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Photonics Research

Towards optimum Franson interference recurrence in mode-locked singly-filtered biphoton frequency combs

Kai-Chi Chang, Xiang Cheng, Murat Can Sarihan, Chee Wei Wong

Published Apr 21, 2023• 22 citations
Publisher

Abstract

Mode-locked biphoton frequency combs exhibit multiple discrete comblike temporal correlations from the Fourier transform of its phase-coherent frequency spectrum. Both temporal correlation and Franson interferometry are valuable tools for analyzing the joint properties of biphoton frequency combs, and the latter has proven to be essential for testing the fundamental quantum nature, the time-energy entanglement distribution, and the large-alphabet quantum key distributions. However, the Franson recurrence interference visibility in biphoton frequency combs unavoidably experiences a falloff that deteriorates the quality of time-energy entanglement and channel capacity for longer cavity round trips. In this paper, we provide a new method to address this problem towards optimum Franson interference recurrence. We first observe mode-locked temporal oscillations in a 5.03 GHz free-spectral range singly filtered biphoton frequency comb using only commercial detectors. Then, we observe similar falloff trend of time-energy entanglement in 15.15 GHz and 5.03 GHz free-spectral range singly filtered biphoton frequency combs, whereas, the optimum central time-bin accidental-subtracted visibility over 97% for both cavities. Here, we find that by increasing the cavity finesse F , we can enhance the detection probability in temporal correlations and towards optimum Franson interference recurrence in our singly filtered biphoton frequency combs. For the first time, via a higher cavity finesse F of 45.92 with a 15.11 GHz free-spectral range singly filtered biphoton frequency comb, we present an experimental ≈3.13-fold improvement of the Franson visibility compared to the Franson visibility with a cavity finesse F of 11.14 at the sixth time bin. Near optimum Franson interference recurrence and a time-bin Schmidt number near 16 effective modes in similar free-spectral range cavity are predicted with a finesse F of 200. Our configuration is versatile and robust against changes in cavity parameters that can be designed for various quantum applications, such as high-dimensional time-energy entanglement distributions, high-dimensional quantum key distributions, and wavelength-multiplexed quantum networks.

DOI
10.1364/prj.483570

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Mode-locked biphoton frequency combs exhibit multiple discrete comblike temporal correlations from the Fourier transform of its phase-coherent frequency spectrum. Both temporal correlation and Franson interferometry are valuable tools for analyzing the joint properties of biphoton frequency combs, and the latter has proven to be essential for testing the fundamental quantum nature, the time-energy entanglement distribution, and the large-alphabet quantum key distributions. However, the Franson recurrence interference visibility in biphoton frequency combs unavoidably experiences a falloff that deteriorates the quality of time-energy entanglement and channel capacity for longer cavity round trips. In this paper, we provide a new method to address this problem towards optimum Franson interference recurrence. We first observe mode-locked temporal oscillations in a 5.03 GHz free-spectral range singly filtered biphoton frequency comb using only commercial detectors. Then, we observe similar falloff trend of time-energy entanglement in 15.15 GHz and 5.03 GHz free-spectral range singly filtered biphoton frequency combs, whereas, the optimum central time-bin accidental-subtracted visibility over 97% for both cavities. Here, we find that by increasing the cavity finesse F , we can enhance the detection probability in temporal correlations and towards optimum Franson interference recurrence in our singly filtered biphoton frequency combs. For the first time, via a higher cavity finesse F of 45.92 with a 15.11 GHz free-spectral range singly filtered biphoton frequency comb, we present an experimental ≈3.13-fold improvement of the Franson visibility compared to the Franson visibility with a cavity finesse F of 11.14 at the sixth time bin. Near optimum Franson interference recurrence and a time-bin Schmidt number near 16 effective modes in similar free-spectral range cavity are predicted with a finesse F of 200. Our configuration is versatile and robust against changes in cavity parameters that can be designed for various quantum applications, such as high-dimensional time-energy entanglement distributions, high-dimensional quantum key distributions, and wavelength-multiplexed quantum networks.
Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (Eof) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).
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