Dynamics of Ca + ions confined in the SPECTRAP ion trap driven by a rotating wall

1. Dynamics of Ca+ ions confined in the SPECTRAP ion trap driven by a rotating wall Shailen Bharadia, Richard Thompson, Danny Segal and Manuel Vogel Work carried out at Imperial College London

2. Aims • To show compression of ion clouds and manipulation of their aspect ratio with the application of the rotating wall drive • To understand how best to set the trapping and rotating wall parameters to achieve maximum fluorescence intensity in the SPECTRAP experiment at GSI • Open question from the outset of this work: is it necessary to sweep the rotating wall drive frequency from low values up to ωc/2 (i.e. the Brillouin limit)?

3. Summary • The rotating wall technique works well with SPECTRAP • We can control the rotation frequency, aspect ratio and density of the cloud • First detailed study of heating resonances • We can set parameters to avoid heating resonances • This behaviour is well described by theory

4. Plan of talk • Introduction • The Imperial College SPECTRAP setup • Laser cooling of the ions • Rotating wall demonstration • Plasma resonances • Aspect ratio of the cloud • Conclusion

5. Penning Trap Operation • Radial confinement is provided by the magnetic field from an open-bore superconducting magnet (B<2.5T, 104mm bore). • Axial confinement is provided by the electric field produced by the cylindrical trap electrodes. • The voltage U0 is applied to the endcaps while the ring and compensation electrodes remain at ground. • Laser system is set up for Doppler cooling and spectroscopy of 40Ca+ ions.

6. The 40Ca+ Ion • Calcium ion energy level diagram in a 1.75T magnetic field. • Two laser frequencies required at 397nm • Four laser frequencies required at 866nm

7. Imperial College SPECTRAP Setup

8. Close-up of trap housing Imaging optical fibre bundle Entrance window • Optical access is only along the bore from below • Fixed mirrors used to direct laser light through the trap radially • Spherical mirror and lens (inside the can) in a confocal arrangement capture fluorescence from the trap • Optical fibre bundle to relay image of ion cloud out of the bore • Electrical connections at the top of the chamber

9. SPECTRAP electrodes • 5-electrode design with additional capture electrodes • Imperial version has holes in ring electrode for laser beams and fluorescence light • Electron filament and calcium oven on axis above and below trap

10. Penning Trap Operation • The trap was operated with a magnetic field of ~1.75T (72A), limited by the operation of the intensified CCD camera. • At this magnetic field, the specific voltage U0=104V gives a spherical ion cloud. • This is at the Brillouin limit which is the maximum achievable density • The single ion motional frequencies were verified by driving with oscillating potentials applied to the trap electrodes • identified by looking for heating resonances as the drive frequency is swept

11. Penning Trap Operation • The motional frequencies were identified with the resonances to be at: ωm/2π = 61.28±0.03 kHz ωz/2π= 275.0±0.5 kHz ωc'/2π = 607.5±0.5 kHz and implies B=1.745±0.002 T C2=0.541±0.002 (d0=9.2mm) • where C2 is the trap efficiency factor accounting for the non-ideal (i.e. non-hyperbolic) trap electrode structure.

12. Penning Trap Operation • Cold ions form a strongly-coupled non-neutral plasma • In the radial plane, the equilibrium state is a rigid uniform rotation about the centre of the trap at frequency ωr • ωr takes a value between ωm and ωc/2 • This implies the laser transition will be blue Doppler shifted by an amount proportional to the distance from the centre of the trap.

13. Penning Trap Operation Doppler cooling laser frequency scan • Due to physical constraints, only radial laser cooling was possible • Axial motion is indirectlycooled through collisional interactions • Measured fluorescence half width is ~130MHz.

14. Temperature of the ion cloud • Measured fluorescence half width is ~130 MHz • Cloud rotation frequency is ωr~90 kHz • Expected Doppler shift across the (half) width of the laser beam for this value of ωr is ~110 MHz • Subtracting the above Doppler shift and the 22MHz natural linewidth gives an estimated HWHM Doppler broadening of ~13MHz • This implies T~0.1K (ignoring power broadening) Part of the linewidth arises from the spatially-dependent Doppler shift due to the cloud rotation

15. Non-neutral plasma in a Penning trap z • A cold ion cloud in a Penning trap has a uniform density and a sharp edge • It rotates as a rigid body at a frequency ωr • Aspect ratio depends on the applied potential • The density n is linked to ωrthrough • The aspect ratio is also linked to ωr • Therefore by changing ωrwe can adjust n and the aspect ratio • Maximum density achieved when ωr= ωc/2 ωr

16. Rotating Wall Investigation • A rotating dipole field or “wall” is applied to the split ring electrode allowing for control of the cloud rotation frequency and implicitly the ion number density • A rotating quadrupole can also be used but needs more electrodes (ideally 8) • Rotating wall drive electronics provided by Dr. S. Stahl

17. Drive Amplitude Scan • Fluorescence rate increases with drive amplitude • Saturates above ~300mV. • Fluorescence remains fairly flat up to large amplitudes: • implies ion cloud is in a low-slip regime • heating in the presence of rotating wall is minimal • An amplitude of 1.5V is used unless otherwise stated

18. Dynamic Response • Change in fluorescence as the rotating wall drive is suddenly switched from 80kHz (ωrot~ωm) to 335kHz (ωc/2). • Fluorescence reaches its maximum within a single CCD exposure of 0.5s • Steady-state or low slip regime must therefore be reached in this short time • Images and line-profiles show compression of the ion cloud as expected • Scanning the rotating wall frequency is not necessary

19. Laser Detuning • Radial line profiles for optimised and weak laser cooling • Blue- both 397nm laser frequencies optimised for maximum fluorescence • Red – one 397nm laser is red detuned by 0.8GHz to reduce laser cooling efficiency • No change in radial extent of ion cloud • Implies minimal heating from the rotating wall • Cloud dimensions are insensitive to the laser detuning

20. Drive Frequency Scan (Low U0) • Low trap potential/frequency • Heating resonances identified: • Strong sharp resonance at the axial frequency • Broad asymmetric resonance from a (2,1) plasma mode • (2,1) heating effects persist up to ωrot=ωc/2

21. (2,1) Plasma Modes • A static perturbation in the lab frame becomes a rotating perturbation in the frame rotating with plasma • Then it can drive internal oscillation modes of the plasma • These can be calculated as a function of trap parameters High U0 Low U0

22. Drive Frequency Scan (High U0) • High trap potential/frequency (for a spherical cloud) • Resonances are degenerate • (2,1) heating response is sharper • Overall, the fluorescence intensity increases as expected up to ωrot=ωc/2 • At even higher U0 resonances are avoided (ω>ωc/2)

23. Drive Frequency Scan • Summary of heating resonances and their -3dB width in fluorescence intensity Plot shows which rotating wall or trap frequencies need to be avoided to reach high densities The most important mode is ω2,1(1)

24. Imaging Analysis • We need to confirm that we can create a spherical cloud to optimise laser excitation and fluorescence detection • Create an oblate (cigar-shaped) cloud by lowering the trap potential • Measure fluorescence with the laser beam • along the confocal imaging axis, and • with it axially offset to separate out the direct and retro-reflected fluorescence. • Compare the widths of the radial and axial line profiles of the direct and retro-reflected fluorescence with that of the superimposed image

25. Imaging Analysis - Axial • Axial line-profile broader than laser beam waist: • Spherical aberration • Power broadening Laser beam width: 0.14mm Image width: 0.20 mm

26. Imaging Analysis - Radial • Axial line-profile broader than laser beam waist: • Spherical aberration • Power broadening • All line widths agree within errors: • Focus of lens and mirror in the same plane and location at the centre of the trap.

27. Aspect Ratio • For B=1.75T and U0=104V, the aspect ratio of the cloud, α=z/r, is unity when ωr=ωc/2 • With a radially-directed laser beam, the axial extent of the cloud (z) is determined by scanning the axial position of the beam: • The cloud has a hard edge so we measure the width of the fluorescence image with the laser beam at the extremities of the cloud and superimpose the images • The radial extent (r) is measured directly off the images z Reflected image Direct image

28. Aspect Ratio at Brillouin Limit • The images from the top and bottom of the cloud show both direct and reflected images • We find α=1.02 ± 0.06 which implies that the Brillouin density (2 x 105 mm-3) was reached Radial scan Axial scan

29. Aspect Ratio as function of ωr • Plot showing how the radial extent of the cloud (r) varies as a function of the rotating wall frequency • Symmetry is expected about ωr= ωc/2 • This is the Brillouin limit (expect spherical cloud) • At other rotation frequencies the cloud is prolate Because the radial extent of the cloud is easier to measure than the axial extent, we plot here r/rB where rB is the radius at Brillouin flow

30. Aspect Ratio as function of U0 • Plot showing how the radial extent of the cloud varies as a function of the trap potential • The cloud is oblate below, and prolate above the spherical trap potential of U0=104V. All these results shown excellent agreement with theory, showing that the cloud behaves as expected We can deduce Debye length =2μm and Γ=16, i.e. cloud is strongly coupled

31. Sense of Rotation of Drive • The rotating wall is usually applied in the sequence 1-2-3-4 to give a positive sense of rotation for good compression • The negative sense 4-3-2-1 gives no effect, as expected • An “intermixture”1-2-4-3gives partial compression 4 1 3 2 Also confirms electrodes are connected correctly!

32. Plasma Mode Diagnostics • Applying the negative sense of rotation allows us to drive a different mode ω2,1(2) whose frequency tells us the cloud density • Confirm by driving at the corresponding ωr in the positive sense • We see no effect, indicating that the applied ωrot matches ωr • Therefore we can measure plasma conditions in absence of any compression from the rotating wall

33. Finally, an unexpected feature: • Under some circumstances the cloud appears to go into a ring configuration • This generally happens when the frequency of one of the two cooling lasers is moved above resonance

34. Summary • The rotating wall technique works well with SPECTRAP • We can control the rotation frequency, aspect ratio and density of the cloud • First detailed study of heating resonances • We can set parameters to avoid heating resonances • This behaviour is well described by theory