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arXiv:2303.12705 · Physical Review A

Quantum entanglement between signal and frequency-up-converted idler photons

Jiaxuan Wang, Alexei V. Sokolov, G. S. Agarwal

Published Dec 8, 2023• 4 citations
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Abstract

Quantum frequency up-conversion is a cutting-edge technique that leverages the interaction between photons and quantum systems to shift the frequency of single photons from a lower frequency to a higher frequency. If a photon before up-conversion was part of an entangled pair, it becomes crucial to comprehend the time-frequency entanglement after up-conversion. In this study, we present a theoretical analysis of the transformation of the time-dependent second-order quantum correlations in photon pairs and find the preservation of such correlations under fairly general conditions. Furthermore, we analyze Hong-Ou-Mandel interference between the signal and frequency-converted idler photons to gain insight into the indistinguishability of the two photons. The visibility of two-photon interference is sensitive to the magnitude of frequency conversion and improves as the frequency separation between two photons decreases.

DOI
10.1103/physreva.108.063706

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Quantum frequency up-conversion is a cutting-edge technique that leverages the interaction between photons and quantum systems to shift the frequency of single photons from a lower frequency to a higher frequency. If a photon before up-conversion was part of an entangled pair, it becomes crucial to comprehend the time-frequency entanglement after up-conversion. In this study, we present a theoretical analysis of the transformation of the time-dependent second-order quantum correlations in photon pairs and find the preservation of such correlations under fairly general conditions. Furthermore, we analyze Hong-Ou-Mandel interference between the signal and frequency-converted idler photons to gain insight into the indistinguishability of the two photons. The visibility of two-photon interference is sensitive to the magnitude of frequency conversion and improves as the frequency separation between two photons decreases.
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Frequency conversion of single photons is an important technology for quantum interface and quantum communication networks. Here, single-photon frequency conversion in the telecommunication band is experimentally demonstrated via cascaded quadratic nonlinear processes. Using cascaded quasi-phase-matched sum and difference frequency generation in a periodically poled lithium niobate waveguide, the signal photon of a photon pair from spontaneous down-conversion is precisely shifted to identically match its counterpart, i.e., the idler photon, in frequency to manifest a clear nonclassical dip in the Hong-Ou-Mandel interference. Moreover, quantum entanglement between the photon pair is maintained after the frequency conversion, as is proved in time-energy entanglement measurement. The scheme is used to switch single photons between dense wavelength-division multiplexing channels, which holds great promise in applications in realistic quantum networks.
The frequency distinguishability of two single photons was successfully erased using single photon frequency up-conversion. A frequency nondegenerate photon pair generated via spontaneous four-wave mixing in a dispersion shifted fiber was used to emulate two telecom-band single photons that were in the same temporal mode but in different frequency modes. The frequencies of these photons were converted to the same frequency by using the sum-frequency generation process in periodically poled lithium niobate waveguides, while maintaining their temporal indistinguishability. As a result, the two converted photons exhibited a nonclassical dip in a Hong-Ou-Mandel quantum interference experiment. The present scheme will add flexibility to networking quantum information systems that use photons with various wavelengths.
We demonstrate a new class of frequency-entangled states generated via spontaneous parametric down-conversion under extended phase-matching conditions. Biphoton entanglement with coincident signal and idler frequencies is observed over a broad bandwidth in periodically poled KTiOPO4. We demonstrate high visibility in Hong-Ou-Mandel interferometric measurements under pulsed pumping without spectral filtering, which indicates excellent frequency indistinguishability between the down-converted photons. The coincident-frequency entanglement source is useful for quantum information processing and quantum measurement applications.
We investigate the relation between indistinguishability and quantum entanglement in Hong-Ou-Mandel interference experiments theoretically and relate these quantum mechanical principles to the theorem of entanglement monogamy. Employing Glauber's theory of quantum coherence we compute the detection statistics in HOM interference of frequency-entangled photons and find an additional term in the coincidence detection probability, which is related to the spectral indistinguishability of the considered photons that arises from finite-bandwidth effects and therefore is relevant in the limit of low-frequency separations or large single-photon bandwidths. Compared to previous work in that context we treat all photonic degrees of freedom on equal footing.