Constraining the Properties of the Antiproton A. Mooser, M. Borchert, J. Harrington, T. Higuchi, H. Nagahama, N. Leefer, G. Schneider, S. Sellner, C. Smorra, M. Wiesinger, K. Blaum, Y. Matsuda, C. Ospelkaus, W. Quint, J. Walz, Y. Yamazaki and S. Ulmer

Different CPT tests ALICE CERN AD CPT invariance is the most fundamental symmetry in the Standard Model Strategy: Compare properties of matter and antimatter conjugates with high precision. CERN AD ALICE Recent Past Planned R.S. Van Dyck et al., Phys. Rev. Lett. 59, 26 (1987). B. Schwingenheuer, et al., Phys. Rev. Lett. 74, 4376 (1995). H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999). G. W. Bennett et al., Phys. Rev. D 73, 072003 (2006). M. Hori et al., Nature 475, 485 (2011). G. Gabriesle et al., PRL 82, 3199(1999). J. DiSciacca et al., PRL 110, 130801 (2013). S. Ulmer, C. Smorra, et al., Nature 524, 196-200 (2015). ALICE Collaboration, Nature Physics 11, 811–814 (2015). M. Hori et al., Science 354, 610 (2016). H. Nagahama, C. Smorra, et al., Nat. Comm. 8, 14084 (2017). M. Ahmadi et al., Nature 541, 506 (2017). antihydrogen 1S-2S The work on CPT invariance tests in general has been summarized in: V. A. Kostelecky, N. Russell, 0801.0287v10 (2017). CPT test with fractional precision of 10 −18 available… why continue measuring?

Concept of CPT violation Basic idea: Add CPT violating extension to Hamiltonian of Standard Model Treat CPT violating terms perturbative 𝐻′= 𝐻 𝑆𝑀 +∆𝑉 < ψ ∗ |∆𝑉|ψ>=∆𝐸 System based on SM CPT violating term Contributions at absolute energy scale - Absolute energy resolution might be more appropriate measure of sensitivity with respect to CPT violation High sensitivity - precise measurement at small intrinsic energy Single particles in Penning traps - precise measurement of frequencies at ueV-energy scales Relative precision Energy resolution Kaon ∆𝑚 ~ 10 −18 ~10 −9 eV p- p q/m ~ 10 −11 ~ 10 −18 eV p- p g-factor ~ 10 −6 ~ 10 −12 eV BASE aims to improve with 10 −9 relative precision

Our Options 𝜔 𝑐, 𝑝 𝜔 𝑐,𝑝 = 𝑞 𝑝 / 𝑚 𝑝 𝑞 𝑝 / 𝑚 𝑝 Determination of Larmor frequency in a given magnetic field Monitoring magnetic field via simultaneous measurement of the free cyclotron frequency 𝜔 𝑐, 𝑝 𝜔 𝑐,𝑝 = 𝑞 𝑝 / 𝑚 𝑝 𝑞 𝑝 / 𝑚 𝑝

Charge-to-Mass-Ratio measurements g-factor measurements Setup All methods are implemented in a 4-Penning trap system Reservoir Trap: Stores a cloud of antiprotons, suspends single antiprotons for measurements. Trap is “power failure save”. Cooling Trap: Fast cooling of the cyclotron motion, τ < 4 s Precision Trap: Homogeneous B-field for frequency measurements, B2 < 0.5 mT / mm2 (10 x improved) Analysis Trap: Inhomogeneous B-field for the detection of antiproton spin flips, B2 = 300 mT / mm2 Charge-to-Mass-Ratio measurements g-factor measurements

Operation of reservoir trap Antiprotons stored from 03.11.2015 – 22.12.2016 Storage of antiprotons for more than one year: 405.5 days Method for extraction of single particles S. Sellner et al., in preparation (2017).

𝑚 H − 𝑚 p = (1+2 𝑚 e 𝑚 p − 𝐸 b 𝑚 p − 𝐸 a 𝑚 p + 𝛼 pol, H − 𝐵 0 2 𝑚 p ) Why not protons Systematic uncertainties due to the particle position are large (~10-9) No significant uncertainties in converting the mass ratio CPT test by a measurement of the cyclotron frequency ratio of antiproton and H- ion 𝐵 0 + 𝐵 1 𝑧 𝐻 − 𝑈 𝐻 − 𝑝 𝑈 𝑝 𝑝 𝑚 H − 𝑚 p = (1+2 𝑚 e 𝑚 p − 𝐸 b 𝑚 p − 𝐸 a 𝑚 p + 𝛼 pol, H − 𝐵 0 2 𝑚 p ) 𝑈 𝑝 Rtheo = 1.0010892187542(2) (0.2 ppt) 𝑈 𝑐 𝑈 0 𝑈 𝑐 + 𝑼 𝒐𝒇𝒇𝒔𝒆𝒕 G. Gabriesle et al., PRL 82, 3199(1999). S. Ulmer, C. Smorra, A. Mooser et al., Nature 524, 196-200 (2015).

One frequency ratio per 4 minutes with ~ 5 ppb uncertainty Measurement scheme Based on reservoir extraction technique and developed methods to prepare negative hydrogen ions we prepared an interesting set of initial conditions H- ion antiproton Comparison of H-/antiproton cyclotron frequencies: One frequency ratio per 4 minutes with ~ 5 ppb uncertainty About > 50 times faster than in precious measurements.

Result (𝑞/𝑚) p (𝑞/𝑚) p −1=1 69 × 10 −12 6521 frequency ratios Result: Rexp,c = 1.001 089 218 755 (64) (26) Rtheo = 1.001 089 218 754 2(2) Cyclotron frequency ratios for p -to- p and H − -to- H − 𝑅 id are also evaluated 𝑅 𝑖𝑑 −1=−3 79 × 10 −12 Consistent with 1 In agreement with CPT conservation Exceeds the energy resolution of previous result by a factor of 4. (𝑞/𝑚) p (𝑞/𝑚) p −1=1 69 × 10 −12 S. Ulmer, C. Smorra, A. Mooser et al., Nature 524 196 (2015)

Parts-per-million measurement of antiproton g-factor

Detection of the spin state Introduce magnetic inhomogeneity axial frequency Time spin down spin up Axial Frequency (arb units) Axial Position (mm) Magnetic Field (T) Dealing with nuclear magneton requires magnetic bottle of

Challenge in spin flip detection The magnetic bottle couples also the magnetic moment to the radial motion to the axial frequency! Φ 𝑀 =− ( μ 𝑝 ⋅ 𝐵 ) 𝐵 𝑧 = 𝐵 0 + 𝐵 2 ( 𝑧 2 − ρ 2 2 ) Measurement needs to be done at constant n+, n-! Spurious noise driving the cyclotron and magnetron modes: Spin-flip frequency shift about same magnitude: Idea: Detect increase of axial frequency fluctuations : Ξ 𝑟𝑒𝑓 < 120 mHz Δ𝜐 𝑧,𝑆𝐹 =183 mHz

Statistical Detection of Spin Flips Spin flips add up Measure axial frequency stability: 1.) reference measurement with detuned drive, 2.) measurement with resonant drive on. Cumulative measurement: Black – frequency stability with superimposed spin flips. Red – background stability Applied to proton 𝑔 𝑝 =5.585 696(50) S. Ulmer, A. Mooser et al., Phys. Rev. Lett 106, 253001 (2011) C. C. Rodegheri et al., New J. Phys. 14 063011 (2012)

Applied and extended for antiproton Co-magnetometer trap allows for in-situ monitoring of magnetic field fluctuations. Larmor Cyclotron H. Nagahama et al., Nat. Comm. 8, 14084 (2017).

H. Nagahama et al., Nat. Comm. 8, 14084 (2017). g-factor results Six fold improved uncertainty of the antiproton magnetic moment SME coefficients for CPT violation improved up to a factor 20 𝑔 𝑝 /2=2.7928465(23) H. Nagahama et al., Nat. Comm. 8, 14084 (2017).

Towards parts-per-billion measurement

Requires clear identification of the spin state Double-trap method Analysis Trap 44 mm Precision Trap 19 mm Requires clear identification of the spin state H. Häffner, Phys. Rev. Lett.85, 5308 (2000)

Challenge: Spin-flip resolution Suppression of voltage noise densities of order 10 – 100 pV / SQRT(Hz) is challenging! Improved rf-filtering and grouding Applied feedback cooling of the axial mode for Reduced line-width for cyclotron mode Improved axial frequency resolution Axial frequency stability after optimization: 48 mHz

Single antiproton spin-flips Single spin transitions can be identified with a high fidelity (Average spin-state fidelity > 92 %) ppb antiproton g-factor measurement in reach C. Smorra, A. Mooser et al., Phys. Lett. B 769, 1-6 (2017).

Summary High-precision comparison of proton to antiproton charge-to-mass ratio Most precise measurement of antiproton magnetic moment Single spin flips – ppb-measurement of magnetic moment in reach BASE Collaboration: Stefan Ulmer, Christian Smorra, Hiroki Nagahama, Takashi Higuchi, Andreas Mooser, Mustafa Besirli, Mathias Borchert, James Harrington, Nathan Leefer, Stefan Sellner, Georg Schneider, Nathalie Schoen, Toya Tanaka, Markus Wiesinger, Klaus Blaum, Yasuyuki Matsuda, Christian Ospelkaus, Wolfgang Quint, Jochen Walz, Yasunori Yamazaki

Thank you for your attention VH-NG-037 Adv. Grant MEFUCO (#290870)