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
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)?
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
Plan of talk
1.
2.
3.
4.
5.
6.
7.
Introduction
The Imperial College SPECTRAP setup
Laser cooling of the ions
Rotating wall demonstration
Plasma resonances
Aspect ratio of the cloud
Conclusion
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.
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
Imperial College SPECTRAP Setup
Close-up of
trap housing
• 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
Entrance
window
Imaging optical
fibre bundle
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
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
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 nonideal (i.e. non-hyperbolic) trap electrode structure.
Penning Trap Operation
• Cold ions form a strongly-coupled nonneutral 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.
  r .x 
v (r , x)  v0 1 

c 

'
0
Penning Trap Operation
Doppler cooling laser frequency scan
• Due to physical constraints,
only radial laser cooling was
possible
• Axial motion is indirectly
cooled through collisional
interactions
• Measured fluorescence half
width is ~130MHz.
Temperature of the ion cloud
Part of the linewidth
arises from the spatiallydependent Doppler shift
due to the cloud rotation
• 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)
Non-neutral plasma in a Penning trap
• 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 ωr through
• The aspect ratio is also linked to ωr
• Therefore by changing ωr we can adjust n
and the aspect ratio
• Maximum density achieved when ωr = ωc/2
z
ωr
Rotating Wall Investigation
V  Vrot cos(  rott )
• 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
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
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
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
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
(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
Low U0
High U0
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)
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)
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
1.
2.
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
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
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.
Aspect Ratio
• For B=1.75T and U0=104V, the aspect ratio
of the cloud, α=z/r, is unity when ωr=ωc/2
z
Reflected
image
• 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
Direct
image
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
Axial scan
Radial scan
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
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
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” 1-2-4-3 gives partial compression
4
1
3
2
Also confirms
electrodes are
connected correctly!
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
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
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