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arXiv:0708.2723 · Physical Review A

Characterizing temporal distinguishability of an N -photon state by a generalized photon bunching effect with multiphoton interference

Z. Y. Ou

Published Apr 22, 2008• 19 citations
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Abstract

The complementarity principle of quantum mechanics relates qualitatively the visibility of quantum interference with path indistinguishability. A quantitative study was recently presented [Z. Y. Ou, Phys. Rev. A 74, 063808 (2006)]. Following the formalism of this study, we investigate another scheme for characterizing quantitatively the degree of temporal distinguishability of an $N$-photon state, based on constructive quantum interference between an $N$-photon and a single-photon state. This scheme is related to a generalized photon bunching effect in the form of a ``bump,'' in contrast to the ``dip'' for the destructive interference effect in the previous study. Generalization to other more complicated cases is straightforward and is much simpler than for the scheme of destructive interference in the previous study. A degree of (in)distinguishability is defined and can be determined experimentally by the measurement of the size of the constructive multiphoton interference effect.

DOI
10.1103/physreva.77.043829

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The complementarity principle of quantum mechanics relates qualitatively the visibility of quantum interference with path indistinguishability. A quantitative study was recently presented [Z. Y. Ou, Phys. Rev. A 74, 063808 (2006)]. Following the formalism of this study, we investigate another scheme for characterizing quantitatively the degree of temporal distinguishability of an NNN-photon state, based on constructive quantum interference between an NNN-photon and a single-photon state. This scheme is related to a generalized photon bunching effect in the form of a bump,'' in contrast to the dip'' for the destructive interference effect in the previous study. Generalization to other more complicated cases is straightforward and is much simpler than for the scheme of destructive interference in the previous study. A degree of (in)distinguishability is defined and can be determined experimentally by the measurement of the size of the constructive multiphoton interference effect.
We present a multimode model to describe an arbitrary NNN-photon state with a wide spectral range and some arbitrary temporal distribution. In general, some of the NNN photons are spread out in time while others may overlap and become indistinguishable. From this model, we find that the temporal (in)distinguishability of photons is related to the exchange symmetry of the multiphoton wave function. We find that simple multiphoton detection scheme gives rise to a more general photon bunching effect with the famous two-photon effect as a special case. We then send this NNN-photon state into a recently discovered multiphoton interference scheme. We calculate the visibility of the multiphoton interference scheme and find that it is related to the temporal distinguishability of the NNN photons. Maximum visibility of one is achieved for the indistinguishable NNN-photon state whereas the visibility degrades when some of the photons are separated and become distinguishable. Thus we can identify an experimentally measurable quantity that may quantitatively define the degree of indistinguishability of an NNN-photon state. This presents a quantitative demonstration of the complementary principle of quantum interference.
We present a multi-mode model to describe an arbitrary N-photon state with a wide spectral range and some arbitrary temporal distribution. In general, some of the NNN photons are spread out in time while other may overlap and become indistinguishable. From this model, we find that the temporal (in)distinguishability of photons is related to the exchange symmetry of the multi-photon wave function. We find that simple multi-photon detection scheme gives rise to a more general photon bunching effect with the famous two-photon effect as a special case. We then send this N-photon state into a recently discovered multi-photon interference scheme. We calculate the visibility of the multi-photon interference scheme and find that it is related to the temporal distinguishability of the NNN photons. Maximum visibility of one is achieved for the indistinguishable N-photon state whereas the visibility degrades when some of the photons are separated and become distinguishable. Thus we can identify an experimentally measurable quantity that may quantitatively define the degree of indistinguishability of an N-photon state. This presents a quantitative demonstration of the complementary principle of quantum interference.
An experiment is performed to demonstrate the temporal distinguishability of a four-photon state and a six-photon state, both from parametric down-conversion. The experiment is based on a multiphoton interference scheme in a recently discovered projection measurement of a maximally entangled N-photon state. By measuring the visibility of the interference dip, we can distinguish the various scenarios in the temporal distribution of the pairs and, thus, quantitatively determine the degree of temporal distinguishability of a multiphoton state.
A number of recent interference experiments involving multiple photons are reviewed. These experiments include generalized photon bunching effects, generalized Hong-Ou-Mandel interference effects and multi-photon interferometry for demonstrations of multi-photon de Broglie wavelength. The multi-photon states used in these experiments are from two pairs of photons in parametric down-conversion. We find that the size of the interference effect in these experiments, characterized by the visibility of the interference pattern, is governed by the degree of distinguishability among different pairs of photons. Based on this discovery, we generalize the concept of multi-photon temporal distinguishability and relate it to a number of multi-photon interference effects. Finally, we make an attempt to interpret the coherence theory by multi-photon interference via the concept of temporal distinguishability of photons.
When photons are indistinguishably in the same temporal mode, their detection probability is greatly enhanced due to constructive multiphoton interference, as compared to the case when they are distinguishable. We observed for what is believed to be the first time such a photon bunching effect for six photons. The observed enhancement factor in six-photon coincidence measurement is 17+/-2, which is close to a factor of 20 for an ideal case. Our result confirms that the six photons that we obtain have a high degree of indistinguishability.
A study of the temporal distribution of an N-photon state is presented. In general, some of the NNN photons are spread out in time while other may overlap and become indistinguishable. The criterion for the photons in a single temporal mode is formulated mathematically. A recently discovered projection measurement involving multi-photon interference is used to quantitatively characterize the degree of the temporal indistinguishability of the N-photon state.