An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen Bertalan Juhász Stefan Meyer Institute for Subatomic Physics, Vienna, Austria on behalf of the ASACUSA collaboration IFA (Århus), ISA (Århus), UB (Brescia), KFKI RMKI (Budapest), ATOMKI (Debrecen), CERN (Geneva), RIKEN (Saitama), UT (Tokyo), SMI (Vienna) PST05, Tokyo, Japan, November 16, 2005 An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.1/19
Outline What is ground-state hyperfine splitting H GS-HFS as CPT symmetry test How we want to measure it Low-velocity H production in Paul trap or cusp trap Sextupole magnets for spin selection and analysis Microwave cavity Monte Carlo simulations Beamline design Expected count rate and precision An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.2/19
GS-HFS of (anti)hydrogen Ground-state hyperfine splitting (GS-HFS): Interaction between (anti)proton and electron (positron) spin magnetic moment M = 1 M = 0 M = �1 F = 1 Results in triplet ( F = 1 ) 1s and singlet ( F = 0 ) M = 0 sublevels F = 0 Between F = 1 and F = 0 : � 3 m e � ν HF ≃ 16 m p µ p α 2 c Ry ≃ 1.42 GHz 3 m p + m e m p µ N ν HF proportional to (anti)proton magnetic moment µ p An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.3/19
SME including CPTV and LIV Kostelecky et al. : Standard Model extension (SME) including Charge-Parity-Time invariance violating (CPTV) Lorentz invariance violating (LIV) terms in Lagrangian ⇒ correction to sublevel energies: 0 + a p 00 m e − c p ∆ E H ( m J , m I ) = a e 0 − c e 00 m p + +( − b e 3 + d e 30 m e + H e 12 ) m J / | m J | +( − b p 3 + d p 30 m p + H p 12 ) m I / | m I | ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.4/19
SME including CPTV and LIV Kostelecky et al. : Standard Model extension (SME) including Charge-Parity-Time invariance violating (CPTV) Lorentz invariance violating (LIV) terms in Lagrangian ⇒ correction to sublevel energies: 0 + a p 00 m e − c p ∆ E H ( m J , m I ) = a e 0 − c e 00 m p + +( − b e 3 + d e 30 m e + H e 12 ) m J / | m J | +( − b p 3 + d p 30 m p + H p 12 ) m I / | m I | Parameters a and b have dimension of energy ⇒ not relative but absolute precision matters ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.4/19
SME including CPTV and LIV Kostelecky et al. : Standard Model extension (SME) including Charge-Parity-Time invariance violating (CPTV) Lorentz invariance violating (LIV) terms in Lagrangian ⇒ correction to sublevel energies: 0 + a p 00 m e − c p ∆ E H ( m J , m I ) = a e 0 − c e 00 m p + +( − b e 3 + d e 30 m e + H e 12 ) m J / | m J | +( − b p 3 + d p 30 m p + H p 12 ) m I / | m I | Parameters a and b have dimension of energy ⇒ not relative but absolute precision matters Parameters a , d , and H reverse sign for antihydrogen An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.4/19
Measurement of H GS-HFS Highest precision for H: ∼ 10 − 12 with hydrogen maser ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.5/19
Measurement of H GS-HFS Highest precision for H: ∼ 10 − 12 with hydrogen maser But: maser is not possible for H ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.5/19
Measurement of H GS-HFS Highest precision for H: ∼ 10 − 12 with hydrogen maser But: maser is not possible for H Spectroscopy with trapped H: low precision due to strong confining field ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.5/19
Measurement of H GS-HFS Highest precision for H: ∼ 10 − 12 with hydrogen maser But: maser is not possible for H Spectroscopy with trapped H: low precision due to strong confining field Best candidate: atomic beam with microwave resonance ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.5/19
Measurement of H GS-HFS Highest precision for H: ∼ 10 − 12 with hydrogen maser But: maser is not possible for H Spectroscopy with trapped H: low precision due to strong confining field Best candidate: atomic beam with microwave resonance no H trapping needed – you would need ultra-cold (< 1 K) H for that ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.5/19
Measurement of H GS-HFS Highest precision for H: ∼ 10 − 12 with hydrogen maser But: maser is not possible for H Spectroscopy with trapped H: low precision due to strong confining field Best candidate: atomic beam with microwave resonance no H trapping needed – you would need ultra-cold (< 1 K) H for that AB method can work up to 50-100 K ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.5/19
Measurement of H GS-HFS Highest precision for H: ∼ 10 − 12 with hydrogen maser But: maser is not possible for H Spectroscopy with trapped H: low precision due to strong confining field Best candidate: atomic beam with microwave resonance no H trapping needed – you would need ultra-cold (< 1 K) H for that AB method can work up to 50-100 K inhomogeneous magnetic field needed to guide the neutral H atoms grabbed by their magnetic moment ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.5/19
Measurement of H GS-HFS Highest precision for H: ∼ 10 − 12 with hydrogen maser But: maser is not possible for H Spectroscopy with trapped H: low precision due to strong confining field Best candidate: atomic beam with microwave resonance no H trapping needed – you would need ultra-cold (< 1 K) H for that AB method can work up to 50-100 K inhomogeneous magnetic field needed to guide the neutral H atoms grabbed by their magnetic moment Measurement at the Antiproton Decelerator (AD) of CERN after ∼ 2007 An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.5/19
Ground-state H or H in magnetic field Energies of hyperfine states change in magnetic field Increase for ( F, M ) = (1, − 1) and (1,0) ⇒ low-field seekers ( µ < 0 ) Decrease for ( F, M ) = (1,1) and (0,0) ⇒ high-field seekers ( µ > 0 ) e + p 2.0 1 low-field H (F,M)=(1,-1) 1.5 seekers 2 p s p 1 1 2 1.0 (F,M)=(1,0) 0.5 (GHz) 0.0 (F,M)=(1,1) n -0.5 -1.0 3 (F,M)=(0,0) high-field -1.5 seekers 4 -2.0 0.00 0.02 0.04 0.06 0.08 0.10 B (T) An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.6/19
Focusing in sextupole field µ � potential: V = − � B force: � µ � F = − grad V = grad ( � B ) S If dθ B /dt ≪ ω L and µ constant: � F = µ grad ( B ) Sextupole field (cylindrical coord.): r B ( r ) = (3 Cr 2 sin 3 φ, 3 Cr 2 cos 3 φ, 0) � N B ( r ) = 3 Cr 2 ⇒ F r = µ ∂B/∂r = 6 Cµr ⇒ harmonic oscillation: � ω = 6 Cµ/m S ⇒ point-to-point focusing for single v z : � l f = πv z m/ 6 Cµ 0 0.5 1 x An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.7/19
Schematic layout + p and e trap antihydrogen recombination detector sextupole 1 microwave sextupole 2 cavity low-velocity H atoms from recombination source ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.8/19
Schematic layout + p and e trap antihydrogen recombination detector sextupole 1 microwave sextupole 2 cavity low-velocity H atoms from recombination source 1st sextuple focuses low-field seekers, defocuses high-field seekers (spin selection) ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.8/19
Schematic layout + p and e trap antihydrogen recombination detector sextupole 1 microwave sextupole 2 cavity low-velocity H atoms from recombination source 1st sextuple focuses low-field seekers, defocuses high-field seekers (spin selection) microwave cavity flips spin ⇒ conversion from low-field seeker to high-field seeker ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.8/19
Schematic layout + p and e trap antihydrogen recombination detector sextupole 1 microwave sextupole 2 cavity low-velocity H atoms from recombination source 1st sextuple focuses low-field seekers, defocuses high-field seekers (spin selection) microwave cavity flips spin ⇒ conversion from low-field seeker to high-field seeker 2nd sextupole analyzes spin An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.8/19
H source „Conventional” way: nested Penning trap ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.9/19
H source „Conventional” way: nested Penning trap source size too large for atomic beam method ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.9/19
H source „Conventional” way: nested Penning trap source size too large for atomic beam method limited extraction and optical access ▽ An atomic beamline to measure the ground-state hyperfine splitting of antihydrogen – p.9/19
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