[PPT] - Single Trapped Proton A. Mooser, K. Blaum, S. Bruninger, K. Franke, PowerPoint Presentation

SLIDE 1

Observation of Spin Flips with a Single Trapped Proton

A. Mooser, K. Blaum, S. Bräuninger, K. Franke, H. Kracke,
C. Leiteritz, W. Quint, C.C. Rodegheri, C. Smorra
S. Ulmer and J. Walz

SLIDE 2

Motivation

Precise test of the CPT theorem comparing proton and antiproton g-factor

) 24 ( 585690 . 5 

p

g ) 46 ( 585694713 . 5 

p

g

P. F. Winkler et al., Phys. Rev. A 5, p. 83 (1972).
J. DiSciacca et al., Phys. Rev. Lett. 110, 130801 (2013).
Here, aim first direct ppb measurement of proton g-factor

SLIDE 3

2

L p

e g B m  

Determination of the g-factor

L



B

2 2

L L c c

g      

c p

e B m  

Determination of Larmor frequency in a given magnetic field Monitoring magnetic field via simultaneous measurement

f the free cyclotron frequency

SLIDE 4

axial modified cyclotron magnetron

The Penning trap

Superposition of homogeneous magnetic field and electrostatic quadrupole potential Invariance Theorem:

2 2 2 2  

      

z c

B 

Correction Correction Ring Endcap Endcap

Vc Vc V0

[L. S. Brown and G. Gabrielse, Phys. Rev. A, 25:2423, 1982.]

z

e B B   

           2 ) , (

2 2 2

  z c U z radial confinement axial confinement kHz 10 



 MHz 29 



 kHz 700 

z



axial magnetron

modified cyclotron

SLIDE 5

Measurement of eigenfrequencies

623600 623700 623800 623900 624000 624100

136
134
132
130
128
126
124
122
120
118
116

Amplitude (dBm) Frequency (Hz)

Coupling of modes via rf-sideband coupling, or

 

         

z rf z rf

Amplitude modulation of the axial motion
Image current detection using parallel tuned circuit
Measurement of free cyclotron frequency with precision of ppb

SLIDE 6

Detection of the spin state The continuous Stern-Gerlach effect

           2

2 2 2

 z B B Bz

Introduce magnetic inhomogeneity, the magnetic bottle… …which adds spin dependent quadratic potential to axial potential… …leading to a shift of the axial frequency

Time

spin down spin up

z p z

B    

SLIDE 7

Detection of spin state Challenge

radial z z z z

E B B B m V c m q

2 , 2 , 2 2

2 1 2 1 2 2 1         

1

Hz/µeV 1 /

  

 E

z



Dealing with nuclear momentum requires huge magnetic bottle of to obtain frequency jump due to spin transition of

7

10 * 2 mHz 190



    

z z z

  

2 2

T/cm 30  B

Challenging! Tiny energy fluctuations in radial modes cause huge axial frequency shifts electrostatic potential spin momentum radial angular momentum

SLIDE 8

)) ( ) ( ( t T t

z z z

      

2 2

) ( 1

z z

n       



500 1000 1500 2000 2500 674423 674424 674425 674426 674427 674428 674429 674430 674431

Axial frequency (Hz) # Measurement

Frequency jump due to spin flip

Statistical measurement of g-factor in inhomogeneous magnetic field

Axial frequency fluctuation  increases due to spin transitions Detecting spin transitions in a statistical measurement!

2 2

,SF z ref

SF SF

P      

  150mHz - not stable enough for observation single spin transition

S. Ulmer, C. C. Rodegheri, K. Blaum, H. Kracke, A. Mooser, W. Quint, J. Walz , Phys. Rev. Lett 106, 253001 (2011)

relative precision of 10-4

SLIDE 9

g-Factor measurement

Larmor frequency measurement with a relative uncertainty of 1.8*10-6
With cyclotron frequency measurement

g = 5. 585 696 (50)

C. C. Rodegheri, K. Blaum, H. Kracke, A. Mooser, W. Quint, S. Ulmer, J. Walz , New J. Phys. 14 063011 (2012)

reduction of axial temperature by application of active electronic feedback

SLIDE 10

Double Penning trap technique

I. Determination of Spin State
V. Determination of Spin State
III. Driving Spin & Determining B-Field
IV. Transport

to AT

High Precision measurement demands homogeneous magnetic field
Introduce two traps – double Penning trap setup (H. Häffner, Phys. Rev. Lett.85, 5308 (2000))
II. Transport

to PT

B

19 mm 43.7 mm

Precision Trap: Measurement of frequencies Analysis Trap: Detection of spin state

II. Transport

to PT

Demands detection of single spin flip – higher frequency stability necessary

SLIDE 11

sf

+sf

100 200 300 400 500 600 25 50 75 100 125 150 175 200 225

Total Fluctuations Random Walk FFT Avaraging Frequency Fluctuation (mHz) FFT Avaraging Time (s) 3

Size of spin transition

Improvement of frequency stability in magnetic bottle

Increasing frequency stability – e.g. advanced detection system Spin state can be detected with high probability at low energies

mHz

pt

55  

Under ideal conditions - low cyclotron energies

at optimum

SLIDE 12

Observation of single spin flips

Determination of spin state using Bayes theorem – conditional probabilities
No significant jumps at off-resonant drive
Series of axial frequency measurements in AT
Apply resonant and off-resonant spin flip drives – background check

Fidelity of 88% - fraction of correctly assigned spin states in a series of measurement in analysis trap

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

Related observations are discussed in J. DiSciacca et al., Phys. Rev. Lett. 110, 140406 (2013).

SLIDE 13

Towards the double trap technique

Cyclotron frequency measurement in PT demands heating of cyclotron mode
Low energies are needed in AT for high fidelity spin state detection
Preparation at low energy by coupling to thermal bath of cyclotron detector

in PT and transport to AT - statistical process

lower statistics at higher fidelity higher statistics at lower fidelity 3 hours for one spin flip trail in PT at fidelity of 75%

Fidelity: fraction of correctly assigned spin flips in precision trap

SLIDE 14

resonant SF-drive

ffresonant SF-drive

Demonstration of double trap technique

g-factor measurement with precision of 10-9 in reach

A. Mooser et al., Phys. Lett. B 723, 78–81 (2013).

Observation of spin flips excited in the homogeneous magnetic field of the PT

Detect spin state - magnetic bottle in analysis trap
Excite spin transition in precision trap
Detect spin state - magnetic bottle in analysis trap

Measurement:

SLIDE 15

VH-NG-037

Thank you for your attention

Adv. Grant MEFUCO (#290870)

SLIDE 16

Quality of spin state detection Bayes and threshold method

Bayes method superior to threshold method - Optimal fidelity of 88% Fidelity: fraction of correctly assigned spin states in a series of measurements Threshold method: Accept spin flip if frequency jump above given threshold Bayes rule – conditional probability of having a spin state Update of state probability given complete frequency, noise and previous state information