1. 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

2. 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, (2006).
M. Hori et al., Nature 475, 485 (2011).
G. Gabriesle et al., PRL 82, 3199(1999).
J. DiSciacca et al., PRL 110, (2013).
S. Ulmer, C. Smorra, et al., Nature 524, (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, (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, v10 (2017).
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. 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

5. 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

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

8. 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 𝑚 p )
𝑈 𝑝
Rtheo = (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, (2015).

9. 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.

10. Result (𝑞/𝑚) p (𝑞/𝑚) p −1=1 69 × 10 −12
6521 frequency ratios
Result:
Rexp,c = (64) (26)
Rtheo = (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 (2015)

11. Parts-per-million measurement of antiproton g-factor

12. 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

13. 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

14. 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 = (50)
S. Ulmer, A. Mooser et al., Phys. Rev. Lett 106, (2011)
C. C. Rodegheri et al., New J. Phys (2012)

15. 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, (2017).

16. 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= (23)
H. Nagahama et al., Nat. Comm. 8, (2017).

17. Towards parts-per-billion measurement

18. 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)

19. 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

20. 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).

21. 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

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