A cloud of cold atoms is trapped between two mirrors. Light is shone through it, and the atoms start to emit collectively: this effect is called superradiance. But the atoms don't just 'glow': their spins (internal magnetic arrows) interact with light in two distinct ways. One depends only on intensity, the other on the direction of polarization. When these two mechanisms compete, the threshold for turning on superradiance shifts.
It all comes down to the angle between the polarization of the pump and that of the field inside the cavity. By rotating it, you can smoothly tune the weight of the vector coupling relative to the scalar one. But there's also the Pauli exclusion principle: two identical fermions cannot occupy the same state. Because of this, triggering superradiance requires a sufficient depth of the optical lattice — the light must 'shove' the atoms apart, overcoming their quantum unsociability.
The authors considered a mixture of two atomic species — call them 'spin up' and 'spin down'. If one type outnumbers the other, the transition can become sharp, abrupt, as if part of the crowd suddenly jumped up at once. If they are equal, the transition is smooth. But the boundary beyond which ordered emission begins is still determined by the competition between scalar and vector interactions. This conclusion holds universally for both fermions and bosons.
The Pauli principle prevents two electrons (or fermionic atoms) from being in the same quantum state. This very property stops atoms from 'collapsing' into each other and ensures the stability of matter.