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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Effects of pump depletion on spatial and spectral properties of parametric down-conversion

Alessia Allevi, Marco Lamperti, Radek Machulka, Ottavia Jedrkiewicz, E. Brambilla, A. Gatti, Jan Peřina, Ondřej Haderka, Maria Bondani

Published May 7, 2015• 5 citations
Publisher

Abstract

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.

DOI
10.1117/12.2178469

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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.
We observed the spectral coherence structure of twin beam states generated by spontaneous parametric down-conversion by using a simple fiber spectrometer synchronized with a pulsed laser source. The recorded single-shot spectra exhibit a well-defined peak structure, where the peak wavelengths change values from shot to shot. We studied the number and the width of the peaks as a function of the different parameters in the experimental setup (pump power, iris size, iris distance from the BBO crystal). Moreover, we evaluated the number of modes in the intensity distribution of the light in different portions of the spectrum. The experimental results indicate that the number of modes from statistics and the number and width of the peaks evolve differently with the parameters.
Using the model of parametric interaction based on the spatiospectral Schmidt modes and generalized parametric approximation, we analyze coherence and the mode structure of ultraintense twin beams generated in the regime with pump depletion. We show that the increase of spatial and spectral coherence with the increasing pump power observed for moderate powers is replaced by a decrease for the pump powers at which pump depletion occurs. This behavior of coherence is opposed to that exhibited by a number of spatiospectral modes effectively constituting the twin beam. The conditions for maximal coherence are analyzed by considering pump-beam parameters (spectral width and transverse radius). The existence of additional coherence maxima occurring at even higher pump powers is predicted and explained by the oscillatory evolution of the modes' populations.
We present the experimental investigation of the coherence properties of the light produced by parametric down conversion in the macroscopic regime, also including pump depletion. In particular, we compare the results obtained in very similar geometric conditions by using two nonlinear crystals having different lengths. We observe that the number of generated photons, the size of spatio-spectral coherence areas, and the number of modes in the photon number statistics exhibit a similar behavior in the two crystals as a function of pump mean power, even if we notice that the absolute values are different. The available theory of parametric down conversion cannot account for these differences.
Parametric down-conversion (PDC) is mostly known in the low-gain (spontaneous) regime, in which the correlated photon pairs are produced. Spontaneous PDC (SPDC) plays a very important role for quantum optics as a variety of quantum states is produced via SPDC. In the high-gain case PDC leads to generation of bright states having up to hundreds mW mean power. With such states almost any nonlinear optical interaction or light-matter interaction becomes more efficient. Even being macroscopically bright, the produced states maintain nonclassical properties as, for example, the fluctuations of electric field quadratures are squeezed below the shot-noise level. The high-gain PDC could be used not only in the same applications as SPDC, it also can provide new ones. Apart from that the high-gain PDC has many remarkable spectral and statistical properties, which are in the focus of this work. The description starts from the PDC generation in normal and anomalous group velocity dispersion ranges. The spectrum and mode content of high-gain PDC is considered as well as their change with the parametric gain are demonstrated. Then, there are the interference effects emerging from the PDC correlations presented, namely the macroscopic analogue of the Hong-Ou-Mandel interference. In addition, it is shown how spatial and temporal walk-off matching could be used for the generation of giant narrowband twin beams. Finally, the statistical properties of high-gain PDC are reviewed as well as their use for multiphoton effects is demonstrated. Photon-number fluctuations of PDC are studied via normalized correlation functions and probability distributions. These fluctuations enhance the generation efficiency for multiphoton effects by orders of magnitude and lead to tremendously fluctuating light described by heavy-tailed photon-number probability distributions.
Abstract The photon statistics of spontaneous parametric down-conversion (SPDC) exhibit dependencies on wavelength, pump power, and coincidence time. Notably, the average photon numbers were found to asymmetrically increase with increasing pump power around the degenerate wavelength of emission. We employ a four-detector Hanbury Brown and Twiss interferometer to study the photon statistics of the signal beam. Coupling the detection scheme to a spectrometer enabled the dynamic probing of different bandwidths within the broadband emission. Spectrally resolving the photon statistics revealed that shorter wavelengths increased nonlinearly with pump power, while longer wavelengths showed more linear behavior, indicating a wavelength-dependent efficiency in the generation of the SPDC. The detection and characterization of complex light sources has wide ranging applications in the fields of quantum metrology, quantum communications, and quantum computing, more specifically, a system that is sensitive to wavelength and photon number distribution.
Abstract Properties of intense twin beams generated in parametric down-conversion in periodically poled LiNbO3 crystals and their chirped variants by intense pump fields are analyzed along the model of intense parametric down-conversion that allows for pump depletion and uses the dual spatio-spectral Schmidt modes. Spectral and spatial intensity auto- and cross-correlation functions are determined as they depend on the pump power. Temporal correlations in intense twin beams at the fs time scale are investigated using the Hong-Ou-Mandel interferometer and the process of sum-frequency generation.