Employing Supervised and Unsupervised Machine Learning Techniques to Detect the Superfluid Phase Transition of a Strongly Interacting Fermi Gas

We employ supervised and unsupervised machine learning techniques to detect the onset of superfluidity in time-of-flight (ToF) of strongly correlated fermions in the crossover from the Bose-Einstein condensation of molecules (BEC) to Cooper pairing of fermions (BCS). While a direct observation of Cooper pairs is already not possible due to their breaking upon release from the trap, the remaining imprint of pairing on the momentum distribution is also strongly obscured by temperature, interactions and inhomogeneities of the harmonic trap. To overcome this, we implement a supervised neural network as an advanced image recognition technique to reconstruct the condensate fraction from singular ToF images, which enables the determination of the phase transition over the whole crossover. In an alternative approach, we apply an autoencoder network in an unsupervised learning procedure to the ToF data, which organizes the data by temperature and interaction in a low dimensional latent space without any additional inputs. We are able to identify a feature in the latent space which we interpret as the superfluid phase transition.