[Paper Review] Spectral and statistical properties of high-gain parametric down-conversion

Kirill Yu. Spasibko|arXiv (Cornell University)|Jul 25, 2020

Advanced Fiber Laser Technologies155 references4 citations

TL;DR

This thesis investigates high-gain parametric down-conversion (PDC) as a source of bright squeezed vacuum (BSV) states with strong nonclassical and statistical properties. It demonstrates that high-gain PDC generates macroscopically bright, quadrature-squeezed light with heavy-tailed photon-number distributions, enhancing multiphoton processes like harmonic generation by up to two orders of magnitude compared to coherent light, enabling new applications in ultrafast spectroscopy and quantum-enhanced imaging.

ABSTRACT

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.

Motivation & Objective

• To investigate the spectral and statistical properties of high-gain parametric down-conversion (PDC) beyond the conventional low-gain regime.
• To understand how high parametric gain leads to macroscopically bright, nonclassical light with strong photon-number fluctuations.
• To demonstrate the use of high-gain PDC as a pump for multiphoton processes, significantly enhancing efficiency.
• To explore novel applications enabled by giant twin beams and heavy-tailed photon statistics in high-gain PDC.
• To establish experimental and theoretical frameworks for characterizing spectral correlations, mode content, and interference effects in high-gain PDC.

Proposed method

• Theoretical modeling of PDC in normal and anomalous group velocity dispersion (GVD) regimes to analyze spectral and mode structure.
• Experimental measurement of joint spectral intensity (JSI) and correlation functions (CF) using narrowband filtering and intensity difference noise analysis.
• Use of temporal and spatial walk-off matching in nonlinear crystals to generate narrowband, high-gain twin beams.
• Application of normalized correlation functions and complementary cumulative distribution functions (CCDF) to characterize photon-number fluctuations.
• Implementation of beam splitter interference experiments to observe macroscopic Hong-Ou-Mandel (HOM) effects in high-gain PDC.
• Demonstration of second, third, and fourth harmonic generation from BSV, comparing efficiency to coherent light pumping.

Experimental results

Research questions

• RQ1 How do spectral and mode properties of high-gain PDC evolve with increasing parametric gain, especially in anomalous GVD regimes?
• RQ2 What is the nature of interference effects, such as macroscopic HOM interference, in high-gain PDC?
• RQ3 To what extent do photon-number fluctuations in bright squeezed vacuum (BSV) enhance multiphoton processes like harmonic generation?
• RQ4 How can spatial and temporal walk-off matching be used to generate giant, narrowband twin beams in high-gain PDC?
• RQ5 What statistical properties, such as heavy-tailed photon-number distributions, emerge in high-gain PDC and how do they affect nonlinear processes?

Key findings

• High-gain PDC produces bright squeezed vacuum (BSV) states with up to hundreds of milliwatts of mean power while maintaining sub-shot-noise quadrature fluctuations.
• The normalized correlation functions of BSV remain unchanged under narrowband filtering, confirming the robustness of nonclassical correlations.
• Multiphoton processes such as second, third, and fourth harmonic generation are enhanced by up to two orders of magnitude when pumped with BSV compared to coherent light.
• Extreme photon-number fluctuations in BSV lead to heavy-tailed probability distributions, with events exceeding the mean by over 100 times observed frequently.
• Supercontinuum generation from BSV exhibits power-law photon-number distributions with exponents less than 2, resulting in undefined mean photon number and heavy-tailed statistics.
• Macroscopic Hong-Ou-Mandel interference is experimentally observed, demonstrating collective quantum behavior in high-gain PDC systems.