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International Journal of Quantum Information

BIPHOTON WAVE PACKETS GENERATED IN APERIODICALLY POLED CRYSTALS

G. Kh. Kitaeva, Sergey Kovalev, Kirill A. Kuznetsov

Published Jan 1, 2009• 2 citations
Publisher

Abstract

The influence of disordering of quasi-phase-matched structures on the properties of biphoton fields generated by spontaneous parametric down-conversion in periodically poled crystals is studied in the general form, taking into consideration arbitrary one-dimensional spatial distribution of the crystal second-order susceptibility. It is shown that the spectral amplitudes of the biphoton wave function become complex and gain frequency- and angle-dependent phase shifts in the structures with unequal lengths of domains. Effects of the spectrum broadening and the phase shifting are expressed in terms of the crystal non-linear transfer function. Spectrum of the first-order correlation function is found to be strictly dependent on the transfer function module, but insensitive to the phase shifts. Availability of the phase shifts makes the second-order temporal correlation function of the broadened as-generated biphoton field to be almost the same as in case of a single-domain crystal. At the same time, possibility of strong temporal biphoton compression appears further if an additional phase-compensating element is placed after the aperiodically poled crystal.

DOI
10.1142/s0219749909004736

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The influence of disordering of quasi-phase-matched structures on the properties of biphoton fields generated by spontaneous parametric down-conversion in periodically poled crystals is studied in the general form, taking into consideration arbitrary one-dimensional spatial distribution of the crystal second-order susceptibility. It is shown that the spectral amplitudes of the biphoton wave function become complex and gain frequency- and angle-dependent phase shifts in the structures with unequal lengths of domains. Effects of the spectrum broadening and the phase shifting are expressed in terms of the crystal non-linear transfer function. Spectrum of the first-order correlation function is found to be strictly dependent on the transfer function module, but insensitive to the phase shifts. Availability of the phase shifts makes the second-order temporal correlation function of the broadened as-generated biphoton field to be almost the same as in case of a single-domain crystal. At the same time, possibility of strong temporal biphoton compression appears further if an additional phase-compensating element is placed after the aperiodically poled crystal.
The generation of biphoton wave packets with a broad spectrum owing to quasi-phase-matched spontaneous parametric down-conversion in a crystal with an aperiodic poling has been considered. Biphotons at the exit of such a sample are not Fourier limited; i.e., their correlation time is much larger than the inverse width of the spectrum. It has been shown that if the inverse grating vector varies linearly along the sample length, the generated biphoton wave packets can be compressed in time by transmitting two-photon light through an optical fiber.
The influence of disordering of one-dimensional quasi-phase matched structures in nonlinear optical crystals on spectral characteristics of parametric processes is studied. Two different correlation functions are introduced for describing the random change of the sign of the second-order nonlinear susceptibility. The optimal conditions for quasi-phase matching of the interacting waves are found. The second aim of the paper is the investigation of important features of spontaneous parametric down-conversion (SPDC) in a homogeneous nonlinear slabs with emphasis of spatial inhomogeneity of interacting waves (in paraxial approximation). We estimate the absolute values of the emission rate of photon pairs produced by SPDC when all fields are in single Gaussian modes.
Here we investigate the all-optical control of spectral correlations in spontaneous parametric down-conversion. We show that when photon pairs are projected onto high-order spatial modes, the spatial structure of the pump field defines the phase-matching function of the nonlinear interaction. Thus, by structuring the pump field in both space and spectrum, the biphoton spectral correlations are fully controlled. Considering a standard periodically-poled crystal as the nonlinear medium, we show that the Gouy phase matching method proposed here can generate both spectrally uncorrelated and high-dimensional spectrally entangled photon pairs, similarly to what is achieved with aperiodically-poled crystals. Furthermore, we show that our method can generate a wider class of quantum states if the pump field is a spatiotemporal wavepacket, that is, if its spatial and spectral structures are correlated.
We study the theory of linearly chirped biphoton wave-packets produced in two basic quasi-phase-matching configurations: chirped photonic-like crystals and aperiodically poled crystals. The novelty is that these structures are considered as definite assembles of nonlinear layers that leads to detailed description of spontaneous parametric down-conversion (SPDC) processes through the discrete Gauss sums. We demonstrate that biphoton spectra for chirped photonic crystals involving a small number of layers consist from definite well-resolved spectral lines. We also discuss the forming of broadband spectra of signal (idler) waves in SPDC for both configurations as number of layers increases as well as in dependence of chirping parameters .
Generation of two-photon light with given spectral and temporal properties is of great interest for quantum communication and quantum metrology applications. In particular, preparation of biphotons with ultra-narrow correlation time is a very important task. In a recent series of papers, our group analyzed the generation of twophoton wavepackets, produced by Spontaneous Parametric Down Conversion, in crystals with linearly chirped quasi-phase matching grating. Wavepackets present very broad spectra but a broad spectrum does not necessarily imply small correlation times, although the inverse is true. Indeed, the spectrum broadening induced by the grating is inhomogeneous; for this reason, the two-photon spectral amplitude present a phase (a frequency chirp) that depend nonlinearly on the frequency. Hence, the two-photon wavepackets are not Fourier transform-limited. As suggested in, the ideal way to make the wavepacket perfectly transform limited is to insert in the path of the biphotons a proper optical medium that compensates the non-linear part of the phase factor present in the spectral amplitude. In our work, we investigate the non-local temporal compression of the photons induced by the insertion of a standard optical fibre in the path of one of the two photons. We present and discuss a systematic study of this phenomenon and some optimal situation where the full numerical calculation shows an effect that can be clearly observed with a realistic set-up. The study has open the way to the practical realization of this idea.
In this paper, we have studied the process of monochromatic pump light in linearly chirped Periodically Poled [Formula: see text] (PPKTP) nonlinear crystal to generate single-cycle biphotons under Quasi-Phase-Matching (QPM) conditions through a Spontaneous Parametric Down-Conversion (SPDC). A detailed analysis of the phase mismatching function reveals that in PPKTP crystals, for the proper frequency range, the phase mismatching [Formula: see text] is stable and relatively close to 0 due to the relatively stable refractive index, and therefore has a good phase matching effect. Even when the chirp rate becomes small, it is able to produce single-cycle biphotons due to the near-perfect phase matching. Of course, as the chirp rate increases, the frequency response range becomes wider, the temporal width is narrower, and the number of cycles is smaller.