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Quantum Noise in (High-Gain) FELs

Quantum Noise in (High-Gain) FELs. Kwang -Je Kim Argonne National Laboratory March 8, 2012 Future Light Sources WS Jefferson Laboratory Newport News, VA. EM Field Operator. Complex field amplitude  operator  ( Hermitian conjugate) Intensity = ,

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Quantum Noise in (High-Gain) FELs

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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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