Fundamental impossibility of a superradiant neutrino laser

TL;DR

This paper proves that superradiance cannot occur in a fermionic system like neutrinos, as emission scales linearly with atom number, unlike the quadratic scaling in photon superradiance, making a superradiant neutrino laser impossible.

Contribution

It provides a rigorous proof that fermionic systems cannot exhibit superradiance, contrasting with bosonic systems, and derives the exact solution for the fermionic Dicke model.

Findings

Maximum emission scales as N, not N^2

Superradiance is fundamentally impossible for fermions

States with low excitation can show collective behavior

Abstract

Here we address the fundamental question whether an idealized system of $N$ atoms will show collective behavior and superradiance when it emits fermions instead of photons. We show that the maximum emission is $\propto N$ and not $\propto N^2$ which proves the absence of superradiance and shows that the recent proposal to realize a superradiant neutrino laser is impossible. This can be understood as either destructive interference of fermionic transition amplitudes, or Pauli blockade by collective excitations with fermionic nature. On the other hand, states with low excitation can show collective behavior. We derive the exact solution of the fermionic Dicke problem and analyze the decay dynamics in various regimes.