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Optics and Spectroscopy

Study of the Glauber correlation functions in a pulsed mode

I. N. Agafonov, T. Sh. Iskhakov, Maria V. Chekhova

Published Jul 1, 2007• 0 citations
Publisher

Abstract

A method for measuring the Glauber correlation functions in a pulsed mode is proposed. The effect of the detector dead time on the shape of a measured correlation function is analyzed. The second-order intensity correlation functions for coherent and quasi-thermal radiation, as well as for biphoton light emitted during spontaneous parametric down-conversion, are measured in a nanosecond pulsed mode.

DOI
10.1134/s0030400x07070181

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A method for measuring the Glauber correlation functions in a pulsed mode is proposed. The effect of the detector dead time on the shape of a measured correlation function is analyzed. The second-order intensity correlation functions for coherent and quasi-thermal radiation, as well as for biphoton light emitted during spontaneous parametric down-conversion, are measured in a nanosecond pulsed mode.
We consider normalised intensity correlation functions (CFs) of different orders for light emitted via parametric down-conversion (PDC) and their dependence on the number of photons per mode. The main problem in measuring such correlation functions is their extremely small width, which considerably reduces their contrast. It is shown that if the radiation under study is modulated by a periodic sequence of pulses that are short compared to the CF width, no decrease in the contrast occurs. A procedure is proposed for measuring normalised CFs of various orders in the pulsed regime. For nanosecond-pulsed PDC radiation, normalised second-order CF is measured experimentally as a function of the mean photon number.
The purpose of this investigation was to construct the experimental apparatus for measuring second-order intensity correlation functions of the type T2,2 (x,t,x,t+T) = < : I(x,t)I(x,t+T):>. This measurement was applied to the radiation field produced by a two axial mode Helium-Neon gas laser in order to verify the intensity fluctuation correlations due to the beating of the two axial modes of the laser. The axial mode separation was measured for comparison with a scanning Fabry Perot interferometer and also an RF spectrum analyzer. The correlation measurement was also applied to the second harmonic radiation field produced by the. parametric interaction in a LiNb03 crystal pumped with two axial modes. The experimental determination of the correlation <:I(x,t)I(x,t+T):> involves a time-spectroscopy measurement in which one photon is detected at point x, and another at point x, T seconds later, and measuring the probability of two-fold coincident detection as a function of T. The radiation field was split into two beams at a partially transmitting reflector, each of which was directed incident on the photocathode of a photomultiplier tube. The photoelectron pulses from the tubes were amplified and standardized. These standardized pulses were then temporally correlated with the use of a time-to-amplitude converter (TAC) and a multi-channel pulse height analyzer (MA). The time-to-amplitude conversions generated by the TAC were stored in the channels of the PHA, which was a direct measure of the two-fold delayed coincidence detection rate, R(T). The second-order intensity correlation functions <:I(x,t)I(x,t+T):> are determined from measurements of R(T). The fluctuating components of the second-order intensity correlation functions were found to be in agreement with what would be expected on a classical basis. Correspondingly, the capability is demonstrated of the experimental apparatus measuring a quantity relating to the second-order intensity correlation function.
The second-order correlation function which characterizes the quantum correlation between the optical and terahertz photons generated under spontaneous parametric down-conversion has been measured for the first time. A scheme of experiment based on the analysis of analog signals from terahertz and optical detectors has been proposed. Various approaches to exclude the effect of electronic and thermal noise on the measured correlation level have been discussed. The results make it possible to expand quantum optical technologies such as quantum calibration of detectors, fabrication of single-photon sources, and imaging with single-pixel detectors to the terahertz range.
We study a possibility of measuring the time-resolved second-order autocorrelation function of one of two beams generated in type-II parametric down-conversion by means of temporal magnification of this beam, bringing its correlation time from the picosecond to the nanosecond scale, which can be resolved by modern photodetectors. We show that such a measurement enables one to infer directly the degree of global coherence of that beam, which is linked by a simple relation to the number of modes characterizing the entanglement between the two generated beams. We illustrate the proposed method by an example of photon pairs generated in a periodically poled potassium titanyl phosphate (KTP) crystal with a symmetric group velocity matching for various durations of the pump pulse, resulting in different numbers of modes. Our theoretical model also shows that the magnified double-heralded autocorrelation function of one beam exhibits a local maximum around zero delay time, corresponding to photon bunching at a short time scale.
An experimental scheme and data processing approaches are proposed for measuring by analog photo detectors the normalized second-order correlation function of the biphoton field generated under spontaneous parametric down-conversion. Obtained results are especially important for quantum SPDC-based technologies in the long-wave spectral ranges, where it is difficult to use the single-photon detector at least in one of the two biphoton channels. The methods of discrimination of analog detection samples are developed to eliminate the negative influence of the detection noises and get quantitatively true values of both the correlation function and the detector quantum efficiency. The methods are demonstrated depending on whether two single-photon avalanche photo detectors are used in both SPDC channels, or at least one single-photon detector is replaced by a photo-multiplier tube which cannot operate in the photon counting mode.