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Journal of the Optical Society of America B

Femtosecond spontaneous parametric upconversion and downconversion in a quadratic nonlinear medium

Jinyu Sun, Shian Zhang, Tianqing Jia, Zugeng Wang, Zhenrong Sun

Published Feb 26, 2009• 8 citations
Publisher

Abstract

Spontaneous parametric upconversion (SPUC) and spontaneous parametric downconversion (SPDC) have been observed in the β-barium borate (BBO) crystal, and their mechanisms are experimentally and theoretically investigated. SPUC, tuned from 530 to 600 nm with a FWHM of about 25 nm, can be attributed to the sum frequency between the quantum noise and the fundamental laser pulse in the type II phase matching condition (e+o→e). SPDC, tuned from 480 to 520 nm with a FWHM of about 15 nm, can be attributed to the difference frequency between the quantum noise and the fundamental laser pulse in the type I phase matching condition (e→o+o).

DOI
10.1364/josab.26.000549

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Spontaneous parametric upconversion (SPUC) and spontaneous parametric downconversion (SPDC) have been observed in the β-barium borate (BBO) crystal, and their mechanisms are experimentally and theoretically investigated. SPUC, tuned from 530 to 600 nm with a FWHM of about 25 nm, can be attributed to the sum frequency between the quantum noise and the fundamental laser pulse in the type II phase matching condition (e+o→e). SPDC, tuned from 480 to 520 nm with a FWHM of about 15 nm, can be attributed to the difference frequency between the quantum noise and the fundamental laser pulse in the type I phase matching condition (e→o+o).
The frequency correlation (or decorrelation) of photon pairs is of great importance in long-range quantum communications and photonic quantum computing. We experimentally characterize a spontaneous parametric down conversion (SPDC) source, based on a β-Barium Borate (BBO) crystal cut for type-II phase matching at 1550 nm which has the capability to emit photons with positive or no spectral correlations. Our system, depicted in Fig. 1a), employs a carefully designed detection method exploiting two InGaAs detectors.
Abstract Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
Nonlinear crystals are typically used when interaction of different frequencies of light is requested. In classical optics these nonlinear phenomena are used for second-harmonic generation, sum-frequency generation, optical parametric amplification and many other effects. In quantum optics, dealing with optical interaction on the level of individual photons, the most prominent process is spontaneous parametric down-conversion (SPDC),1 where the crystal is pumped by intensive laser light and the crystal can mediate the splitting of a pump photon to a photon pair. The two generated photons are typically called signal and idler. Influence of magnetic field on these nonlinear processes was not thoroughly tested yet. This topic deserves intensive study both from theoretical and experimental point of view, because the magnetic field can decrease the symmetry of the nonlinear crystal and so it may allow to use new types of phase-matching conditions. We started to test the SPDC process in BBO crystals. Nonlinear magneto-optic tensor of this material is not known and we can hardly predict it. According to our first theoretical derivations the efficiency of the nonlinear processes has to oscillate when rotating the magnetic-field orientation.
We propose a protocol for probing mechanically induced stochastic phase-matching fluctuations in spontaneous parametric downconversion (SPDC) by Hong-Ou-Mandel (HOM) interferometry. The analysis is formulated for collinear type-II SPDC in β-barium borate (BBO). We distinguish the ideal white-jerk limit from the experimentally relevant finite-bandwidth regime. In the ideal limit, the incremental phase variance generated during a photon transit scales as L5; however, for a 5-mm BBO crystal, the transit time is only about 29 ps, so a piezoelectric mechanical drive is quasi-static on this time scale and the L5 law is not assumed as a direct experimental signature. Instead, the measured acceleration power spectral density and the mechanical transfer function are used to calculate the finite-bandwidth phase fluctuations. The connection to HOM visibility is derived through the biphoton joint spectral amplitude: stochastic phase mismatch modifies the phase-matching function, and the ensemble-averaged spectral-exchange overlap determines the coincidence dip. A frequency-independent common phase cancels from this overlap and therefore does not reduce HOM visibility. The resulting formulation provides a directly testable route for phase-stability metrology without requiring the experimentally inaccessible white-noise approximation.