sympathetic cooling of motivation for cooling (anti)proton

Sympathetic Cooling of Single Protons

(and Antiprotons)Markus Wiesinger on behalf of the BASE collaboration

EXA 2021 online conference16.9.2021

This contribution is based on our recent paper:

BASE Collaboration, Sympathetic cooling of a trapped proton mediated by an LC circuit. Nature 596, 514–518 (2021).

https://doi.org/10.1038/s41586-021-03784-wMarkus Wiesinger Sympathetic Cooling of Single Protons (and Antiprotons) - EXA 2021

Motivation for CoolingPrecise comparisons of the fundamental properties of protons and antiprotons, such as magnetic moments and charge-to-mass ratios, provide stringent tests of CPT invariance, and thus, matter-antimatter symmetry.Using advanced Penning-trap methods, we have recently determined the magnetic moments of the proton and the antiproton with a relative precision of 0.3 p.p.b. and 1.5 p.p.b., respectively [1, 2].Both experiments rely on sub-thermal cooling of the particle’s modified cyclotron mode using feedback-cooled tuned circuits. We aim to replace this time-consuming process (several hours) by sympathetic cooling with laser-cooled beryllium ions.

2 Markus Wiesinger Sympathetic Cooling of Single Protons (and Antiprotons) - EXA 2021

(Anti)Proton g-Factor Measurement

Double Penning-trap method:

excitation of spin transition in homogeneous precision trap (PT)

AT PT

spin-state detection in magnetic bottle trap (AT)

3

Continuous Stern-Gerlach effect:

spin state is determined by jump in axial frequency [3,4]

caveat: cyclotron quantum jumps lead to axial frequency fluctuation

22 Chapter 2. Theoretical Basics

analysis trap precision traptransport section target

initialize spin state measure ωc & probe ωL

?

read final spin state

Fig. 2.8: The method starts in the AT where the spin state is determined, e.g. spin down. The particle is thentransported to the PT where wc is measured in the homogeneous magnetic field. Simultaneously the Larmorfrequency is probed with an excitation. Depending on the excitation frequency the proton spin state has changedwith probability pSF. To determine the spin state after the excitation the particle is again transported to the ATand the final spin state is read out.

spin flips were statistically detected for the first time [73]. Finally, in 2013 further improvements inthe axial stability allowed the observation of single discrete spin flips [74]. These advances becamepossible through the implantation of a very strong magnetic bottle B2 = 298 000 T m�2 and the sys-tematic reduction of background noise. Even today the reduction of the background noise is still oneof the crucial experimental difficulties towards detecting single proton spin flips, as will be discussedin detail in section 3.1.

2.9 Double trap scheme

The usage of a strong magnetic bottle is essential for the determination of the proton spin state. Itsstrength, however, poses a fundamental limitation for the determination of the eigenfrequencies.The axial motion oscillates with an amplitude rz which is a function of its energy. For typical axialenergies of Ez = kBTz ⇡ 4 kB the axial amplitude is around 50µm. In the presence of the magneticbottle a change of 50µm corresponds to a change in the magnetic field of 0.8 mT. This leads to shifton the Larmor frequency by 20 kHz on a total frequency of 50 MHz.

An accurate description of the width of the Larmor resonance line yields

dwL =1

mw2z

B2B0

kBTz wL (2.54)

and it was demonstrated that the g factor is limited at the ppm (part per million) level [45, 73]. Thistechnique was also recently used to measure the antiproton g factor with 0.8 ppm [46]. In order toreach precisions at the ppb level or below, a line width reduction is mandatory. However, neitherthe frequencies wz and wL nor the magnetic field B0 can be changed as they are constrained by the

22 Chapter 2. Theoretical Basics

analysis trap precision traptransport section target

initialize spin state measure ωc & probe ωL

?

read final spin state

Fig. 2.8: The method starts in the AT where the spin state is determined, e.g. spin down. The particle is thentransported to the PT where wc is measured in the homogeneous magnetic field. Simultaneously the Larmorfrequency is probed with an excitation. Depending on the excitation frequency the proton spin state has changedwith probability pSF. To determine the spin state after the excitation the particle is again transported to the ATand the final spin state is read out.

spin flips were statistically detected for the first time [73]. Finally, in 2013 further improvements inthe axial stability allowed the observation of single discrete spin flips [74]. These advances becamepossible through the implantation of a very strong magnetic bottle B2 = 298 000 T m�2 and the sys-tematic reduction of background noise. Even today the reduction of the background noise is still oneof the crucial experimental difficulties towards detecting single proton spin flips, as will be discussedin detail in section 3.1.

2.9 Double trap scheme

The usage of a strong magnetic bottle is essential for the determination of the proton spin state. Itsstrength, however, poses a fundamental limitation for the determination of the eigenfrequencies.The axial motion oscillates with an amplitude rz which is a function of its energy. For typical axialenergies of Ez = kBTz ⇡ 4 kB the axial amplitude is around 50µm. In the presence of the magneticbottle a change of 50µm corresponds to a change in the magnetic field of 0.8 mT. This leads to shifton the Larmor frequency by 20 kHz on a total frequency of 50 MHz.

An accurate description of the width of the Larmor resonance line yields

dwL =1

mw2z

B2B0

kBTz wL (2.54)

and it was demonstrated that the g factor is limited at the ppm (part per million) level [45, 73]. Thistechnique was also recently used to measure the antiproton g factor with 0.8 ppm [46]. In order toreach precisions at the ppb level or below, a line width reduction is mandatory. However, neitherthe frequencies wz and wL nor the magnetic field B0 can be changed as they are constrained by the

zν

low energy high energy

time

spin flip spin flip

cyclotron energy (E+ / kB)

spin

det

ectio

n fid

elity

(%)

axia

l fluc

tuat

ion

(Hz)0.30

0.20

0.10

0.00

100

�0

�0

�0

�0

�00.001 0.01 0.1 1 10

Ξn = 40 mHzΞw = 113 mHz

Δνz,SF

resistive cooling

sympatheticlaser cooling

Markus Wiesinger Sympathetic Cooling of Single Protons (and Antiprotons) - EXA 2021

Experimental ApparatusOur trap-can is located in a magnetic field of 1.9 T, surrounded by isolation vacuum, and cooled to a temperature of 4 K.

4

pulsed 532 nm laser: laser ablation of Be

313 nm laser:cooling of 9Be+ ions

vacuum: < 10-18 mbar comparable to the pressure in interstellar space

Analysis Trap (AT): detection of the proton spin state

Precision Trap (PT): precision measurement of Larmor and cyclotron frequency

Cooling Traps (CT): cooling of proton cyclotron mode


Cooling TechniqueLC circuit connected to two traps:

⇒ system of three coupled, damped (9Be+ by the cooling laser), and excited (LC circuit by thermal noise) oscillators

5

BASE Collaboration, Nature 596, 514–518 (2021)

f ≈ 500 kHzQ ≈ 15 000


Coupled Oscillator System

6

experiment

numerical simulation

coup

ling

Readout: FFT of time-domain signal of the LC circuit

preliminary


Cooling ResultsTemperature reduction: 85 %

cooling time constant: ≈ 1s

first ever sympathetic cooling of a proton by induced (image) currents

limitations:heating by RLC circuit: ≈ 2 K temperature resolution: ≈ 2 K

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final proton temperature: 2.6(2.5) K

BASE Collaboration, Nature 596, 514–518 (2021)


OutlookAdditional trap for precise temperature measurement:

magnetic bottle leads to energy dependent axial frequency shift due to CSG effect

temperature resolution: ≈ 10 mK

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Application of more advanced cooling techniques will allow to reach even lower temperatures:

coupling mediated by common end-cap electrode [5]


References & Funding[1] Schneider, G. et al., Science 358, 1081 (2017)

[2] Smorra, C. et al., Nature 550, 371 (2017)

[3] Dehmelt, H., Proc. Natl. Acad. Sci. USA 83, 2291 (1986)

[4] Mooser, A. et al., Phys. Rev. Lett. 110, 140405 (2013)

[5] Heizen, D. J. & Wineland, D. J., Phys. Rev. A 42, 2977 (1990)

We acknowledge financial support from the RIKEN Chief Scientist Program, RIKEN Pioneering Project Funding, the RIKEN JRA Program, the Max-Planck Society, the Helmholtz-Gemeinschaft, the DFG through SFB 1227 ‘DQ-mat’, the European Union (Marie Skłodowska-Curie grant agreement number 721559), the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant agreement numbers 832848-FunI and 852818-STEP) and the Max-Planck-RIKEN-PTB Center for Time, Constants and Fundamental Symmetries.

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sympathetic cooling of motivation for cooling (anti)proton

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