• R. Bonifacio, R. Bonifacio
  Universidade Federal de Alagoas, Maceio
• M. Ferrario
  INFN/LNF, Frascati (Roma)
• N. Piovella
  Universita' degli Studi di Milano, MILANO
• G.R.M. Robb
  Strathclyde University, Glasgow
• A. Schiavi
  Rome University La Sapienza, Roma
• L. Serafini
  INFN-Milano, Milano

Funding: Istituto Nazionale di Fisica Nucleare (INFN), Italy

Quantum effects in high-gain FELs become relevant when ρ'=ρ(mcγ/ ћ k)<1. The quantum FEL parameter ρ' rules the maximum number of photons emitted per electrons. It has been shown that when ρ'<1 a "quantum purification" of the SASE regime occurs: in fact, the spectrum of the emitted radiation (randomly spiky in the usual classical SASE regime) shrinks to a very narrow single line, leading to a high degree of temporal coherence. From the definition of ρ it appears that in order to achieve the quantum regime, small values of ρ, beam energy and radiation wavelength are necessary. These requirements can be met only using a laser wiggler. In this work we state the scaling laws necessary to operate a SASE FEL in the Angstrom region. All physical quantities are expressed in terms of the normalized emittance and of two parameters: the ratio between laser and electron beam spot sizes and the ratio between Rayleigh range and electron β-function. The feasibility study of a Quantum SASE FEL experiment using parameters as those foreseen in the SPARC/PLASMONX projects in construction at the INFN Frascati is explicitly discussed.

• R. Bonifacio
  INFN-Milano, Milano
• N. Piovella
  Universita' degli Studi di Milano, MILANO

We formulate a quantum linear theory of the N-particle free-electron laser Hamiltonian model, quantizing both the radiation field and the electron motion, in the steady state regime. Quantum effects such as frequency shift, line narrowing, quantum limitation for bunching and energy spread and minimum uncertainty states are described. Using a second quantization formalism we demonstrate quantum entanglement between the recoiling electrons and the radiation field.

• R. Bonifacio, R. Bonifacio
  Universidade Federal de Alagoas, Maceio
• N. Piovella
  Universita' degli Studi di Milano, MILANO
• G.R.M. Robb
  Strathclyde University, Glasgow

We present a proof of principle of the novel regime of quantum SASE with propagation effects. Using a self-consistent system of Schrodinger-Maxwell equations, we show that the dynamics of the system is determined by a properly defined "quantum FEL-parameter", ρ', which rules the number of photons emitted per electron, as well as the electron recoil in units of ћk. In the limit ρ'>>1 the quantum model reproduces the classical SASE regime with random spiking behavior and broad spectrum. In this limit we show that the equation for the Wigner function reduces to the classical Vlasov equation. In the opposite limit, ρ'<1, we demonstrate "quantum purification" of SASE: the classical spiking behavior disappears and the power spectrum becomes very narrow so that the temporal coherence of the SASE spectrum is dramatically improved. Photon statistics, electron-photon entangled states, minimum uncertainty states and quantum limitations on bunching and energy spread will be discussed.