J. Eur. Opt. Society-Rapid Publ. 2025, 21, 3 Ó The Author( s), published by EDP Sciences, 2025 https:// doi. org / 10.1051 / jeos / 2024047 Available online at: https:// jeos. edpsciences. org
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Ultra-broad Schmidt modes for biphoton states generated by SPDC in the chirped QPM crystals
Jinbao Wang 1, 2, Zhan Zheng 2,*, Helin Wang 2,*, and Qiang Lin 2,*
1 College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310023, China 2 Zhejiang Province Key Laboratory of Quantum Precision Measurement, College of Physics, Zhejiang University of Technology,
Hangzhou 310023, China Received 8 November 2024 / Accepted 4 December 2024
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.
Keywords: Biphoton, SPDC, Schmidt modes.
1 Introduction
* Corresponding authors: zhan @ zjut. edu. cn; whlin @ zjut. edu. cn; qlin @ zjut. edu. cn
Multimode states are vital resources in quantum optics [ 1 ]. Broadband frequency modes / short temporal modes are ideal candidates to take advantage of the multimodality of optical states. To date, ultrashort quantum pulses of few cycle [ 2 – 4 ], single cycle [ 5 – 7 ], and even subcycle [ 8 ] levels are successfully generated. Though with some developments in classical theory [ 9 ], fundamental tests [ 10, 11 ], and ultrafast applications [ 12 – 14 ], subcycle regime of quantum nonlinear optics is still challenging, due to the lack of subcycle sources.
Biphoton states [ 15 ], generated by spontaneous parametric down-conversion( SPDC), have the characteristic of nonclassical physics and have been widely studied and applied in theory and experiment. In particular, there is a strong correlation between the signal and idler photons generated in the SPDC process, as well as a high degree of entanglement in space and frequency [ 16, 17 ]. It makes them be attractive and widely applied in quantum optics, quantum information and quantum measurement [ 18, 19 ]. The broadband of spectrum for the biphoton, reaches the terahertz( THz) in frequency, shows many non-classical physical properties and opens up entirely new perspectives [ 20 – 22 ]. In order to better control and modulate the spatial and spectral characteristics of the biphoton, the method for quantifying the entanglement based on the Schmidt decomposition has been shown in Refs. [ 23, 24 ]. The eigenvectors have been reduced single particle density matrices which are named as Schmidt modes. The pure single particle Schmidt mode can be formed with a complete orthogonal basis, and each one can be related with an exact counterpart [ 25 ]. Broadband biphoton states are widely generated with short pump pulses in SPDC process [ 26 ]. The spectra can be broadened by using chirping quasi-phase matching( QPM) crystals [ 27 ], and even with( quasi-) monochromatic pump, the biphoton pulses can be generated at the single cycle level [ 28, 29 ] in many Schmidt modes.
2 Theory
To investigate the physical characteristics of biphoton generated by SPDC in the chirped QPM periodically poled lithium niobate( PPLN) crystal, we set a Gaussian pulse with bandwidth x p as a pump beam passing through the chirped QPM PPLN crystal, analysis how does the various pump bandwidths and chirped rate influence with the physical characteristics of biphoton in multi-mode during the SPDC process.
As shown in Figure 1a. in a SPDC process inside a linearly chirped QPM PPLN crystal of length L, thepoled gratings varying along the propagating z axis, with the alternately opposite poled directions. A photon of a generic frequency x 0 p from a classical strong pump field( central frequency x p, bandwidthr p) can split in two: a photon of frequency x and a partner of frequency x 0 p � x, andvice
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