Quantum Noise in (High-Gain) FELs

Kwang-Je Kim

Argonne National Laboratory

March 8, 2012

Future Light Sources WS

Jefferson Laboratory

Newport News, VA

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EM Field Operator Complex field amplitude operator ( Hermitian conjugate)

Intensity = ,

=(annihilation, creation operator)

=1, = number operator from vacuum fluctuation

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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)

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Proof (C. M. Caves, PRD, 1817 (1982))

: Condition for minimum noise: =0

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FEL equation Classical : Field energy density Quantum:=1 :

, ;

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Heisenberg FEL equation in collective variables (R. Bonifacio, et.,al.) Bunching factor Collective momentum Assume . =classical, and small

, , Formally identical to classical equation

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Solution exp(ilt) , maximum growth

;

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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

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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

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Minimum noise wavepacket Require:

: minimum noise To understand phase space distribution, look at Wigner function

Tilted phase space, or chirped

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Magnitude of minimum quantum noise relative Random SASE

Small but not negligible