The Proton Magnetic Moment

Georg Schneider on behalf of the BASE collaboration March 9, 2016, Kanazawa

1. Theoretical basics Who we are? Measurement principle The double Penning trap method Experimental setup Milestones 2 / 25

Who we are? The Proton Magnetic Moment Collaboration of two experiments located at Mainz and CERN JG U 3 / 25

Measurement principle The Proton Magnetic Moment Consider the Larmor- and cyclotron-frequency ω L = g q 2m B ωc = q m B ω L ω c B B g-factor: ω L ω c = g 2 = µp µ N 4 / 25

Measurement principle The Proton Magnetic Moment Measurement of the cyclotron-frequency ν + 29 MHz ν z 600 khz B ν ν+ νz ν 7 khz ν + ν z ν Eigenmotions in the Penning trap Cyclotron-frequency ν c can be calculated by using the invariance theorem Brown, Gabrielse, Phys. Rev. A 25, 2423-2425 ν 2 c = ν2 + + ν2 z + ν2 Image current detection suitable for frequency measurements 5 / 25

Measurement principle Principle of image current detection Particle induces image currents [fa] Penning trap 1cm Particle acts as a perfect short of the resonator s Johnson noise Amplitude [dbm] -116-120 -124-128 -132 Resonant superconducting detection inductor -136 623700 623800 623900 624000 Frequency [Hz] 6 / 25

Measurement principle Measurement of the Larmor-frequency Continuous Stern-Gerlach-Effect Ferromagnetic ring electrode creates field inhomogeneity: magnetic bottle Magnetic bottle modifies the effective potential by V m = µ B ω z,sf = 2qC2 V 0 m 2µzB 2 m potential axial frequency z-axis time Ferromagnetic electrode leads to magnetic bottle Known technique, for example with electrons 7 / 25

Measurement principle The Proton Magnetic Moment Spin up and spin down generate different frequencies ν z = 1 2π 2 µ zb 2 mν z with B = B 0 + B 2 z 2 Proton is quite challenging µ z mν µz z proton mν z electron Strong magnetic bottle needed, to distinguish frequency jumps induced by spin flips from noisy background fluctuations B 2 = 300000 Tm 2 ν z 171 mhz at ν z 748 khz Still small frequency change 8 / 25

Measurement principle The Proton Magnetic Moment Spin flips can be observed by measuring the axial frequency ν z 171 mhz at ν z 748 khz A. Mooser et. al., PRL 110, 140405 T + = 50 mk E + = 4 µev Frequency (mhz) 742068.1 Hz Probability Spin Down 1000 0 1 size of frequency jump 0 0 40 80 120 160 200 220 280 320 Time (min) Single spin flip resolution has been achieved 9 / 25

The double Penning trap method We need a strong magnetic bottle in order to measure the spin state Problem: Strong magnetic bottle limits frequency precision at the p.p.m level precision spin flip probability [%] 70 60 20 khz 50 40 30 20 10 0-10 49.8 49.9 50.0 50.1 50.2 50.3 50.4 rf drive frequency [MHz] 10 / 25

The double Penning trap method We need a strong magnetic bottle in order to measure the spin state Problem: Strong magnetic bottle limits frequency precision at the p.p.m level precision spin flip probability [%] 70 60 20 khz 50 40 30 20 10 0-10 49.8 49.9 50.0 50.1 50.2 50.3 50.4 rf drive frequency [MHz] Solution: Spatial separation of spin flip detection and frequency measurement Double Penning trap allows p.p.b. spin flip detection precision However, this requires single spin flip resolution 10 / 25

The Proton Magnetic Moment The double Penning trap method axial frequency p Analysis tragnetic bottle contains ma trap Precision quency used for freents measurem νlef t -10 0 magnetic signal Mainz double Penning trap 60 20 40 in] time [m νz 0 νright 10 80 1.89 T 1.17 T B2 is around 100000 times smaller in the precision trap 11 / 25

The Proton Magnetic Moment Experimental setup superconducting magnet @1.9 T trap chamber cryostat with liquid helium and nitrogen external electronics detection systems 12 / 25

Milestones The Proton Magnetic Moment Milestones of the BASE collaboration fraction of total counts 0.4 0.3 0.2 0.1 0.0 statistical spin flips S. Ulmer et. al., Phys. Rev. Lett. 106, 253001 (2011) 47 mhz ΞSF Ξref 100 150 200 250 300 axial frequency fluctuations [mhz] 2011 800 600 400 200 0 2012 single spin flips A. Mooser et. al., Phys. Rev. Lett. 110, 140405 (2013) time 2013 p.p.m g-factor measurement C. C. Rodegheri et. al., New J. Phys. 14, 063011 60 50 40 30 20 10 0 2014 BASE at CERN gets approved p.p.b. g-factor measurement A. Mooser et. al., Nature 509, 596 599 (2014) -40-20 0 20 40 g/g CODATA (p.p.b.) 2015 Comparison of the antiproton-to-proton charge-to-mass ratio next talk by A. Mooser In 2014 we performed the most precise and first direct high-precision measurement of the proton g-factor g p = 5.585 694 700(14) stat (12) syst Can be applied to the antiproton to obtain thousandfold improved CPT-test 13 / 25

Milestones The Proton Magnetic Moment Historical measurements Indirect, hydrogen maser Direct, Penning trap with magnetic bottle Direct, double Penning trap Winkler 1972 Rodegheri 2012 DiSciacca & Gabrielse 2012 Mooser 2014 planned 1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 Relative precision Goals for BASE: Proton to sub p.p.b, Antiproton to sub p.p.m. 14 / 25

2. Towards sub-p.p.b. Optimization of the precision trap Optimization of measurement time 15 / 25

Optimization of the precision trap Main limitations in the previous measurement: B 2 in precision trap sets constraint on line width Saturation broadening of the Larmor resonance magnetic field old new B2 4 T/m² 0.5 T/m² line width 200mHz 40mHz relative prec. ~10-9 ~10-10 old setup 1cm new setup analysis trap precision trap 16 / 25

Optimization of the precision trap New trap layout about one order of magnitude higher precision 17 / 25

Optimization of the precision trap New trap layout about one order of magnitude higher precision Self shielding coil (Shielding factor of around 50) 17 / 25

Optimization of the precision trap Long time measurement of the cyclotron frequency stability old setup with 3.p.p.b new setup for < p.p.b. Percentage [a.u.] -60-40 -20 0 20 40 60 9-60 -40-20 0 20 40 60 9 Improvement by one order of magnitude due to smaller B 2 and self shielding coil If B 2 is not the dominant systematic anymore, what else could be problematic? 18 / 25

Optimization of the precision trap Trapping potential optimization must be better 1 10 5 V for sub p.p.b. precision C 4 0 Amplitude dependent frequency 4 trap anharmonicity (C4) 2 0-2 -4 0.8846 0.8847 0.8848 0.8849 trap voltage (tuning ratio) Three day measurement: optimized to level of 4 10 6 can be improved even further, limited by statistics 19 / 25

Optimization of measurement time Spin state analysis requires particle with low cyclotron energy E + νz 170 mhz low energy high energy Problem: Cyclotron quantum jumps ν z,quantum jump = 60mHz vs ν z,spin flip = 170mHz Cyclotron transition rate scales with energy p + n + Decreasing the energy is most important to resolve spin flips 20 / 25

Optimization of measurement time Particle is coupled to the cyclotron detector 1 K bin probability Boltzmann distribution 1 2 3 4 5 6 7 8 9 10 temperature [K] Old cyclotron detector t cool = 120 s and T = 5 K with feedback Cooling performance is limited by the cyclotron detector 21 / 25

Optimization of measurement time Timings thermalize in PT transport to AT old 100 min new 25 min : 4 cold? no yes find spin state in AT 45 min 45 min frequency measurement in PT + Larmor excitation 20 min 2.45 h 20 min 1.30 h : 2 22 / 25

Optimization of measurement time Old cyclotron detector t cool = 120 s and T = 5 K with feedback f res = 28.96 MHz SNR = 20 db Q = 1500 t cool = 60 s T = 5 K, with feedback T = 2 K superconducting coil low noise cryogenic amplifier New cyclotron detector allows faster thermalisation time at lower temperature 23 / 25

Summary The Proton Magnetic Moment In 2014 we reported the most precise measurement of the proton g-factor with a precision of 3.3 p.p.b. 60 50 40 30 20 10 0 A. Mooser et. al., Nature 509, 596 599 (2014) -40-20 0 20 40 g/g CODATA (p.p.b.) Preparations for the next g-factor measurement have started Measurement time was optimized & main limitations reduced Goal: g-factor measurement at the level of 10 10 for proton and antiproton 24 / 25

The Proton Magnetic Moment S. Ulmer RIKEN H. Nagahama RIKEN / Tokyo C. Smorra CERN / RIKEN T. Higuchi RIKEN / Tokyo S. Sellner RIKEN T. Tanaka RIKEN / Tokyo A. Mooser RIKEN G. Schneider RIKEN / Mainz K. Blaum, Y. Matsuda, W. Quint, J. Walz 25 / 25