Photon-pair sources based on nonlinear optical processes, such as four-wave mixing (FWM) in polarization-maintaining fibers (PMFs), have become a key step for advancing quantum communication, computation, and metrology. A great advantage of these sources is that they can encode information in multiple degrees of freedom, including transverse spatial modes and frequencies, enabling high-dimensional quantum states that significantly enhance the capacity and security of quantum networks. However, fully characterizing the quantum state of such photon pairs presents a great challenge due to the complexity of their high-dimensional correlations. Traditional techniques, like quantum state tomography (QST), while accurate, require long measurement times, single-photon sensitivity and extensive computational resources.
In this regard, a recent study by the group of Prof. Virginia Lorenz at the Illinois Quantum Information Science & Technology Center (IQUIST) of the University of Illinois Urbana-Champaign, published in ArXiv, demonstrates a novel approach to achieving efficient and detailed spatio-spectral state estimation by using stimulated emission [link].
In this study, the signal beam of our femtosecond optical parametric oscillator (OPO) InspireTM HF100, tuned at 620 nm, was employed to pump a few-mode PMF, generating photon pairs through spontaneous four-wave mixing. This nonlinear process relies on the c(3) nonlinear optical susceptibility of the fiber to annihilate two pump photons and create a signal and an idler photon pair. In parallel, a narrow-linewidth CW seed beam was carefully prepared to match specific transverse modes and frequencies of the idler photons, stimulating the generation of signal-idler pairs in defined quantum states. A general scheme of this process is depicted in Fig. 1.
Figure 1: Experimental scheme on the photon-pair generation in PMFs by stimulated emission. (a) Intensity distributions of linearly polarized (LP) modes in PMFs. (b) Different stages of the photon-pair generation setup used in the experiment. Figure adapted from [1].
This process amplified specific photon-pair generation pathways, allowing to selectively probe the quantum state’s structure. By combining stimulated emission with advanced detection techniques, including spectrometry and transverse-mode imaging, the authors were able to map out the joint spectral intensities (JSIs) of the photon pairs (Fig. 2.a). This mapping revealed detailed inter- and intra-degree-of-freedom correlations that are difficult to access through spontaneous emission measurements alone. In addition, numerical simulations of the JSIs revealed that a new factor accounting for a parity birefringence dispersion (δ) between the signal and the idler photons was needed in order to reproduce the experimental results, i.e. the spectral separation observed between different FWM processes (Fig. 2.b).
Figure 2: (a) transverse-mode profiles (top) and JSI plot (down) for the case in which the pump and the seed transverse modes are equal to |d⟩. (b) Numerical simulation of the JSIs plots for two different parity birefringence dispersion factors (δ). Figure adapted from [1].
Increasing the spectral and spatial overlap between the FWM processes maximizes entanglement and reduces decoherence, which is essential for optimizing photon-pair generation. In order to test this, the authors performed a transverse-mode quantum state estimation from transverse-mode-resolved JSIs by using shorter optical fibers (2.5 cm-long PMFs) fused together using the cross-splicing method. This results in a wider spectral bandwidth of the phase-matching and minimum temporal walk-off between the |𝑒⟩ and |𝑜⟩ modes, respectively (Fig. 2.b). Despite not achieving maximum spectral and spatial overlap between FWM processes, likely due to the fiber parameters, the authors obtained much richer quantum state predictions by stimulated emission than with conventional transverse-mode quantum state tomography (QST).
The implications of this technique are significant. In quantum communication, the ability to efficiently characterize high-dimensional entangled states is critical for scaling up secure networks and increasing information capacity. The method is equally valuable in quantum computation, where precise control over quantum states is essential for error-corrected operations. The ability to diagnose and mitigate imperfections in photon-pair sources, such as spectral overlaps or modal mismatches, opens up new possibilities for hybrid quantum systems that integrate multiple degrees of freedom.
By using stimulated emission to characterize photon-pair sources with unprecedented detail and efficiency, this study represents a significant step forward in the development of quantum technologies. It provides a robust framework for understanding and optimizing complex quantum states, leading the way for new innovations in quantum communication and computation.
To learn more about how femtosecond OPO systems can enhance your research and development efforts, please contact us directly at info@radiantis.com.
We express our gratitude for the collaboration of Prof. Virginia Lorenz’s group, with special thanks to Dong Beom Kim, for their contributions to the preparation of this application note.
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- D. B. Kim, X. Hu, A. B. U’Ren, K. Garay-Palmett, V. O. Lorenz. “Spatio-Spectral Quantum State Estimation of Photon Pairs from Optical Fiber Using Stimulated Emission”, arXiv preprint arXiv.2410.00298 (2024).
