The pairing ratio, a crucial metric assessing a biphoton source's ability to generate correlated photon pairs, remains underexplored despite theoretical predictions. This study presents experimental findings on the pairing ratio, utilizing a double-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="normal">Λ</a:mi></a:math> spontaneous four-wave mixing biphoton source in cold atoms. At an optical depth (OD) of 20, we achieved an ultrahigh biphoton generation rate of up to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>1.3</c:mn><c:mo>×</c:mo><c:msup><c:mn>10</c:mn><c:mn>7</c:mn></c:msup></c:mrow></c:math> per second, with a successful pairing ratio of 61%. Increasing the OD to 120 significantly improved the pairing ratio to 89%, while maintaining a consistent biphoton generation rate. This achievement, marked by high generation rates and robust biphoton pairing, holds great promise for advancing efficiency in quantum communication and information processing. Additionally, in a scenario with a lower biphoton generation rate of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>5.0</d:mn><d:mo>×</d:mo><d:msup><d:mn>10</d:mn><d:mn>4</d:mn></d:msup></d:mrow></d:math> per second, we attained an impressive signal-to-background ratio of 241 for the biphoton wavepacket, surpassing the Cauchy-Schwarz criterion by approximately <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>1.5</e:mn><e:mo>×</e:mo><e:msup><e:mn>10</e:mn><e:mn>4</e:mn></e:msup></e:mrow></e:math> times. Published by the American Physical Society 2024
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