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arXiv:quant-ph/0702200 · Physical Review Letters

Spectral Density Matrix of a Single Photon Measured

Wojciech Wasilewski, Piotr Leszek Kolenderski, Robert Frankowski

Published Sep 17, 2007• 66 citations
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Abstract

We propose and demonstrate a method for measuring the spectral density matrix of a single photon pulse. The method is based on registering Hong-Ou-Mandel interference between a photon to be measured and a pair of attenuated and suitably delayed laser pulses described by a known spectral amplitude. The density matrix is retrieved from a two-dimensional interferogram of coincidence counts. The method has been implemented for a type-I down-conversion source, pumped by ultrashort laser pulses. The experimental results agree well with a theoretical model which takes into account the temporal as well as spatial effects in the source.

DOI
10.1103/physrevlett.99.123601

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We propose and demonstrate a method for measuring the spectral density matrix of a single photon pulse. The method is based on registering Hong-Ou-Mandel interference between a photon to be measured and a pair of attenuated and suitably delayed laser pulses described by a known spectral amplitude. The density matrix is retrieved from a two-dimensional interferogram of coincidence counts. The method has been implemented for a type-I down-conversion source, pumped by ultrashort laser pulses. The experimental results agree well with a theoretical model which takes into account the temporal as well as spatial effects in the source.
We propose and demonstrate a method for measuring the joint spectrum of photon pairs via Fourier spectroscopy. The biphoton spectral intensity is computed from a two-dimensional interferogram of coincidence counts. The method has been implemented for a type-I downconversion source using a pair of common-path Mach-Zehnder interferometers based on Soleil compensators. The experimental results agree well with calculated frequency correlations that take into account the effects of coupling into single-mode fibers. The Fourier method is advantageous over scanning spectrometry when detectors exhibit high dark count rates leading to dominant additive noise.
We propose and demonstrate a method for measuring the joint spectrum of photon pairs via Fourier spectroscopy. The biphoton spectral intensity is computed from a two-dimensional interferogram of coincidence counts. The method has been implemented for a type-I downconversion source using a pair of common-path Mach-Zender interferometers based on Soleil compensators. The experimental results agree well with calculated frequency correlations that take into account the effects of coupling into single-mode fibers. The Fourier method is advantageous over scanning spectrometry when detectors exhibit high dark count rates leading to dominant additive noise.
Hong-Ou-Mandel interference between independent photon sources (HOMI-IPS) plays an important role in quantum information processing. A variety of HOMI-IPS experiments have been demonstrated at near-infrared wavelengths or telecom wavelengths [1]. In all the previous HOMI-IPS experiments, the HOM dips are obtained by recording the four-fold coincidence counts as a function of the temporal delay. However, the spectral correlation during the interference is omitted, partially due to technical difficulties, e.g., the acquisition time is too long for measuring a joint spectral distribution. Spectral information, as the conjugate of the temporal information in the Fourier transformation, is definitely of great importance and should be investigated. Very recently, a new technique of spectral correlation measurement in a HOM interference has been developed by Gerrits, et al [2]. This technique has the merits of high speed and high resolution, therefore, has been used as a powerful tool to analyse the spectral correlation in a HOM interference between signal and idler photons from one spontaneous parametric down conversion (SPDC) source. In this work, we measure the joint spectral distribution in HOMI-IPS using the new technique developed in [2]. The experimental setup is shown in Fig. 1 (Left). The two independent sources are based on SPDC from two 30-mm-long periodically poled KTiOPO4 (PPKTP) crystals pumped by picosecond laser pulses (76 MHz, 792 nm, temporal duration ~ 2 ps). In Fig. 1 (Left), the dispersion compensation fiber model (DCFMs), the superconducting nanowire single-photon detectors (SNSPDs) [3,4,5] and the time interval analyzer (TIA) constitute a fiber spectral analyzer [6]. Fig. 1(Right: (a)) is the measured four-fold HOM interference between signal1 and signal2, with idler1 and idler2 as heralders. Without subtraction of any background counts, the raw visibility of the HOM dip is 69.9±3.2%, which is consistent with our previous results in [1,7,8]. Fig. 1(Right: (b)-(g)) are the measured joint spectral intensities at different delay positions. The splitting phenomenon in the joint spectral distribution is clearly observed. The experimental results agree well with our theoretical simulations. This experiment not only can deepen our understanding of HOMI-IPS from the viewpoint of spectral domain, but also can be used to improve the visibility of HOMI-IPS by temporal filtering.
Abstract Frequency entangled biphoton sources have played an important role in quantum information. There are two key characteristics which determine the extent of their applications: the spectral indistinguishability and the degree of frequency entanglement. Previously, the spectral indistinguishability of the biphoton state is measured by the Hong–Ou–Mandel (HOM) interference visibility, whereas the degree of frequency entanglement is normally characterized with independent spectral measurements. However, these two quantum features have not been successfully measured with a single experimental setup. In this paper, we deduce the temporal distribution of a short-pulse pumped type-II spontaneous parametric down converted (SPDC) biphoton source and its relevant temporal entanglement parameter R t for operationally quantifying the degree of frequency entanglement. Furthermore, we theoretically and experimentally demonstrate, due to the inherent group delay, the difference between the signal and idler photons at the exit of the type-II nonlinear crystal, resulting in a HOM-shape dip at both sides of the center fringed envelope of the MZ interferometric coincidence diagram. By measuring the HOM-shape dip depth, the separation between the two sideband dips as well as the MZ fringed envelope width, both the spectral indistinguishability and the temporal entanglement parameter can thus be simultaneously quantified. This implementation provides us a unified and convenient method to characterize the frequency entanglement of the short-pulse pumped biphotons.
In this work we demonstrate spectral-temporal correlation measurements of the Hong-Ou-Mandel (HOM) interference effect with the use of a spectrometer based on a photon-counting camera. This setup allows us to take, within seconds, spectral temporal correlation measurements on entangled photon sources with sub-nanometer spectral resolution and nanosecond timing resolution. Through post processing, we can observe the HOM behaviour for any number of spectral filters of any shape and width at any wavelength over the observable spectral range. Our setup also offers great versatility in that it is capable of operating at a wide spectral range from the visible to the near infrared and does not require a pulsed pump laser for timing purposes. This work offers the ability to gain large amounts of spectral and temporal information from a HOM interferometer quickly and efficiently and will be a very useful tool for many quantum technology applications and fundamental quantum optics research.