Quantum-State Purity of Heralded Single Photons Produced from Frequency-Anti-Correlated Biphotons

TL;DR

This paper investigates how the purity of heralded single photons from frequency-anti-correlated biphotons depends on detector response time, enabling the engineering of photon states via time-frequency entanglement.

Contribution

It demonstrates the dependence of quantum-state purity on detector response time and shows how to engineer photon states using time-frequency entanglement.

Findings

Purity approaches unity with short trigger response time.

Long trigger response time results in mixed heralded photon states.

Time-frequency entanglement enables photon shaping through spectral modulation.

Abstract

We analyze the quantum-state purity of heralded single photons produced from frequency-anti-correlated biphotons. We find that the quantum-state purity in time-frequency domain depends strongly on the response time uncertainty of the trigger-photon detector that heralds the generation of its paired photon. If the trigger response time is much shorter than the two-photon coherence time, the time-frequency quantum-state purity of heralded single photons approaches unity and the heralded single photon is in a nearly pure state. If the trigger response time is much longer than the two-photon coherence time, the heralded photon is then projected onto a mixed state. Making use of the time-frequency entanglement, heralded single photons with a well-defined temporal wave function or a frequency superposition state can be produced and engineered. This time-frequency entanglement allows for shaping heralded single photons through nonlocal spectral modulation.