1. 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

2. 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
( /nphys3432)
Planned by others
ASACUSA / ALPHA / ATRAP
Red: Recent tests
Purple: Past tests
Green: Planned
S. Ulmer et al., Nature (2015)
J. diSciacca et al., PRL (2013)
muon g
A. Mooser et al., Nature 509, 596 (2014)
CPT test with fractional precision of 10 −18 available… why continue measuring?

3. 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

4. [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.]

5. 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

6. 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

7. 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

8. Separate and Merge Potential (V) Position (mm) 14 12 10 8 6 4 2
Potential (V)
Position (mm)

9. 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).

10. 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

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

12. Basic Principle Rtheo = 1.0010892187542(2)
Measure free cyclotron frequencies of antiproton and H- ion. [TRAP ]
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 𝑚 p )
Rtheo = (2)

13. 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.

14. 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

15. 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 = (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 = (64) (26)
Rtheo = (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 (2015)

16. 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)

17. 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 > Q/M comparison at level 20 ppt possible.

18. Towards an measurement of the antiproton magnetic moment

19. 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

20. 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

21. 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!

22. 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

23. 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

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