Beating the shot-noise limit

The current shot-noise of an electron beam is proportional to its average current and the frequency bandwidth. This is a consequence of the Poisson distribution statistics of particles emitted at random from any source. Here we demonstrate noise suppression below the shot-noise limit in optical frequencies for relativistic electron beams. This process is made possible by collective Coulomb interaction between the electrons of a cold intense beam during beam drift1. The effect was demonstrated by measuring a reduction in optical transition radiation power per unit of electron-beam pulse charge. This finding indicates that the beam charge homogenizes owing to the collective interaction, and its distribution becomes subPoissonian. The spontaneous radiation emission from such a beam would also be suppressed (Dicke’s subradiance2). Therefore, the incoherent spontaneous radiation power of any electron-beam radiation source (such as free-electron lasers3,4) can be suppressed, and the classical coherence limits5 of seed-injected free-electron lasers6 may be surpassed. Current shot-noise suppression in an electron beam in the optical frequency regime is an effect of particle self-ordering and charge homogenization on the scale of optical wavelengths7, which statistically corresponds to the exhibition of sub-Poissonian electron number statistics (similarly to photons in squeezed light8). A dispute over the feasibility of this effect at optical frequencies is resolved in the experiment reported here. We have evidence for electron-beam noise suppression from measurement of the optical transition radiation (OTR) power emitted by a beam on incidence on a metal screen after passing through a drift section. The OTR emission is proportional to the current shot-noise of the incident beam. In a randomly distributed stream of particles that satisfies Poisson statistics, the variance of the number of particles that pass through any cross-section at any time period T is equal to the number of particles NT that pass this cross-section during the same time T , averaged over different times of measurements. Consequently, the current fluctuation is I = e √ NT/T = e √ IbT/e/T = √ eIb/T . When formally calculated, the average beam shot-noise spectral power (−∞<ω<∞) is: