Fig. 1: Principles of the quantum Pauli engine.
a, Schematic of the experimental set-up. The atom cloud (purple ellipsoid) is trapped in the combined fields of a magnetic saddle potential (orange surface) and an optical dipole trap potential (blue cylinder) operating at a wavelength of 1,070 nm. The absorption pictures are taken with an imaging beam (purple arrow) in the −z direction. The scale bar on the absorption picture corresponds to 50 μm. b, Cycle of the Pauli engine. Starting with a molecular BEC that macroscopically populates the ground state of the trap at well-defined temperature T (point A), the first step, A → B, performs work W1 on the system by compressing the cloud through an increase of the radial trap frequency \({\bar{\omega }}_{{\rm{B}}} > {\bar{\omega }}_{{\rm{A}}}\). This is achieved by enhancing the power of the trapping laser. The second stroke, B → C, increases the magnetic field strength from BA = 763.6 G (76.36 mT) to the resonant field BC = 832.2 G, while keeping the trap frequency constant. This leads to a change in the quantum statistics of the system as the working medium now forms a Fermi sea with an associated addition of Pauli energy \({E}_{2}^{{\rm{P}}}\), which substitutes the heat stroke. Step C → D expands the trap back to the frequency \({\bar{\omega }}_{{\rm{A}}}\) and corresponds to the second work stroke W3. Finally, the system is brought back to the initial state with bosonic quantum statistics during step D → A by reducing BC to BA, which corresponds to a change in the Pauli energy \({E}_{4}^{{\rm{P}}}\). The population distributions in the harmonic trap of the atoms with spin up (blue) and spin down (red) are indicated at each corner. c, Examples of absorption pictures at each point of the engine cycle, where the particular change in size from B → C is due to the Pauli stroke indicating that the Pauli energy increases the size of the cloud in the external potential. Scale bars, 50 μm.
