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arXiv:2006.02580 · Quantum

Self-referenced hologram of a single photon beam

Wiktor Szadowiak, Sanjukta Kundu, Jerzy Szuniewicz, Radek Lapkiewicz

Published Aug 3, 2021• 4 citations
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Abstract

Quantitative characterization of the spatial structure of single photons is essential for free-space quantum communication and quantum imaging. We introduce an interferometric technique that enables the complete characterization of a two-dimensional probability amplitude of a single photon. Importantly, in contrast to methods that use a reference photon for the phase measurement, our technique relies on a single photon interfering with itself. Our setup comprises of a heralded single-photon source with an unknown spatial phase and a modified Mach-Zehnder interferometer with a spatial filter in one of its arms. The spatial filter removes the unknown spatial phase and the filtered beam interferes with the unaltered beam passing through the other arm of the interferometer. We experimentally confirm the feasibility of our technique by reconstructing the spatial phase of heralded single photons using the lowest order interference fringes. This technique can be applied to the characterization of arbitrary pure spatial states of single photons.

DOI
10.22331/q-2021-08-03-516

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Quantitative characterization of the spatial structure of single photons is essential for free-space quantum communication and quantum imaging. We introduce an interferometric technique that enables the complete characterization of a two-dimensional probability amplitude of a single photon. Importantly, in contrast to methods that use a reference photon for the phase measurement, our technique relies on a single photon interfering with itself. Our setup comprises of a heralded single-photon source with an unknown spatial phase and a modified Mach-Zehnder interferometer with a spatial filter in one of its arms. The spatial filter removes the unknown spatial phase and the filtered beam interferes with the unaltered beam passing through the other arm of the interferometer. We experimentally confirm the feasibility of our technique by reconstructing the spatial phase of heralded single photons using the lowest order interference fringes. This technique can be applied to the characterization of arbitrary pure spatial states of single photons.
Summary form only given. The spatial structure of a photon has proved to be indispensable resource allowing the experimental realization of free-space quantum cryptography or high dimensional entanglement. Although efficient methods for manipulating spatial characteristic of individual photons can be easily transferred from the field of classical optics, their spatial structure cannot be measured using the standard interferometric reference-based methods such as optical holography due to their completely undefined-global phase. Hence, the full recovery of a transverse photon wavefunction still remains a challenging task tackled so far exclusively using indirect methods such as the quantum tomography [1] and weak values measurements [2].Here we present and experimentally demonstrate a different approach based on spatially resolved detection of two-photon interference [3,4]. Although such measurements are usually perceived to be insensitive to the relative phase between two interfering photons we show that rarely considered local phase dependence can be still observed and utilized for direct recovery of a single photon quantum wavefunction. In particular we experimentally show that the complex transversal wavefunction of the unknown photon can be fully recovered from the 2D spatial coincidence pattern resulting from its two-photon interference with the reference photon [5].
Holography exploits the interference of a light field reflected/transmitted from an object with a reference beam to obtain a reconstruction of the spatial shape of the object. Classical holography techniques have been very successful in diverse areas such as microscopy, manufacturing technology, and basic science. However, detection constraints for wavelengths outside the visible range restrict the applications for imaging and sensing in general. For overcoming these detection limitations, we implement phase-shifting holography with nonclassical states of light, where we exploit quantum interference between two-photon probability amplitudes in a nonlinear interferometer. We demonstrate that it allows retrieving the spatial shape (amplitude and phase) of the photons transmitted/reflected from the object and thus obtaining an image of the object despite those photons are never detected. Moreover, there is no need to use a well-characterized reference beam, since the two-photon scheme already makes use of one of the photons as reference for holography.
We present experimental demonstrations of two-photon interference involving temporally separated photons within two types of interferometers: a Mach-Zehnder interferometer and a polarization-based Michelson interferometer. The two-photon states are probabilistically prepared in a symmetrically superposed state within the two interferometer arms by introducing a large time delay between two input photons; this state is composed of two temporally separated photons, which are in two different or the same spatial modes. We then observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simultaneously in a single interferometric setup. The observed two-photon interference fringes provide simultaneous observation of the interferometric properties of the single-photon and two-photon wavepackets. The observations can also facilitate a more comprehensive understanding of the origins of the interference phenomena arising from spatially bunched/anti-bunched two-photon states comprised of two temporally separated photons within the interferometer arms.
Reading quantum information of single photons is commonly realized by quantum tomography or the direct (weak) measurement approach. However, these methods are time-consuming and face enormous challenges in characterizing single photons from an ultrafast light source due to the stringent temporal mode matching requirements. Here, we retrieve the spatial wavefunction of indistinguishable single photons from both a continuous wave source and a femtosecond light source using a self-referencing interferometer. Our method only requires nine ensemble-averaged measurements. This technique simplifies the measurement procedure of single-photon wavefunction and automatically mode matches each self-interfering single photon temporally, which enables the measurement of the spatial wavefunction of single photons from an ultrafast light source.
With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally characterize the multiphoton spatial wave function including the entangled amplitude and phase information at different evolutionary stages. However, there is no effective method to measure it. Quantum state tomography is costly, and quantum holography requires additional references. Here, we introduce quantum Shack-Hartmann wavefront sensing to perform efficient and reference-free measurement of the biphoton spatial wave function. The joint probability distribution of photon pairs at the back focal plane of a microlens array is measured and used for amplitude extraction and phase reconstruction. In the experiment, we observe that the biphoton amplitude correlation becomes weak while phase correlation shows up during free-space propagation. Our work is a crucial step in quantum physical and adaptive optics and paves the way for characterizing quantum optical fields with high-order correlations or topological patterns.