A Test of Charge Parity Time Invariance at the Atto-Electronvolt Scale A. Mooser, C. Smorra, H. Nagahama, J. Harrington, T. Higuchi, N. Leefer, G. Schneider, S. Sellner, T. Tanaka, K. Blaum, Y. Matsuda, W. Quint, J. Walz, Y. Yamazaki and S. Ulmer

Different CPT tests ALICE CERN AD Planned by others 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 Nature Physics (10.1038/nphys3432) Planned by others ASACUSA / ALPHA / ATRAP Red: Recent tests Purple: Past tests Green: Planned S. Ulmer et al., Nature 524 196 (2015) J. diSciacca et al., PRL 110 130881 (2013) muon g A. Mooser et al., Nature 509, 596 (2014) 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

[L. S. Brown and G. Gabrielse, Phys. Rev. A, 25:2423, 1982.] The Penning Trap Superposition of homogeneous magnetic field and electrostatic quadrupole potential radial confinement axial confinement Endcap axial magnetron modified cyclotron Correction Vc Ring V0 Correction Vc Endcap axial modified cyclotron magnetron Invariance Theorem: [L. S. Brown and G. Gabrielse, Phys. Rev. A, 25:2423, 1982.]

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

Detection of the spin state The continuous Stern-Gerlach effect Introduce magnetic inhomogeneity, the magnetic bottle Coupling of spin moment to axial oscillation axial frequency Time spin down spin up Spin flip results in shift of the axial frequency

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

Separate and Merge Potential (V) Position (mm) 14 12 10 8 6 4 2 Potential (V) -40 -20 0 20 40 Position (mm)

Tuning of the Separation Fraction upstream Fraction downstream Total Adjusting CE offset bevor separation 𝑁 𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚 = 𝑧 0 ∞ 𝑑𝑧 |𝑧| exp − 𝑚 ( 𝜔 𝑧 𝑧) 2 2𝑘 𝐵 𝑇 𝑧 Loss free separation and merging over 50 cycles We use up to 200 particles (upper limit unknown) Merging can be used to accumulate several AD shots Can be used to prepare single particles C. Smorra et al., A reservoir trap for antiprotons, Int. Journ. Mass. Spec. 389, 10 (2015).

Reservoir Operation Mode Particles in trap caught on 12th of November 2015 Consume typically 1 particle per month (mainly software glitches and human errors) 12 Antiprotons still in Reservoir trap

High-precision comparison of the antiproton-to-proton charge-to-mass ratio

Basic Principle Rtheo = 1.0010892187542(2) Measure free cyclotron frequencies of antiproton and H- ion. [TRAP 1990-1998] antiproton H- ion G. Gabrielse, Phys. Rev. Lett. 82, 3198 (1999) *using proton=>opposite charge=>position in the trap changes Take a ratio of measured cyclotron frequency antiproton ν c p to H- ion ν c H − => reduces to antiproton to proton charge-to-mass ratio 𝑅= ν c p ν c H − = (𝑞/𝑚) p (𝑞/𝑚) H − x 𝐵/2π 𝐵/2π = (𝑞/𝑚) p (𝑞/𝑚) H − Magnetic field cancels out! 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 ) Rtheo = 1.0010892187542(2)

H- ions details of H- trapping have yet to be understood. typical yield H- /pbar = 1/3. managed to prepare a clean composite cloud of H- and antiprotons.

Measurement Schema Based on reservoir extraction technique and developed methods to prepare negative hydrogen ions we prepared an interesting set of initial conditions Measurement scheme is triggered to the AD cycle in order to avoid beats between deceleration cycle and frequency measurements. Using this measurement scheme we are able to perform one frequency ratio comparison within 240s. About > 50 times faster than in precious measurements. Measurement is less sensitive to external magnetic drifts. High sampling rate allows for investigation of sidereal variations. First high-precision mass spectrometer which applies this technique

Result (𝑞/𝑚) p (𝑞/𝑚) p −1=1 69 × 10 −12 Rexp = 1.001 089 218 872 (64) 6521 frequency ratios Experimental result: Rexp = 1.001 089 218 872 (64) Cyclotron frequency ratios for p -to- p and H − -to- H − 𝑅 id are also evaluated Consistent with 1 𝑅 𝑖𝑑 −1=−3 79 × 10 −12 Corrected result: Rexp,c = 1.001 089 218 755 (64) (26) Rtheo = 1.001 089 218 754 2(2) (𝑞/𝑚) p (𝑞/𝑚) p −1=1 69 × 10 −12 In agreement with CPT conservation Exceeds the energy resolution of previous result by a factor of 4. S. Ulmer et al., Nature 524 196 (2015)

What else can we learn? Anisotropic CPT-violating couplings would cause diurnal variations No sidereal variations in charge-to-mass ratio observed at the level of 720 p.p.t. Assuming CPT invariance allows to constrain gravitational anomaly 𝜔 𝑐,𝑝 = 𝜔 𝑐 ,𝑝 𝑟→∞ 𝜔 𝑐,𝑝 − 𝜔 𝑐, 𝑝 𝜔 𝑐,𝑝 =−3( 𝛼 𝑔 −1) 𝑈/ 𝑐 2 𝑟= R 𝜔 𝑐,𝑝 ? 𝜔 𝑐 ,𝑝 Our 69ppt result sets a new upper limit of 𝛼 𝑔 −1 < 8.7× 10 −7 R.J. Hughes and M.H. Holzscheiter, Phys. Rev. Lett. 66, 854 (1991)

Towards an Improved Comparison New magnet implemented: Set of many shim coils enables improved tuning of B-field in the measurement trap (systematic correction reduced by factor of 10). Implementation of a self-shielded coil – reduction of magnetic field fluctuations 12ppb 5.5 ppb 1.25 ppb RMS fluctuation of magnetic field improved by factor of 4. With conditions of beamtime 2014 -> Q/M comparison at level 20 ppt possible.

Towards an measurement of the antiproton magnetic moment

Antiproton Magnetic Moment Beamtime 2015: Shuttling along entire trap stack (20cm/5s) established. Current situation: difficult 13 antiprotons in reservoir trap Single antiproton in precision trap Single antiproton in analysis trap

Detection of spin state - Challenge axial frequency Time spin down spin up Applied with great success for electron g -factors – Bohr magneton spin momentum Dealing with nuclear magneton requires huge magnetic bottle of to obtain frequency jump due to spin transition of radial angular momentum BUT Challenging! Tiny energy fluctuations in radial modes cause huge axial frequency shifts

Frequency fluctuation X Single Spin-Flip Resolution under ideal conditions – low cyclotron energies Axial frequency fluctuation X increases due to frequency jump caused by spin transitions Measure XSF and Xref → obtain SF-Probability!!! Detecting spin transitions in a statistical measurement!

Statistical Detection of Spin Flips Measure axial frequency stability: 1.) reference measurement with detuned drive on, 2.) measurement with resonant drive on. Spin flips add up Cumulative measurement: Black – frequency stability with superimposed spin flips. Red – background stability

Summary High-precision comparison of proton to antiproton charge-to-mass ratio Commissioning of all Penning traps – especially Reservoir trap and Analysis trap Detected fist antiproton spin flips – improved measurement of antiproton magnetic moment in reach Experiments with antiproton are still ongoing are Mainz CERN BASE Collaboration: Stefan Ulmer, Christian Smorra, Hiroki Nagahama, Takashi Higuchi, Andreas Mooser, Mustafa Besirli, Mathias Borchert, James Harrington, Nathan Leefer, Stefan Sellner, Georg Schneider, Toya Tanaka, Klaus Blaum, Yasuyuki Matsuda, Christian Ospelkaus, Wolfgang Quint, Jochen Walz, Yasunori Yamazaki

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