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Journal of the Optical Society of America B

Statistics of twin-beam states by photon-number resolving detectors up to pump depletion

Alessia Allevi, Maria Bondani

Published Aug 19, 2014• 31 citations
Publisher

Abstract

We use hybrid photodetectors endowed with partial photon-number resolution to characterize the photon-number distribution of twin-beam states produced at different intensity regimes up to pump depletion. To match the detectors’ dynamics, the light of signal and idler is strongly attenuated by neutral-density filters. Since the filters do not modify the nature of any classical-light statistics, we find that signal and idler are described by a multimode thermal distribution at any pump power. The number of modes decreases at increasing pump power until pump depletion, when the number starts increasing again. The effect is qualitatively interpreted as a selective mode amplification induced by the high-gain parametric process.

DOI
10.1364/josab.31.000b14

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We use hybrid photodetectors endowed with partial photon-number resolution to characterize the photon-number distribution of twin-beam states produced at different intensity regimes up to pump depletion. To match the detectors’ dynamics, the light of signal and idler is strongly attenuated by neutral-density filters. Since the filters do not modify the nature of any classical-light statistics, we find that signal and idler are described by a multimode thermal distribution at any pump power. The number of modes decreases at increasing pump power until pump depletion, when the number starts increasing again. The effect is qualitatively interpreted as a selective mode amplification induced by the high-gain parametric process.
Joint signal-idler photoelectron distributions of twin beams have been measured recently in two distinct regimes: either the mean number of photon pairs per one pump pulse is lower that the number of independent modes or vice versa. Exploiting a microscopic quantum theory for joint quasi-distributions in parametric down-conversion based on the model of superposition of signal and noise we characterize properties of twin beams in terms of quasidistributions using experimental data. In parallel to the microscopic model, joint signal-idler photon-number distribution is reconstructed using the method of maximum likelihood. Negative values as well as oscillating behavior in quantum region are characteristic for the joint signal-idler quasi-distributions of integrated intensities. The larger the mean number of photon pairs per mode the weaker the quantum features are. However, they survive even in the mesoscopic regime, i.e. when tens of photon pairs per mode are present on average. Also the conditional and difference photon-number distributions are shown to be sub-Poissonian and sub-shot-noise, respectively. Violation of classical inequalities for photon-number distributions is discussed.
It is well known that optical twin-beam states (TWB) generated by spontaneous parametric down-conversion (PDC) exhibit spatial and spectral correlations, which can appear in single-shot images obtained by using an imaging spectrometer to resolve emission angles and wavelengths simultaneously. By analyzing series of single-shot images recorded by an EMCCD camera at different powers of the pump beam, we studied the evolution of several quantities characterizing the generated TWB. In particular, we demonstrated that correlation widths in spectrum and space increase monotonically at low pump powers and then start decreasing at higher powers due to the onset of pump depletion. In a complementary way, the Fedorov ratio decreases and then increases again. At the same time, the number of modes evaluated from photon statistics follows a complementary behavior to correlation widths that can be interpreted in terms of the evolution of the number of Schmidt modes in the field.
Twin-beam coherence properties are analyzed in both spatial and spectral domains at high gain, including also the regime of pump depletion. We show an increase in the size of the intensity autocorrelation and cross-correlation areas at increasing pump power, replaced by a decrease in the pump depletion regime. This effect is interpreted as a progressive loss in the mode selection occurring at high-gain amplification. The experimental determination of the number of spatiospectral modes from the measurements of the g(2){g}^{(2)}g(2)-intensity autocorrelation coefficient confirms this explanation.
Changes in the statistical properties of light undergoing second-harmonic generation are investigated in the photon-number-resolving domain. We theoretically demonstrate that when a portion of multimode thermal light produced by parametric down-conversion is up-converted, both the second-harmonics and the residual beam at the fundamental wavelength are endowed with super-thermal photon-number distributions. The experimental results, which were obtained by exploiting the photo-number-resolving capability of hybrid photodetectors, are in excellent agreement with the theoretical expectations.
Joint signal-idler photoelectron distributions of twin beams containing several tens of photons per mode have been measured recently. Exploiting a microscopic quantum theory for joint quasidistributions in parametric down-conversion developed earlier we characterize properties of twin beams in terms of quasidistributions using experimental data. Negative values as well as oscillating behavior in the quantum region are characteristic for the subsequently determined joint signal-idler quasidistributions of integrated intensities. Also the conditional and difference photon-number distributions are shown to be sub-Poissonian and sub-shot-noise, respectively.
The measurement of photon-number statistics of fields composed of photon pairs, generated in spontaneous parametric down-conversion and detected by an intensified charge-coupled device (iCCD) camera, is described. Final quantum detection efficiencies, electronic noises, finite numbers of detector pixels, transverse intensity spatial profiles of the detected beams, as well as losses of single photons from a pair are taken into account in a developed general theory of photon-number detection. The measured data provided by an iCCD camera with single-photon detection sensitivity are analyzed along the developed theory. Joint signal-idler photon-number distributions are recovered using the reconstruction method based on the principle of maximum likelihood. The range of applicability of the method is discussed. The reconstructed joint signal-idler photon-number distribution is compared with that obtained by a method that uses superposition of signal and noise and minimizes photoelectron entropy. Statistics of the reconstructed fields are identified to be multimode Gaussian. Elements of the measured as well as the reconstructed joint signal-idler photon-number distributions violate classical inequalities. Sub-shot-noise correlations in the difference of the signal and idler photon numbers as well as partial suppression of odd elements in the distribution of the sum of signal and idler photon numbers are observed.