Fig. 4: Verification of ML-aided detection : density fluctuations and thermodynamic compressibility.
From: Heuristic machinery for thermodynamic studies of SU(N) fermions with neural networks
a, b Classification accuracy of the correct class as a function of the cutoff momentum kc of the mask. The dotted line indicates the accuracy of 94%. c Measurement of density fluctuations with a snapshot. In a line-of-sight integrated density profile, a series of bins containing on average \({\overline{N}}_{a}\) atoms are chosen along the azimuthal direction. Each bin is about 10 (in azimuthal direction) by 17 (in radial direction) µm−1, which is much larger than the optical resolution of the imaging system. The density profile at kx = 0 is shown. d The normalized compressibility of SU(N) fermions κ/κ0 is measured by relative density fluctuations as κ/κ0 = ζSU(N)/ζSU(1). The error bar shows the SE. The dashed line indicates the theory curve \(\kappa /{\kappa }_{0}={[1+\frac{2}{\pi }{k}_{\mathrm{{F}}}{a}_{\mathrm{s}}(N-1)(1+\epsilon {k}_{\mathrm{F}}{a}_{\mathrm{s}})]}^{-1}\) with the uncertainty represented by the shaded region considering the SE of ζSU(1). The inset shows the distribution of the atom number per bin from three images for each spin multiplicity. The distribution is plotted around the average normalized by the degenerate temperature, \((N-{\overline{N}}_{\mathrm{a}})/(T/{T}_{\mathrm{F}})\), where \({\overline{N}}_{\mathrm{a}}\) is the average atom number.
