n-n" oscillations beyond the quasi-free limit or n-n" oscillations in the presence of magnetic field

Size: px

Start display at page:

Download "n-n" oscillations beyond the quasi-free limit or n-n" oscillations in the presence of magnetic field"

Eleanore Horton
5 years ago
Views:

1 n-n" oscillations beyond the quasi-free limit or n-n" oscillations in the presence of magnetic field E.D. Davis North Carolina State University Based on: Phys. Rev. D 95, (with A.R. Young) INT workshop INT-17-69W

2 Contents Magnetic field (in the propagation region): much ado about nothing? Propagation region dynamics: mapping to spinor evolution problem Perturbative and non-perturbative analysis in noisy fields Exploring the use of NMR quantum control protocols 2

3 The magnetic field: much ado about nothing? From D.G. Phillips II et al., Phys. Rep. 621, 1: For the magnetic shielding geometries of both the previous ILL experiment and the proposed experiment, the dominant component of the residual magnetic field inside the shield is the component along the axis of the shield. The internal shield for the previous ILL experiment strongly suppressed transverse components of the magnetic field and rendered the longitudinal component sufficiently uniform that it could be largely compensated by a homogeneous external field generated by a coil wrapped on the outside of the shield. Once this major component to the residual field was removed, another set of coils were able to trim out the residual transverse fields. Current loops for shield demagnetization, an active compensation system for external magnetic field variations (including transverse fields), internal magnetometry, and removal of large external sources of magnetic field gradients were also required to ensure maintenance of the quasi-free condition. Since this experiment was performed a great deal has been learned about large volume magnetic shield technology in the course of R&D performed for experiments which search for the neutron electric dipole moment [125].? l = 300 m shield idealization = optimal adaptation of shield s magnetization to external fields Magnetically shielded propagation region I. Altarev et al., Rev. Sci. Instrum. 85, : A magnetically shielded room with ultra low residual field and gradient The ideal case (no joints) 3

4 What do ILL field profiles look like? (After a daily shield idealization) field variations are much worse than with no shield at all. At every joint and at every welding seem [sic] (three per tube segment) the magnetic flux leaks out and distorts the earth field considerably. (T. Bitter et al, NIMA 309, 521) Unavoidable irregular inhomogeneities that change randomly after each idealization 10 nt The spikes visible at the beginning and at the end of the field profile do not noticeably disturb the neutron-antineutron oscillation process, so we did not bother to further suppress them. (T. Bitter, NIMA 309, 521) What constraints are placed on control of the residual magnetic field with a propagation region of increased length l? 4

5 L dependence: reason for anxiety? S. Dickerson et al., Rev. Sci. Instrum. 83, Axial field inside 14 segment shield (Peaks at 13 joints) Effect of shield length l on ambient field (Simulation) Simulation (offset by 150 mg) Data Increase in peak heights due to increase in magnetic field channeled within shield Approximately quadratic dependence on L Radius of shields Dashed line: 1.2 m shield Solid line: 8.5 m shield (same length as 14 segment shield) 5

6 Propagation region dynamics: mapping to spinor evolution problem Starting point: Pauli-Schrödinger equation in rest frame of system Larmor frequency vector ω 5 (t) = γb(t) iħ d dt / χ, (t) χ," (t) = ħ 0 σ 3 ω 5 δi 0 δi 0 / 0 σ 3 ω 5 To lowest order in δ, n" detection probability where Time-ordered exponential F F χ, (t) χ," (t) P," t = δ 2 t 2 / dta dtaa Tr U E t 0 (t A ) 0 U 0 (t AA ) 0 Quasi-free estimate G G U 0 t = exp K L dta σ 3 ω 5 (t A ) Phase averaging suppression factor G F nn" interaction 6

7 Phase averaging suppression? Example of longitudinal noise : B = b t kq Average of P," over ensemble of neutrons studied with Z/ P," = δ 2 t 1 x cos ω L tx exp χ tx dx [/ χ τ where power spectral density G ωτ sin 2 ω 2 0 S ωl ω dω S ωl ω = / ω 5(t + τ 2 ) ω 5 ω 5 (t τ 2 ) ω 5 G Stationary Gaussian process cos ωτ dτ Fourier transform of auto-correlation function of random process ω 5 (t) Identical factor controls free inductive decay in NMR Can quantum controls protocols within NMR combat phase averaging suppression? 7

8 Perturbative treatment of noisy magnetic field (in shielded region) Ignore hiccups Treat P," as functional of random process ω 5 Minimalist stochastic model: assume ω 5 t is wide sense stationary (Due to active compensation) To 2 nd order in small ω 5, P," (t) δ 0 t 0 = 1 / /0 ω 5 0 t dω G S de (ω) F(ωt) ω 0 Wide sense stationary? Expectation value ω 5 Auto-correlation functions (Lh) C de t /, t 0 time independent = ω 5,L t / ω 5,L ω 5,h t 0 ω 5,h depend on τ = t 0 t / only S de ω = j S de,l (ω) Filter function F x = 2 1 sinc 0 m 0 25/10/2017 Llm,n,o E.D. Davis: INT-17-69W 8

9 Quasi-free propagation efficiency η (as in NIMA 309, 521) Involves average of P," (t) over axial speed distribution n v of neutrons Average over n v η Quasi-free estimate of P," (t) r P," t δ 0 t 0 r r P,",r(v) δ 0 l 0 n v dvw r tuv Weak v [0 n v dv r tuv Substitute t in P," (t) by l/v Minimum speed to avoid collisions with drift vessel η = 1 / /0 ω 5 0 μ [y μ [0 l dω μ ({) v [0 n v dv G S de (ω) ω 0 r v [0 F ωl v r tuv Flight path length l: apparent quadratic dependence dv n(v) μ ([0) 9

l-dependence of η (weak fields) Markovian noise η = 1 } }~ ω 5 0 + 2β σ 5 0 Ingredients ƒ ƒ ~ l 0 β η

10 l-dependence of η (weak fields) Markovian noise η = 1 } }~ ω β σ 5 0 Ingredients ƒ ƒ ~ l 0 β η versus l: B mean = 2(5 nt) = B rms β 1 l = 10 m v L, = l/(0.5 s) Approximately linear! l = 0 White noise 10

11 Non-perturbative treatment of white Gaussian longitudinal noise Can obtain exact P," (t) in closed analytic form (functional integrals Gaussian) Inference: perturbative estimate too conservative 11

12 Influence of an elementary quantum control protocol Rabi-like field configuration B = B Ž kq + B cos ωt ı + sin ωt ȷ (Phys. Rev. D 91, ) P," t δ 0 = ω, ω ω Ž,5 ω,5 0 t oscillatory terms Demand uniformity of B Ž other quantum control protocols (Rev. Mod. Phys. 76, 1037) 12

Carr-Pound-Meiboom-Gill-like spin-flip sequence For uniform holding field, P," t = δ 0 t 0 sinc 0 ω 5t 2n for n bang-bang spin flips (Flips separated by interval t = t/n with

13 Carr-Pound-Meiboom-Gill-like spin-flip sequence For uniform holding field, P," t = δ 0 t 0 sinc 0 ω 5t 2n for n bang-bang spin flips (Flips separated by interval t = t/n with 1 st flip at time = } ~ t) Filter function is high-pass filter with cutoff frequency approximately equal to ω n 0, F ω = / 0 ω, ω = ω, ω = 2ω, Filter function n = 10 flips 13

14 Conclusions Revisited the magnetic field studies of the ILL n-n" experiment with a view to establishing scaling with size of the system. NOT a problem. Synthesis with quantum information methodologies developed since the ILL experiment could be productive Helpful in search for mirror neutrons at HFIR? Thank you! 14

LINEAR RESPONSE THEORY

MIT Department of Chemistry 5.74, Spring 5: Introductory Quantum Mechanics II Instructor: Professor Andrei Tokmakoff p. 8 LINEAR RESPONSE THEORY We have statistically described the time-dependent behavior