification of four-photon indistinguishability

“…The first layer of the interferometer is realized by inserting two beam splitters (BS) on input modes 2 and 5. In this way the four-photon input is probabilistically split to six modes (1,2,3,4,5,6). Each BS of the first layer is realized with a half-wave plate and a PBS.…”

“…Photon indistinguishability is a key concept in quantum physics, which can be characterized via two-particle interference [1]. From the first experimental observation carried out using entangled photons produced by a parametric down-conversion source [2], the quantum signature of this phenomenon, known as Hong-Ou-Mandel (HOM) effect, has proved to be essential for tasks such as characterization of single photon sources, practical protocols of quantum communication [3][4][5] and quantum computation. Recent proposals use twophoton interference for the realization of two-qubit gates, essential elements for photon-based quantum computing schemes [6].…”

Mapping and measuring large-scale photonic correlation with single-photon imaging

“…Thankfully, recent advances of charge-coupled device (CCD) cameras make it possible to directly image spatial output results at a single-photon level [17][18][19][20][21][22][23][24]. HOM interference was also successfully verified by low-noise correlation detection on two modes with an intensified camera [25].…”

“…In practice, it may still be acceptable to place single photon detector behind each spatial mode for comparably small systems [9, 14-16]. However, it will become both technically challenging and economically unfeasible to address thousands of modes simultaneously with single photon detectors, and therefore become a decisive bottleneck preventing from detecting state spaces large enough for real quantum applications.Thankfully, recent advances of charge-coupled device (CCD) cameras make it possible to directly image spatial output results at a single-photon level [17][18][19][20][21][22][23][24]. HOM interference was also successfully verified by low-noise correlation detection on two modes with an intensified camera [25].An alternative and elegant approach we present in this work is to convert the modes in different degrees of freedom into the modes in position, and then measure all the spatial modes accordingly by the large number of units in singlephoton-sensitive cameras.…”