Heuristic machinery for thermodynamic studies of SU(N) fermions with neural networks

Abstract

The power of machine learning (ML) provides the possibility of analyzing experimental measurements with a high sensitivity. However, it still remains challenging to probe the subtle effects directly related to physical observables and to understand physics behind from ordinary experimental data using ML. Here, we introduce a heuristic machinery by using machine learning analysis. We use our machinery to guide the thermodynamic studies in the density profile of ultracold fermions interacting within SU(N) spin symmetry prepared in a quantum simulator. Although such spin symmetry should manifest itself in a many-body wavefunction, it is elusive how the momentum distribution of fermions, the most ordinary measurement, reveals the effect of spin symmetry. Using a fully trained convolutional neural network (NN) with a remarkably high accuracy of ~94% for detection of the spin multiplicity, we investigate how the accuracy depends on various less-pronounced effects with filtered experimental images. Guided by our machinery, we directly measure a thermodynamic compressibility from density fluctuations within the single image. Our machine learning framework shows a potential to validate theoretical descriptions of SU(N) Fermi liquids, and to identify less-pronounced effects even for highly complex quantum matter with minimal prior understanding.

Interference dynamics of matter-waves of SU($N$) fermions

“…This feature implies that, for repulsive interaction, we can access the number of particles N p ; for attractive interaction we can access on the number of components. Therefore, by following the above protocol, we can access both N p and N separately (see [55] for characterization of SU(N ) systems through neural networks).…”

“…We demonstrate how the resulting interference patterns reflect important features of the system, including the specific angular momentum fractionalization and parity effects characterizing the system. Particularly, we highlight how our approach may be utilized to detect the number of particles and components, both of which are notoriously hard to extract from an experimental setting [55].…”

Observing a topological phase transition with deep neural networks from experimental images of ultracold atoms

“…We further visualize the filters and convoluted result of the trained neural network and find that the spin imbalance information plays a significant role when the neural network makes the classification, which implies that the probability curve represents the phase transition between two distinct phases instead of simple interpolation. This suggests that the neural network analysis not only processes previously unknown information [16] but also performs a conventional analysis in a noise-resilient manner. It will be interesting to systematically investigate how the neural network can be resilient to systematic noises (e.g.…”

“…This understanding may to some extent exclude the possibility that the probability curve in Fig. 3b is a simple interpolation, and also allow to generalize the application of machine learning analysis to various manybody quantum systems [16,[25][26][27][28][29][30][31]. In our work, the machine learning analysis of topological quantum phases can guide us to extract right features from experimental images.…”

“…Recently, machine learning techniques, such as deep convolutional neural network, have become an indispensable tool in many technological areas and also proven its power in quantum many-body physics [12][13][14][15][16]. For example, both supervised learning and unsupervised learning have been used to determine topological phases [17] and further map out the phase diagram [18,19] due to their ability to classify or identify massive data sets such as experimental images.…”