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arXiv:2311.08164 · Physical Review A

Full characterization of biphotons with a generalized quantum interferometer

Baihong Li, Changhua Chen, Boxin Yuan, Xiao-Fei Zhang, Ruifang Dong, Shougang Zhang, Rui‐Bo Jin

Published Apr 2, 2024• 4 citations
arXivHTMLPDF

Abstract

Entangled photons (biphotons) in the time-frequency degree of freedom play a crucial role in both foundational physics and advanced quantum technologies. Fully characterizing them poses a key scientific challenge. Here, we propose a theoretical approach to achieving the complete tomography of biphotons by introducing a frequency shift in one arm of the combination interferometer. Our method, a generalized combination interferometer, enables the reconstruction of the full complex joint spectral amplitude associated with both frequency sum and difference in a single interferometer. In contrast, the generalized Hong-Ou-Mandel and N00N state interferometers only allow for the partial tomography of biphotons, either in frequency difference or frequency sum. This provides an alternative method for full characterization of an arbitrary two-photon state with exchange symmetry and holds potential for applications in high-dimensional quantum information processing.

DOI
10.1103/physreva.109.043703

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We propose theoretically a quantum interferometer in which the NOON state interferometer is combined with the Hong-Ou-Mandel interferometer. With this interferometer, the temporal interference patterns associated with biphoton frequency sum and difference can be shown in different parts of a single interferogram. It is thus possible to simultaneously obtain the spectral correlation information of biphotons in both frequency sum and difference by taking the Fourier transform from such an interferogram. This provides a method for complete spectral characterization of an arbitrary two-photon state with exchange symmetry and might be useful in quantum Fourier-transform spectroscopy where direct spectral measurement is difficult. Furthermore, as it can realize the measurement of time intervals on three scales at the same time, we expect that it can provide a method in quantum metrology. Finally, we discuss another potential application of such an interferometer in the generation and characterization of high-dimensional and phase-controlled frequency entanglement.
Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source.
The Hong-Ou-Mandel interferometer is a versatile tool for analyzing the joint properties of photon pairs, relying on a truly quantum interference effect between two-photon probability amplitudes. While the theory behind this form of two-photon interferometry is well established, the development of advanced photon sources and exotic two-photon states has highlighted the importance of quantifying precisely what information can and cannot be inferred from features in a Hong-Ou-Mandel interference trace. Here we examine Hong-Ou-Mandel interference with regard to a particular class of states, so-called quantum frequency combs, and place special emphasis on the role spectral phase plays in these measurements. We find that this form of two-photon interferometry is insensitive to the relative phase between different comb line pairs. This is true even when different comb line pairs are mutually coherent at the input of a Hong-Ou-Mandel interferometer and the fringe patterns display sharp temporal features. Consequently, Hong-Ou-Mandel interference cannot speak to the presence of high-dimensional frequency-bin entanglement in two-photon quantum frequency combs.
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.