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arXiv:quant-ph/0311011 · Journal of Physics B Atomic Molecular and Optical Physics

Quantum theory of two-photon wavepacket interference in a beamsplitter

Kaige Wang

Published Sep 5, 2006• 54 citations
arXivHTMLPDF

Abstract

A general theory is derived for the interference of a two-photon wavepacket in a beamsplitter. The theory is presented in the Schrödinger picture so that the quantum nature of the two-photon interference is explicitly revealed. We find that the topological symmetry of the probability-amplitude spectrum of the two-photon wavepacket dominates the nature of the two-photon interference, which may be distinguished by the increase or decrease of the coincidence probability in the absence of interference. However, two-photon entanglement can be identified by the nature of the interference. We demonstrate the necessary and sufficient conditions for perfect two-photon interference. It is shown that a two-photon entangled state with an anti-symmetric spectrum passes through a 50/50 beamsplitter with perfect transparency. The theory provides us with a unified understanding of the various two-photon interference effects.

DOI
10.1088/0953-4075/39/18/r01

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A general theory is derived for the interference of a two-photon wavepacket in a beamsplitter. The theory is presented in the Schrödinger picture so that the quantum nature of the two-photon interference is explicitly revealed. We find that the topological symmetry of the probability-amplitude spectrum of the two-photon wavepacket dominates the nature of the two-photon interference, which may be distinguished by the increase or decrease of the coincidence probability in the absence of interference. However, two-photon entanglement can be identified by the nature of the interference. We demonstrate the necessary and sufficient conditions for perfect two-photon interference. It is shown that a two-photon entangled state with an anti-symmetric spectrum passes through a 50/50 beamsplitter with perfect transparency. The theory provides us with a unified understanding of the various two-photon interference effects.
We study theoretically the interference of a two-photon wavepacket in a beam splitter. We find that the spectrum symmetry for the two-photon wavepacket dominates the perfect coalescence and anti-coalescence interference. The coalescence interference is unrelated to photon entanglement. Only the anti-coalescence interference has evidence of photon entanglement. We prove that the two-photon wavepacket with an anti-symmetric spectrum is transparent to pass the 50/50 beam splitter, showing perfect anti-coalescence interference.
We report an interference experiment in which the two-photon entangled state interference cannot be pictured in terms of the overlap and bunching of two individual photons on a beamsplitter. We also demonstrate that two-photon interference, or photon bunching effect on a beamsplitter, does not occur if the two-photon Feynman amplitudes are distinguishable, even though individual photons do overlap on a beamsplitter. Therefore, two-photon interference cannot be viewed as interference of two individual photons, rather it should be viewed as two-photon or biphoton interfering with itself. The results may also be useful for studying decoherence management in entangled two-qubit systems as we observe near complete restoration of quantum interference after the qubit pairs, generated by a femtosecond laser pulse, went through certain birefringent elements.
We present a general theory on the interference of a two-photon wave packet associated with spatial modes at a beam splitter. We find that the topological symmetry of the two-photon angular spectrum governs the nature of the two-photon interference. We distinguish between the coalescence interference and anticoalescence interference according to the decrease or increase of the coincidence probability in the absence of interference, respectively, and demonstrate that the symmetric and antisymmetric two-photon angular spectra are responsible for perfect coalescence interference and anticoalescence interference, respectively. Then we prove that anticoalescence interference never occurs for two independent photons, and it turns out that anticoalescence interference is the signature of two-photon entanglement. On the basis of this feature, we propose a special Mach-Zehnder interferometer, incorporated with two spiral phase plates, which can change the interference from a coalescence to an anticoalescence type only for a two-photon entangled state. The scheme is simple and straightforward compared with a test of Bell's inequality.
We report on a ``postponed compensation'' experiment in which the observed two-photon entangled state interference cannot be pictured in terms of the overlap of the two individual photon wave packets of a parametric down-conversion pair on a beam splitter. In the sense of a quantum eraser, the distinguishability of the different two-photon Feynman amplitudes leading to a coincidence detection is removed by delaying the compensation until after the output of an unbalanced two-photon interferometer.