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Journal of the European Optical Society Rapid Publications

Ultra-broad Schmidt modes for biphoton states generated by SPDC in the chirped QPM crystals

Wang Jinbao, Zhan Zheng, Helin Wang, Qiang Lin

Published Dec 4, 2024• 0 citations
Publisher

Abstract

In the realm of quantum optics, the manipulation and characterization of biphoton states hold significant importance for advancing quantum information processing and communication technologies. This study explores the Schmidt decomposition of ultra-broad biphoton states, revealing that most modes are fulfilled with the frequency response points, and certain modes exhibit exceptionally broad Schmidt spectra. These Schmidt modes in frequency domain are significantly reshaped and widened by a crystal at a moderate chirp-rate when pump bandwidth is about several Giga-Hertz.

DOI
10.1051/jeos/2024047

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In the realm of quantum optics, the manipulation and characterization of biphoton states hold significant importance for advancing quantum information processing and communication technologies. This study explores the Schmidt decomposition of ultra-broad biphoton states, revealing that most modes are fulfilled with the frequency response points, and certain modes exhibit exceptionally broad Schmidt spectra. These Schmidt modes in frequency domain are significantly reshaped and widened by a crystal at a moderate chirp-rate when pump bandwidth is about several Giga-Hertz.
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.
As some of the most promising quantum applications such as high resolution quantum optical coherence tomography (QOCT) [1] with dispersion cancellation as well as quantum key distribution require frequency entanglement. Therefore, frequency entanglement light sources are an essential importance for implement of many quantum optical applications. So Far, the most prominent method used for the entangled photon pair generation is spontaneous parametric down-conversion (SPDC) in nonlinear crystals. Recently, with adopting chirp quasi-phase matching (QPM) PPSLT (periodically poled stoichiometric lithium tantalate) has been used as source of entangled photons with large bandwidth [2]. However, improving the overall system efficiency is still remain challenging.
The full Schmidt decomposition of spatiotemporally entangled states generated from spontaneous parametric down-conversion (SPDC) has not been carried out until now due to the immense computational complexity arising from the large dimensionalities of the states. In this Letter, we utilize the rotational symmetry of the states to reduce the complexity by at least four orders of magnitude and carry out the decomposition to reveal the precise forms of the spatiotemporal Schmidt modes and the Schmidt spectrum spanning over 10^4 modes. We show that the Schmidt modes have a phase profile with a transverse spatial vortex structure that endows them with orbital angular momentum at all frequencies. In the high-gain regime, these Schmidt modes broaden and the Schmidt spectrum narrows with increasing pump strength. Our work can spur novel applications at the intersection of quantum imaging and spectroscopy that utilize entangled states produced from SPDC.
Parametric down-conversion of light (PDC) in a quasi-phase-matched (QPM) nonlinear crystal can be spectrally very broad when the spatial frequency of periodical poling is linearly chirped. The present day technology makes possible the fabrication of chirped QPM crystals phase-matched for PDC in all optical spectrum. In the low-gain regime this allows for generation of biphotons with the correlation time of the order of a single optical cycle. A natural next step is the study of the PDC light produced by such a crystal in the high-gain regime, where PDC is widely used as a source of squeezed states of light. Up to now only a classical treatment of this regime was undertaken. In the present work we demonstrate a possibility to generate single-cycle squeezing in a chirped QPM nonlinear crystal with squeezing spectrum covering almost all the optical octave.