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Neutron Resonance Interferometry

Neutron Resonance Interferometry. | IRI ; S.V.Grigoriev, W.H.Kraan, M.Th.Rekveldt > | PNPI ; S.V.Grigoriev , Yu.O.Chetverikov, A.V.Syromyatnikov >. Resonance!!!. Delft. h . 2 m n B 0. h . Petersburg. Contents. The concept of Neutron Resonance Interferometry

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Neutron Resonance Interferometry

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  1. Neutron Resonance Interferometry |IRI ; S.V.Grigoriev, W.H.Kraan, M.Th.Rekveldt > |PNPI ; S.V.Grigoriev, Yu.O.Chetverikov, A.V.Syromyatnikov > Resonance!!! Delft h 2mnB0 h Petersburg

  2. Contents • The concept of Neutron Resonance Interferometry • Multiwave interference phenomena • SESANS as an existing application of NRI. • Four-wave NRSE and composite correlation function

  3. Larmor precession as interference of spin states B B0 Homogeneous magnetic field exp(i(kx -t))(|> + |> ) x Ep Conservation energy law: h2 k 2/2mn= h2 k+2/2mn - 2mnB= . = h2 k-2/2mn + 2mnB Potential energy 2mnB0 x Ek k± = k0 ± mnB0/hv k+=k0+Dk Kinetic energy k0 Precession phase: = i(k+-k-)dx x k-=k0-Dk

  4. “Zero Field” precession B B0 Homogeneous magnetic field B0 and the resonance coil producing oscillating field B1 with frequency w0 exp(i(kx -t))(|> + |> ) x Resonance : neutron wave absorbs or emits the energy due to spin flip hw0 = 2mnB0 Ep Resonance!!! Resonance!!! Potential energy 2mnB0 Conservation law is not hold inside the resonance coil, but it works at its boundaries: entrance and exit. x Ek k++=k0+2Dk Entrance: k+ = k0 + mnB0/hv Exit: k++ = k0 + 2mnB0/hv Kinetic energy k+=k0+Dk k0 x Precession phase: j = i(k++- k- -)dx k-=k0-Dk k- -=k0 - 2Dk

  5. What does mean RESONANCE !!! for neutrons? The specific behaviour of neutrons in the magnetic field. The magnetic field B forces the neutron spin to presses with frequency L = B. This magnetic field may change the direction in time and in space with the speed H . 1) Adiabatic case L >> H: the spin follows the field 2) Non adiabatic case L <<H : the spin doesn’t react on the field change 3) Resonance case L = H : spin is excited and unstable. The transition probability is  = sin2(BRF/2), where  = l/v. Resonance!!! h Resonance : neutron wave absorbs or emits the energy due to spin flip hw = 2mnB 2mnB0 h x

  6. Sketch of the fields and (k,x) diagram RES: =1/2 RES: =1/2 B Homogeneous magnetic field B0 and oscillating B1 with frequency w0 x Precession phase: j1= i(k++- k- -)dx j2 = i(k++- k+ -)dx j3= i(k++- k-+)dx j4= i(k+-- k-+)dx j5= i(k+-- k- -)dx j6= i(k-+- k- -)dx k(x) k++ k+ k+- k0 x k-+ k- k--

  7. 1 2 3= (2 + 1)/2 3’= 3= (2 + 1)/2 4’= 4= (2 - 1)/2 4= (2 - 1)/2 S.V. Grigoriev, W.H.Kraan, F.M.Mulder, M.Th.Rekveldt, Phys.Rev.A, 62 (2000) 63601

  8. Neutron multiwave interference phenomena RES: =1/2 RES: =1/2 a B B0 l L B1 x k++ k+ b k1 One can vary  = [0 - 1] One can vary B1 = [B0 ± B] k- k0 x

  9. B SF1: =1/2 SF2: =1/2 SF3: =1/2 SF4: =1/2 SF5: =1/2 SF6: =1/2 a B0 B1 x k++ 20 21 22 23 24 25 26 N b k+ k+- x k0 N c 1 B1  6 SF1 15 20 x 15 6 1

  10.  = BRF l/(2v);  = sin2() One can vary  = [0 - 1] One can vary B1 = [B0 ± B] One can measure the probability R to find spin in state-(up) or state-(down) after the system of N =100 Resonant coils, so-called “QUANTUM CARPET” 2 One can vary  = [0 to1]   = B L/v One can vary B1 = [B0 ± B] 0  2

  11. “QUANTUM CARPET” is governed by the simple law of Multi-Wave Interference: R =  sin2(N /2)/ sin2(/2) and cos(/2) = (1- )1/2 cos(/2)  = B L/v  = [0 - 1] B = B1 - B0 On the picture:  is varied at different N and  = 1/2 The number of sub-maxima is nsub=(N-2)/2

  12. 5 DC small coils B0 B0 B1 B1 CM SF A D P DC Large coils 6 RF-coils

  13. The EXPERIMENT has been done for the number of resonance coils N = 6 at  = sin2() =1/16 and 1/2, = /12 and = /4, respectively. The value of  was varied. The experiment is in good agreement with the theory. S.V. Grigoriev et.al. Phys.Rev.A, 68 (2003) 33603

  14. Neutron multimode interference phenomena SF6: =1/2 a B SF5: =1/2 SF4: =1/2 SF3: =1/2 SF2: =1/2 SF1: =1/2 B0 l 1 = m=1N-1 Am (sin)N-m(cos)m exp(i m(x,t)) 2 = m=1N-1 Am (sin)m(cos)N-m exp(-i m(x,t)) x N waves  c 20 21 22 23 24 25 N waves +0+5 1 20 21 22 23 24 25 4 b +0+4 1 6 +0+2 6 5 4 k+ 1 +0 10 k1 k- 10  1 x 5 4 -2 6 1 6 k0 x 4 -4 1 -5

  15. Analytical solutiondifferent N R = 12 - 22. R = { sin2(N(x,t)/2)}/{sin2((x,t)/2)}. cos{(x,t)/2} = {1 -}1/2cos((x,t)/2). (x,t) = k (x-x0) - (t - t0), At the condition  =  = 2k l = 2m

  16. Analytical solutiondifferent  Computer calculations: (t1+ ) = C(t1, , 0) (t1), (t1+ N) = C(t1+N, , 0+N) C(t1+(N-1), , 0+(N-1))….. C(t1+, , 0+) C(t1, , 0) (t1), ti=t1+(i-1) (i=1,2,… N). i = *(t1+N) i( t1+N) , R=(1-Pzz)/2.

  17. Calculations at different  The condition  =  = 2k l 2m

  18. Conclusion • The multimode MIEZE may be done • without analyzers and • very compact.

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