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arXiv:1007.2599 · New Journal of Physics

Accessing the purity of a single photon by the width of the Hong–Ou–Mandel interference

K. N. Cassemiro, Kaisa Laiho, Christine Silberhorn

Published Nov 29, 2010• 59 citations
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Abstract

We demonstrate a method for determining the spectral purity of single photons. The technique is based on the Hong–Ou–Mandel (HOM) interference between a single-photon state and a suitably prepared coherent field. We show that the temporal width of the HOM dip is related not only to the reciprocal of the spectral width but also to the underlying quantum coherence. Therefore, by measuring the width of both the HOM dip and the spectrum, one can directly quantify the degree of spectral purity. The distinct advantage of our proposal is that it obviates the need for perfect mode matching, since it does not rely on the visibility of the interference. Our method is particularly useful for characterizing the purity of heralded single-photon states.

DOI
10.1088/1367-2630/12/11/113052

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We demonstrate a method for determining the spectral purity of single photons. The technique is based on the Hong–Ou–Mandel (HOM) interference between a single-photon state and a suitably prepared coherent field. We show that the temporal width of the HOM dip is related not only to the reciprocal of the spectral width but also to the underlying quantum coherence. Therefore, by measuring the width of both the HOM dip and the spectrum, one can directly quantify the degree of spectral purity. The distinct advantage of our proposal is that it obviates the need for perfect mode matching, since it does not rely on the visibility of the interference. Our method is particularly useful for characterizing the purity of heralded single-photon states.
We present and experimentally demonstrate a method for determining the spectral characterization of a single-photon state. This technique is based on the Hong-Ou-Mandel interference between a well-defined weak coherent state and a measured single-photon state. We estimate the spectrum of the single-photon state by fitting the measured interference dip with proposed model and least square method. Our method is particularly useful for characterising spectral property the single-photon state. It opens a way for robust and efficient on-line monitoring the single-photon emitters.
Two-photon interference, commonly known as Hong-Ou-Mandel (HOM) interference [1] , has attracted a great deal of interest in quantum sensing, including the precision timing measurements [2] and quantum optical coherence tomography [3] . While the dip of the HOM interference is the direct measure of the purity of the single-photon, the width of the HOM dip relates to the coherence time of the interfering photons. The broad consensus for using the HOM interferometer for sensing application remained the HOM dip width as the limiting factor for the precision measurements. As a consequence, the ultra-broadband photon sources have long been hailed as a vital prerequisite for ultra-precise HOM interferometry. Here, we have studied the variation in the width of the HOM dip with the crystal length for the continuous-wave pump laser and measured the HOM dip as low as 8.2 ± 0.2 µm corresponding to the spectral width of the single-photon source of 79.6±1.9 nm useful for sensitive sensing applications.
The temporal purity of single photons is crucial to the indistinguishability of independent photon sources for the fundamental study of the quantum nature of light and the development of photonic technologies. Currently, the technique for single photons heralded from time-frequency entangled biphotons created in nonlinear crystals does not guarantee the temporal-quantum purity, except using spectral filtering. Nevertheless, an entirely different situation is anticipated for narrow-band biphotons with a coherence time far longer than the time resolution of a single-photon detector. Here we demonstrate temporally pure single photons with a coherence time of 100 ns, directly heralded from the time-frequency entangled biphotons generated by spontaneous four-wave mixing in cold atomic ensembles, without any supplemented filters or cavities. A near-perfect purity and indistinguishability are both verified through Hong-Ou-Mandel quantum interference using single photons from two independent cold atomic ensembles. The time-frequency entanglement provides a route to manipulate the pure temporal state of the single-photon source.
Hong–Ou–Mandel (HOM) interference is a standard method for characterizing photon indistinguishability. However, in practical systems, the measured interference visibility is not solely determined by intrinsic spectral–temporal mismatch but can also be affected by photon-number statistics, multiphoton background, and technical noise. Here, we establish an observable-level framework for HOM interference in practical sources. Within this framework, under stationary-field and fixed-detection conditions, the measured coincidence rate is decomposed into a delay-dependent interference term and a stationary background term that is independent of the HOM interference. The former is described by an effective spectral overlap function G(τ), while the latter mainly originates from source statistics and additive imperfections. This separation shows that the dip profile and intrinsic depth are governed by overlap-limited interference, whereas the observed visibility can be further degraded by statistical and external backgrounds. For single-photon and weak coherent-state inputs, G(τ) represents the effective temporal–spectral mode overlap. For the stationary thermal field, its delay-dependent envelope can be related to the first-order temporal coherence function g(1)(τ), whereas photon bunching contributes separately through g2(0). We further clarify that post-selection suppresses background and reveals intrinsic interference more directly but cannot improve the intrinsic spectral–temporal overlap. This framework provides a unified basis for distinguishing genuine indistinguishability loss from measurement-induced visibility degradation.
, with a Gaussian phase-matching function and a transform-limited Gaussian pump, to achieve near-unity spectral purity in heralded single photons at telecommunication wavelength. Theory shows that these phase-matching and pump conditions are sufficient to ensure that a biphoton state with a circularly symmetric joint spectral intensity profile is transform limited and factorable. We verify the heralded-state spectral purity in a four-fold coincidence measurement by performing Hong-Ou-Mandel interference between two independently generated heralded photons. With a mild spectral filter we obtain an interference visibility of 98.4±1.1% which corresponds to a heralded-state purity of 99.2%. Our heralded photon source is potentially an essential resource for measurement-based quantum information processing and quantum network applications.