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Fundamental impossibility of a superradiant neutrino laser

Yu-Kun Lu, Hanzhen Lin, Wolfgang Ketterle

TL;DR

The paper investigates whether an ensemble of fermionic emitters can exhibit superradiance when emitting fermions (neutrinos) rather than photons. By formulating an idealized fermionic Dicke model and solving it analytically, it shows that collective emission amplitudes do not add coherently for fermions, constraining the maximum emission rate to $N\Gamma_0$ rather than $N^2\Gamma_0$, thereby ruling out a neutrino laser based on true superradiance. The analysis uses a Lindblad framework with a single dominant neutrino mode, derives exact dynamics for multiple damping regimes, and discusses multi-mode extensions and dephasing. Overall, the work clarifies a fundamental difference between fermionic and bosonic collective emission and places strong limits on proposed fermionic superradiant devices, while highlighting that collective behavior can still arise for low-excitation states.

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.

Fundamental impossibility of a superradiant neutrino laser

TL;DR

The paper investigates whether an ensemble of fermionic emitters can exhibit superradiance when emitting fermions (neutrinos) rather than photons. By formulating an idealized fermionic Dicke model and solving it analytically, it shows that collective emission amplitudes do not add coherently for fermions, constraining the maximum emission rate to rather than , thereby ruling out a neutrino laser based on true superradiance. The analysis uses a Lindblad framework with a single dominant neutrino mode, derives exact dynamics for multiple damping regimes, and discusses multi-mode extensions and dephasing. Overall, the work clarifies a fundamental difference between fermionic and bosonic collective emission and places strong limits on proposed fermionic superradiant devices, while highlighting that collective behavior can still arise for low-excitation states.

Abstract

Here we address the fundamental question whether an idealized system of atoms will show collective behavior and superradiance when it emits fermions instead of photons. We show that the maximum emission is and not 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.
Paper Structure (8 sections, 22 equations, 3 figures)

This paper contains 8 sections, 22 equations, 3 figures.

Table of Contents

  1. End Matter
  2. Fermions emitting fermions
  3. Calculation of the emission matrix elements
  4. Lindblad equation for atoms
  5. Steady state (with a non-zero $\kappa$):
  6. Lossless limit $(\kappa=0)$:
  7. Weak damping limit $(\kappa\ll g\sqrt{N})$:
  8. Bad cavity limit $(\kappa\gg g\sqrt{N})$ (adiabatic elimination):

Figures (3)

  • Figure 1: Superradiant "laserlike" emission of light has been observed from sodium BEC after laser excitation SR_Rayleigh. Recently, it has been suggested that radioactive BEC can be used to realize neutrino lasers neutrino_laser_jones_formaggio. However, as we explain in this paper, fermionic emission cannot be enhanced.
  • Figure 2: Comparison of the collective emission process for bosonic and fermionic radiation. In the bosonic case, the emission occurs along Dicke "ladders", whereas for fermions the emission stops after emitting a single neutrino due to Pauli blocking by a fermionic excitation left behind after the emission. For neutrino emission, the states form coupled pairs of bright and dark states.
  • Figure 3: Fermion emission structure for 4 atoms and 3 modes. The 16 total possible states are grouped into two sectors of 8 states each. Each sector is coupled by solid, dashed and dotted lines representing fermion emission into mode A, B and C. Connectivity in each sector is identical to a cube. For two modes, the dotted lines are eliminated, and the states fragment into 4 groups of 4 states.