Fig. 4. Comparison of the performance of quantum many-body devices.

a,b, Work output (a) and efficiency (b) as a function of the number of atoms $N_{\mathrm{A}}^i$ in one spin state for a compression ratio ${\overline{\omega }}_{\mathrm{B}}/{\overline{\omega }}_{\mathrm{A}}=1.5$ for the Pauli engine (cyan dots) and the Feshbach cycle (orange diamonds). Small symbols denote individual realizations; large symbols indicate mean values of 20 repetitions with error bars indicating 1σ statistical fluctuations. For comparison, calculations for a non-interacting gas (black dashed line) and an ideal gas (purple solid line) are shown. Dotted lines are fits to the respective work output W ∝ N^α. The fitted exponents α are 1.73(18) and 1.58(13) for the Pauli engine and Feshbach cycle, respectively, well reproduced by our theoretical model (solid cyan and orange lines). Importantly, the efficiency of the Feshbach cycle is essentially zero. c, Accumulated work output (cyan dots) and efficiency (blue triangles) of the Pauli engine over several cycles for a compression ratio ${\overline{\omega }}_{\mathrm{B}}/{\overline{\omega }}_{\mathrm{A}}=1.5$ and an initial number of atoms in one spin state of about Nⁱ = 2.5 × 10⁵.