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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.

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Genetically encoded fluorescent voltage indicators are ideally suited to reveal the millisecond-scale interactions among and between targeted cell populations. However, current indicators lack the requisite sensitivity for in vivo multipopulation imaging. We describe next-generation green and red voltage sensors, Ace-mNeon2 and VARNAM2, and their reverse response-polarity variants pAce and pAceR. Our indicators enable 0.4- to 1-kilohertz voltage recordings from >50 spiking neurons per field of view in awake mice and ~30-minute continuous imaging in flies. Using dual-polarity multiplexed imaging, we uncovered brain state–dependent antagonism between neocortical somatostatin-expressing (SST + ) and vasoactive intestinal peptide–expressing (VIP + ) interneurons and contributions to hippocampal field potentials from cell ensembles with distinct axonal projections. By combining three mutually compatible indicators, we performed simultaneous triple-population imaging. These approaches will empower investigations of the dynamic interplay between neuronal subclasses at single-spike resolution.