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arXiv:1405.1190 · Optics Express

Spatial properties of twin-beam correlations at low- to high-intensity transition

Radek Machulka, Ondřej Haderka, Jan Peřina, Marco Lamperti, Alessia Allevi, Maria Bondani

Published May 27, 2014• 26 citations
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Abstract

It is shown that spatial correlation functions measured for correlated photon pairs at the single-photon level correspond to speckle patterns visible at high intensities. This correspondence is observed for the first time in one experimental setup by using different acquisition modes of an intensified CCD camera in low and high intensity regimes. The behavior of intensity auto- and cross-correlation functions in dependence on pump-beam parameters including power and transverse profile is investigated.

DOI
10.1364/oe.22.013374

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•Jan 1, 2012•0 citations
It is shown that spatial correlation functions measured for correlated photon pairs at the single-photon level correspond to speckle patterns visible at high intensities. This correspondence is observed for the first time in one experimental setup by using different acquisition modes of an intensified CCD camera in low and high intensity regimes. The behavior of intensity auto- and cross-correlation functions in dependence on pump-beam parameters including power and transverse profile is investigated.
Spatiospectral properties of twin beams at their transition from low to high intensities are analyzed in parametric and paraxial approximations using decomposition into paired spatial and spectral modes. Intensity auto- and cross-correlation functions are determined and compared in the spectral and temporal domains as well as the transverse wave-vector and crystal output planes. Whereas the spectral, temporal, and transverse wave-vector coherence increases with the increasing pump intensity, coherence in the crystal output plane is almost independent of the pump intensity owing to the mode structure in this plane. The corresponding auto- and cross-correlation functions approach each other for larger pump intensities. The entanglement dimensionality of a twin beam is determined with a comparison of several approaches.
Spatial and spectral coherence of high-intensity twin-beam states propagating from the near-field to the far-field configurations is experimentally investigated by measuring intensity auto- and cross-correlation functions. The experimental setup includes a moving crystal and an iCCD camera placed at the output plane of an imaging spectrometer. Evolution from the tight near-field spatial position cross-correlations to the far-field momentum cross-correlations, accompanied by changeless spectral cross-correlations, is observed. Intensity autocorrelation functions and beam profiles are also monitored as they provide the number of degrees of freedom constituting the down-converted beams. The strength of intensity cross-correlations as an alternative quantity for the determination of the number of degrees of freedom is also measured. The relation between the beam coherence and the number of degrees of freedom is discussed.
We review and compare the results of quantum spatial correlation measurements in parametric down-conversion in the high-gain pulsed regime, with preliminary measurements performed in the low-gain cw-pumped regime. The diagnostics is based on a high quantum efficiency CCD camera, and in the second case the radiation pattern is recorded after temporal integration of the "single-photon" spatial distribution. The effect of the detected number of temporal modes on the accessibility of the sub-shot noise regime is discussed, together with the identification of suitable regimes for weak image detection.
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.
The dynamics of intense twin beams in pump-depleted parametric down-conversion is studied. A generalized parametric approximation is suggested to solve the quantum model. Its comparison with a semiclassical model valid for larger twin-beam intensities confirms its applicability. The experimentally observed maxima in the spectral and spatial intensity auto- and cross- correlation functions depending on pump power are explained in terms of different speeds of the (back-) flow of energy between the individual down-converted modes and the corresponding pump modes. This effect is also responsible for the gradual replacement of the initial exponential growth of the down-converted fields by the linear one. Furthermore, it forms a minimum in the curve giving the effective number of twin-beam modes. These effects manifest a tight relation between the twin-beam coherence and its internal structure, as clearly visible in the model. Multiple maxima in the intensity correlation functions originating in the oscillations of energy flow between the pump and down-converted modes are theoretically predicted.
The spatial correlations between the photon pairs produced by spontaneous parametric down conversion (SPDC) have been investigated in a number of different configurations over the last two decades (1). The high dimensionality of the transverse spatial degrees of freedom (DOF) of the photon pairs can be explored either by projections onto a discrete (infinite) basis, such as the LG modes, or by using a continuous basis defined by the transverse position or momentum of the photons. For instance, it has been shown that their transverse position and momentum display EPR-type correlations (2). Despite the continuous and unbounded nature of both these bases, the most common measurements to date have relied upon the scanning of a single avalanche photodiode or a very small number of individual detectors. This sequential scanning or small number of detectors negates any information capacity advantage in the use of spatial states. Recent years have seen a rapid advance in imaging technologies, particularly for low light levels. Of these technologies the highest quantum efficiency is achieved using electron multiplying CCDs (EMCCD). Developments in low noise EMCCD cameras suggest they are capable of greater than 80% quantum efficiencies and if operated in an ultra-low light environment whilst being maintained at low temperatures, can provide single photon sensitivity (3). EMCCDs have been used in measurements of sub-shot-noise correlations of intensity fluctuations (4, 5) as well as in intensity correlations measurements (6) in the far field of the photon pairs from SPDC. Here we report the observation of spatial correlations from SPDC using an EMCCD camera in both the image and far-field planes of the down conversion crystal. We pump a BBO crystal at 355nm with a few milli-Watts of optical power and use a simple lens system to relay the down-converted light to an EMCCD array which can be positioned in either the image plane or the far-field of the crystal. Our photon flux is around 1/100 per pixel, which approximately doubles the signal obtained when the light is blocked. We typically record 100,000 individual frames and then sum the auto-correlation of the individual frames. We observed intensity correlation and anti-correlation in the image and far-field planes, respectively. In both cases we make the correlations more visible by subtracting a background which is obtained as the average correlation obtained between successive frames. Using this approach we are able to visualize the strength of the correlations in both position and momentum, showing a variance product nearly one order of magnitude below the classical limit in both x and y directions.