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arXiv:2310.15989

Detecting the phase transition in a strongly-interacting Fermi gas by unsupervised machine learning

D. Eberz, M. Link, A. Kell, Moritz Breyer, Gao, K., Michael Köhl

Published Oct 24, 2023• 0 citations
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Abstract

We study the critical temperature of the superfluid phase transition of strongly-interacting fermions in the crossover regime between a Bardeen-Cooper-Schrieffer (BCS) superconductor and a Bose-Einstein condensate (BEC) of dimers. To this end, we employ the technique of unsupervised machine learning using an autoencoder neural network which we directly apply to time-of-flight images of the fermions. We extract the critical temperature of the phase transition from trend changes in the data distribution revealed in the latent space of the autoencoder bottleneck.

DOI
10.48550/arxiv.2310.15989

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We study the critical temperature of the superfluid phase transition of strongly-interacting fermions in the crossover regime between a Bardeen-Cooper-Schrieffer (BCS) superconductor and a Bose-Einstein condensate (BEC) of dimers. To this end, we employ the technique of unsupervised machine learning using an autoencoder neural network which we directly apply to time-of-flight images of the fermions. We extract the critical temperature of the phase transition from trend changes in the data distribution revealed in the latent space of the autoencoder bottleneck.
We study the critical temperature of the superfluid phase transition of strongly interacting fermions in the crossover regime between a Bardeen-Cooper-Schrieffer superconductor and a Bose-Einstein condensate of dimers. To this end, we employ the technique of unsupervised machine learning using an autoencoder neural network, which we directly apply to time-of-flight images of the fermions. We extract the critical temperature of the phase transition from trend changes in the data distribution revealed in the latent space of the autoencoder bottleneck.
We determine the phase diagram of strongly correlated fermions in the crossover from Bose-Einstein condensates of molecules (BEC) to Cooper pairs of fermions (BCS) utilizing an artificial neural network. By applying advanced image recognition techniques to the momentum distribution of the fermions, a quantity which has been widely considered as featureless for providing information about the condensed state, we measure the critical temperature and show that it exhibits a maximum on the bosonic side of the crossover. Additionally, we backanalyze the trained neural network and demonstrate that it interprets physically relevant quantities.
This thesis covers two fields of research carried out in the context of ultracold Fermi gases: Non-equilibrium physics in the BEC-BCS crossover and the use of machine learning methods in physics. \n\t \nThe BEC-BCS crossover is of particular interest for the investigation of low-temperature superconductivity and related many-body phenomena. We realise the BEC-BCS crossover experimentally by cooling a mixture of two hyperfine states of fermionic lithium atoms far below degeneracy. To tune the interaction between the constituents, we make use of a broad magnetic Feshbach resonance between the states. We achieve temperatures far in the degenerate regime that can be tuned by a trap release heating procedure. Being able to tune temperature and interaction allows us to access the whole BEC-BCS crossover regime and investigate related phenomena. \n\t \nOne key quantity across the crossover is the critical temperature of the thermal to superfluid phase transition that signals condensation of pairs. The critical temperature can be calculated in the limits of weak interactions, however, for strong interactions theoretical treatment is difficult. In this thesis, we use neural networks to explore the critical temperature in the whole crossover regime with unprecedented accuracy. We show that a supervisedly trained neural network can not only detect the critical temperature, but also distinguish between Cooper pairs and Feshbach molecules, which was not possible before. Moreover, we show that an unsupervisedly trained autoencoder network is able to determine the critical temperature without any external input other than time-of-flight pictures. \n\t \nAnother important quantity in the crossover regime is the superfluid gap parameter. We measure the gap by exciting the Higgs mode through radio-frequency modulation of the atom population. In the BCS limit, the frequency of the Higgs mode is given by twice the gap frequency. By observing the frequency dependent response of the system we can therefore measure the gap parameter. Towards strong interactions, the observed feature broadens, signalling an instability of the mode due to the gradual violation of the required particle-hole symmetry. \n\t \nExploring the non-equilibrium behaviour of a Fermi gas in the BEC-BCS crossover might hold the key to understand the formation dynamics of pairs and how to induce superconductivity in a system that does not exhibit superconductivity in its equilibrium state. In this work, we present two ways to expose the system to a sudden change of interaction, resulting in a non-equilibrium response. Firstly, we use a fast radio-frequency transfer of one of the hyperfine states into a different, third state. We observe dynamics on several timescales in the momentum distribution and condensate fraction. Secondly, we develop a new coil system that is able to change the magnetic field at the atom position by tens of Gauss within a few microseconds. We detail the construction, testing and alignment process and present investigations into the long-time response of the system. \n\t \nMachine learning procedures can not only be used for data analysis, but also to improve upon the control over experimental systems. In this work we present a novel approach to improve the detection and correction of experimental errors exponentially. We use two machine learning approaches, principal component analysis and small, fully connected neural networks to create an empirical model of the experimental setup. Using this model allows us to reduce the required amount of data for compensation of noise sources exponentially. We demonstrate both approaches in the context of micromotion compensation on a single trapped ytterbium ion in a radio-frequency Paul trap.
We determine the size of the critical region of the superfluid transition in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover of a three-dimensional fermion gas, using a renormalization-group approach to a bosonic theory of pairing fluctuations. For the unitary Fermi gas, we find a sizable critical region $[{T}_{G}^{\ensuremath{-}},{T}_{G}^{+}]$, of order Tc{T}_{c}Tc​, around the transition temperature Tc{T}_{c}Tc​ with a pronounced asymmetry: $|{T}_{G}^{+}\ensuremath{-}{T}_{c}|/|{T}_{G}^{\ensuremath{-}}\ensuremath{-}{T}_{c}|\ensuremath{\sim}8$. The critical region is strongly suppressed on the BCS side of the crossover but remains important on the BEC side.
The strongly correlated regime of the crossover from Bardeen-Cooper-Schrieffer pairing to Bose-Einstein condensation can be realized by diluting a system of two-component fermions with a short-range attractive interaction. We investigate this system via a novel continuous-space-time diagrammatic determinant Monte Carlo method and determine the universal curve Tc/epsilonF for the transition temperature between the normal and the superfluid states as a function of the scattering length with the maximum on the Bose-Einstein condensation side. At unitarity, we confirm that Tc/epsilonF=0.152(7).
We theoretically investigate the specific heat at constant volume C V in the BCS(Bardeen-Cooper-Schrieffer)-BEC(Bose-Einstein-condensation)-crossover regime of an ultracold Fermi gas, below the superfluid phase transition temperature T c . Within the strong-coupling framework developed by Nozières and Schmitt-Rink, we show that the temperature dependence of C V drastically changes as one passes through the crossover region, and is sensitive to strong fluctuations in the Cooper channel near the unitarity limit. We also compare our results to a recent experiment on a 6 Li unitary Fermi gas. Since fluctuation effects are a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how the fermionic BCS superfluid changes into BEC with increasing the interaction strength, from the viewpoint of specific heat.