Quantum vortices naturally emerge in rotating Bose–Einstein condensates (BECs) and, similarly to their classical counterparts, allow the study of a range of interesting out-of-equilibrium phenomena, such as turbulence and chaos. However, the study of such phenomena requires the determination of the precise location of each vortex within a BEC, which becomes challenging when either only the density of the condensate is available or sources of noise are present, as is typically the case in experimental settings. Here, we introduce a machine-learning-based vortex detector motivated by state-of-the-art object detection methods that can accurately locate vortices in simulated BEC density images. Our model allows for robust and real-time detection in noisy and non-equilibrium configurations. Furthermore, the network can distinguish between vortices and anti-vortices if the phase profile of the condensate is also available. We anticipate that our vortex detector will be advantageous for both experimental and theoretical studies of the static and dynamic properties of vortex configurations in BECs.

量子涡流自然出现在旋转的玻色-爱因斯坦凝聚 (BEC) 中，并且与经典的对应物类似，允许研究一系列有趣的非平衡现象，例如湍流和混沌。然而，对此类现象的研究需要确定 BEC 内每个涡流的精确位置，这在只有冷凝物密度可用或存在噪声源时变得具有挑战性，这在实验环境中是典型的情况。在这里，我们介绍了一种基于机器学习的涡流检测器，其由最先进的对象检测方法驱动，可以准确定位模拟 BEC 密度图像中的涡流。我们的模型允许在嘈杂和非平衡配置中进行稳健和实时的检测。此外，如果冷凝水的相位分布也可用，则网络可以区分涡流和反涡流。我们预计我们的涡流检测器将有利于 BEC 中涡流配置的静态和动态特性的实验和理论研究。