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arXiv:2301.13046

Interferometric imaging of amplitude and phase of spatial biphoton states

Danilo Zia, Nazanin Dehghan, Alessio D’Errico, Fabio Sciarrino, Ebrahim Karimi

Published Jan 30, 2023• 3 citations
arXivHTMLPDF

Abstract

High-dimensional biphoton states are promising resources for quantum applications, ranging from high-dimensional quantum communications to quantum imaging. A pivotal task is fully characterising these states, which is generally time-consuming and not scalable when projective measurement approaches are adopted. However, new advances in coincidence imaging technologies allow for overcoming these limitations by parallelising multiple measurements. Here, we introduce biphoton digital holography, in analogy to off-axis digital holography, where coincidence imaging of the superposition of an unknown state with a reference one is used to perform quantum state tomography. We apply this approach to single photons emitted by spontaneous parametric down-conversion in a nonlinear crystal when the pump photons possess various quantum states. The proposed reconstruction technique allows for a more efficient (3 order-of-magnitude faster) and reliable (an average fidelity of 87%) characterisation of states in arbitrary spatial modes bases, compared with previously performed experiments. Multi-photon digital holography may pave the route toward efficient and accurate computational ghost imaging and high-dimensional quantum information processing.

DOI
10.48550/arxiv.2301.13046

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High-dimensional biphoton states are promising resources for quantum applications, ranging from high-dimensional quantum communications to quantum imaging. A pivotal task is fully characterising these states, which is generally time-consuming and not scalable when projective measurement approaches are adopted. However, new advances in coincidence imaging technologies allow for overcoming these limitations by parallelising multiple measurements. Here, we introduce biphoton digital holography, in analogy to off-axis digital holography, where coincidence imaging of the superposition of an unknown state with a reference one is used to perform quantum state tomography. We apply this approach to single photons emitted by spontaneous parametric down-conversion in a nonlinear crystal when the pump photons possess various quantum states. The proposed reconstruction technique allows for a more efficient (3 order-of-magnitude faster) and reliable (an average fidelity of 87%) characterisation of states in arbitrary spatial modes bases, compared with previously performed experiments. Multi-photon digital holography may pave the route toward efficient and accurate computational ghost imaging and high-dimensional quantum information processing.
Abstract High-dimensional biphoton states are promising resources for quantum applications, ranging from high-dimensional quantum communications to quantum imaging. A pivotal task is fully characterizing these states, which is generally time-consuming and not scalable when projective measurement approaches are adopted; however, new advances in coincidence imaging technologies allow for overcoming these limitations by parallelizing multiple measurements. Here we introduce biphoton digital holography, in analogy to off-axis digital holography, where coincidence imaging of the superposition of an unknown state with a reference state is used to perform quantum state tomography. We apply this approach to single photons emitted by spontaneous parametric down-conversion in a nonlinear crystal when the pump photons possess various quantum states. The proposed reconstruction technique allows for a more efficient (three orders of magnitude faster) and reliable (an average fidelity of 87%) characterization of states in arbitrary spatial modes bases, compared with previously performed experiments. Multiphoton digital holography may pave the route toward efficient and accurate computational ghost imaging and high-dimensional quantum information processing.
Biphoton phase imaging via two-photon coincidence detection is essential for quantum holography and related quantum imaging applications. Although camera-based methods have been predominantly used in previous studies, we here introduce a two-dimensional scanning method for biphoton phase imaging in quantum holography, which leverages a high-efficiency single-photon detector, improving signal-to-noise ratio (SNR). Using this platform, we obtained a quantum holographic phase image with an SNR above 19 and experimentally verified the noise-resilient nature of quantum holography under scanning-based detection. By using the brighter quantum sources, our method offers an efficient route toward faster two-photon coincidence imaging, which is expected to facilitate broader applications of quantum imaging in noisy environments.
The complete measurement of the quantum state of two correlated photons requires reconstructing the amplitude and phase of the biphoton wavefunction. We show how, by means of spatially resolved single photon detection, one can infer the spatial structure of biphotons generated by spontaneous parametric down conversion. In particular, a spatially resolved analysis of the second-order correlations allows us to isolate the moduli of the pump and phase-matching contributions to the two-photon states. When carrying this analysis on different propagation planes, the free-space propagation of pump and phase-matching is observed. This result allows us, in principle, to gain enough information to also reconstruct the phase of the pump and the phase-matching and thus the full biphoton wavefunction. We show this in different examples where the pump is shaped as a superposition of orbital angular momentum modes or as a smooth amplitude with a phase structure with no singularities. The corresponding phase structure is retrieved employing maximum likelihood or genetic algorithms. These findings have potential applications in fast, efficient quantum state characterization that does not require phase locking of the unknown source with a reference biphoton.
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.
ABSTRACT Sources of light characterized by a well‐defined number of photons are widely used in quantum experiments and technologies due to their peculiar properties, which include sub‐Poissonian statistics, spatial, temporal, and frequency correlations, as well as maximal and high‐dimensional entanglement. Searching for the best experimental approaches that allow us to visualize the quantum state of two (or more) photons has been a long‐standing fundamental question, which has been mainly addressed via mode projection techniques. The rapid development of single‐photon‐sensitive cameras, however, has opened the pathway to conceptually simple, yet faster and more efficient, measurement techniques. This review explores the latest advancements in measuring the spatial structure of the quantum state of light using 3D imaging techniques. An overview of the most used single‐photon camera technologies is given, highlighting their differences and respective advantages. Besides the fundamental interest in reconstructing experimentally one of the most mysterious concepts of microscopic physics, this review illustrates how the techniques developed in this direction can lead to new ideas in the fields of imaging and sensing, for instance, superresolution measurements and phase‐enhanced and sub‐shot noise imaging.
High-dimensional photonic entangled states are key resources for advancing quantum imaging, quantum sensing, secure communication, and quantum computation. The most common method for generating such states is spontaneous parametric down-conversion (SPDC), in which a pump photon splits into two daughter photons that share correlations across multiple photonic degrees of freedom. Characterising these high-dimensional states, however, is highly challenging, as it scales quadratically with the state dimensionality and usually requires large sets of projective measurements within the framework of positive operator-valued measures (POVMs).