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Understanding Quantum Noise in High-Gain Free Electron Lasers

This presentation by Kwang-Je Kim from Argonne National Laboratory discusses the role of quantum noise in high-gain Free Electron Lasers (FELs). It elaborates on the complex field amplitude operators and the relationship between annihilation creation operators and intensity, emphasizing the impact of vacuum fluctuations. The talk covers the conditions for minimum noise, Heisenberg FEL equations, and the classical vs. quantum limitations of noise suppression. The findings aim to elucidate the behavior of high-gain devices and how quantum noise can influence electron distribution and amplification.

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Understanding Quantum Noise in High-Gain Free Electron Lasers

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  1. Quantum Noise in (High-Gain) FELs Kwang-Je Kim Argonne National Laboratory March 8, 2012 Future Light Sources WS Jefferson Laboratory Newport News, VA

  2. EM Field Operator • Complex field amplitudeoperator •  ( Hermitian conjugate) • Intensity= • , • =(annihilation, creation operator) • =1, = number operator • from vacuum fluctuation Quantum Noise KJK FLS 2012

  3. Linear amplifier • =(input, output) field operator • ; =amplitude gain • operator for gain medium; = • | • =+; 2 =power gain • In the absence of initial photons; • Can show • The minimum noise is ½ input photon from VF and ½ input photon from amplifier reaction • Low noise in gain device (oscillator) Quantum Noise KJK FLS 2012

  4. Proof (C. M. Caves, PRD, 1817 (1982)) •  • : •  • Condition for minimum noise: =0 Quantum Noise KJK FLS 2012

  5. FEL equation • Classical • : • Field energy density • Quantum:=1 •  : • , • ; Quantum Noise KJK FLS 2012

  6. Heisenberg FEL equation in collective variables (R. Bonifacio, et.,al.) • Bunching factor • Collective momentum • Assume . =classical, and small • , , • Formally identical to classical equation Quantum Noise KJK FLS 2012

  7. Solution exp(ilt) • , maximum growth • ; Quantum Noise KJK FLS 2012

  8. Amplified power • The first two terms are classical coherent amplification and SASE, respectively • Random electron distribution • Noise suppression schemes ( A. Gover,..)  • Classical (KJK and RRL, FEL 2011) and quantum limitation of the suppression Quantum Noise KJK FLS 2012

  9. Quantum noise • ; • representation • Assume Gaussian wavefunction Cross terms do not contribute (C. Schroder, C. Pellegrini, P.Chen) • Minimum =3/2 • However the minimum should be 1=1/2+1/2 Quantum Noise KJK FLS 2012

  10. Minimum noise wavepacket • Require:  : minimum noise • To understand phase space distribution, look at Wigner function • Tilted phase space, or chirped Quantum Noise KJK FLS 2012

  11. Magnitude of minimum quantum noise relative Random SASE • Small but not negligible Quantum Noise KJK FLS 2012

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