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Direct generation of frequency-bin entangled photons via two-period quasi-phase-matched parametric downconversion

Fumihiro Kaneda, Hirofumi Suzuki, Ryosuke Shimizu, and Keiichi Edamatsu

Open Access Open Access

Abstract

We report a simple scheme for direct generation of frequency-bin entangled photon pairs via spontaneous parametric downconversion. Our fabricated nonlinear optical crystal with two different poling periods can simultaneously satisfy two different, spectrally symmetric nondegenerate quasi-phase-matching conditions, enabling the direct generation of entanglement in two discrete frequency-bin modes. Our produced photon pairs exhibited Hong-Ou-Mandel interference with high-visibility beating oscillations— a signature of two-mode frequency-bin entanglement. Moreover, we demonstrate deterministic entanglement-mode conversion from frequency-bin to polarization modes, with which our source can be more versatile for various quantum applications. Our scheme can be extended to direct generation of high-dimensional frequency-bin entanglement, and thus will be a key technology for frequency-multiplexed optical quantum information processing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Figures (4)
Fig. 1
Fig. 1 Schematic diagram of the generation of frequency-bin entangled photon pairs. (a) The illustration of two-period QPM crystal. (b) Frequency-bin entanglement generation. (c) Polarization entanglement generation demonstrated in [34]. PBS: polarizing beamsplitter, DM: dichroic mirror. (d) Theoretical tuning curves for a PPLN crystal with our designed poling periods ( Λ 1 = 9.25 μm and Λ2 = 9.50 μm) and a pump wavelength of 775 nm.

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Fig. 2
Fig. 2 Illustration of the experimental setup for (a) generation and detection of frequency-bin entangled photons and (b) detection of polarization entanglement. PPLN: periodically poled lithium niobate, PBS: polarizing beamsplitter, QWP: quarter-wave plate, HWP: half-wave plate, SMF: single-mode fiber, SPD: single-photon detector, DM: dichroic mirror, PA: polarization analyzer. Each PA consists of a QWP, a HWP, and a PBS.

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Fig. 3
Fig. 3 Characterization of the frequency-bin entanglment. (a) Observed HOM interference for (a) -3 ps ≤ τ ≤ 3 ps and (b) -0.5 ps ≤ τ ≤ 0.5 ps. (c) Reconstructed density matrix. Error bars were calculated from Poissonian photon-counting statistics.

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Fig. 4
Fig. 4 Measured polarization-mode density matrices after the entanglement-mode transfer for τ = (a) 0 fs, (b) 47 fs, and (c) -20 fs.

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Tables (1)

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Table 1 Characteristics of the polarization-mode density matrices. τ, time delay in the Michelson interferometer; I ( τ ) / N, normalized coincidence count rate in the HOMI; ϕ, phase of the frequency entangled state predicted from the HOMI; F, state fidelity to the ideal density matrix | ψ p 〉 for ϕ; C, concurrence.

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Equations (8)

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| FB n 〉 = ∑ j = 1 n 1 n | ω j 〉 | ω n − j + 1 〉 ,
Δ ω = ω p − ω s − ω i = 0 ,
Δ k = k p − k s − k i − 2 π Λ 1 ( 2 ) = 0 ,
| ψ 〉 = 1 2 ( | H , ω 1 〉 | V , ω 2 〉 + e i ϕ | V , ω 1 〉 | H , ω 2 〉 ) ,
| ψ f 〉 = 1 2 ( | ω 1 〉 A , H | ω 2 〉 B , V + e i ϕ | ω 2 〉 A , H | ω 1 〉 B , V ) ,
| ψ p 〉 = 1 2 ( | H 〉 A , ω 1 | V 〉 B , ω 2 + e i ϕ | V 〉 A , ω 1 | H 〉 B , ω 2 ) .
I ( τ ) = { N 2 { 1 − V cos  ( δ ω τ ) ( 1 − | τ τ c | ) } for | τ | ≤ τ c N 2 for | τ | > τ c
ρ F = p | ω 1 ω 2 〉 〈 ω 1 ω 2 | A B + ( 1 − p ) | ω 2 ω 1 〉 〈 ω 2 ω 1 | A B + V 2 ( e i ϕ | ω 1 ω 2 〉 〈 ω 2 ω 1 | A B + e − i ϕ | ω 2 ω 1 〉 〈 ω 1 ω 2 | A B ) ,
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