This page: http://monitor.mikes.fi/ionclock/
- 2019-11-08: -C2 Zeeman component linewidth estimate of 800 Hz.
- 2019-11-05: Zeeman peaks with B-shield (1.6 uT estimate).
- 2019-11-04: Now with first B-shield. Laminated plywood + metglas.
- 2019-07-12: Zeeman peaks in ambient (66uT estimate) B-field.
- 2019-07-10: Initial clock-transition search...
- 2019-07-10: Page created.
08:00Z ion seems to have disappeared!?
Try a bit of 405, 1033, and 461..., and re-lock to Rb-line.
10:00Z Longer run over lunch, 6x6x6 = 216 pts. n_phot=300k
11:30Z progress to pt 93/215 - so this run is >2 hours long..
Optimal voltages [ 0.24380421 26.67929547 43.62223335]
Data file 5009
Contrasts at Vopt ( 2.5, 2.7, 2.8) %
Ball-size is abs(contrast), +sign is green, -sign is red. sum figure shows sqrt(A^2+B^2+C^2)
optimal point is blue ball (size not to scale) in sum-figure.
0900Z: Run the NPLv3-umotion-optimizer, around previous voltages, with n_phot=100k
4x4x4 = 64 voltage-combinations, x3 beams. Data file 5004.
New optimal voltages (-5.5 V12cm): [ 0.24315127 26.67666472 43.61507129]
V1 = -5.7432, V2 = -5.2568, V3 = -16.938399999999998, V4 = 70.2918
Here n_phot=300k contrasts are: (2.5, 2.7, 3.1) % - (?not so great - same as before?)
micromotion contrasts are now slightly worse.
(A, B, C ) = (2.4, 3.1, 4.8) % repeated (2.0, 3.1, 4.6) % - measured with n_photons=300k and n_bins=25
voltages from y-day were (-5.5, +0.2668, +26.719, +43.503) V = (V12cm, V12dif, V34cm, V34dif)
Fluorescence from all beams ABC was quite steady at 37(1) kCPS through the night.
This is about 700 CPS in the usual 20ms detection window
at some point Rb-lock was lost! detuning was down to 170MHz for tickler - this made the lock jump to the next Shiner-peak?
when locked to wrong shiner-peak, fluorescence was 200counts/20ms (required long camera exposure) - after re-locking to right peak >700counts/20ms.
micromotion investigations. How does V12cm change the optimal u-motion voltages?
d V12dif / d V12cm = -0.81 mV/V
d V34cm / d V12cm = 1.30 V/V - strong coupling!?
d V34dif / dV12cm = 18 mV/V
V12cm controls the secular ratio
V12cm = 0 V -> wz/wr = 1.52 and 1.57
V12cm = -3.5 V -> wz/wr = 1.76 and 1.84
V12cm = -5.5 V -> wz/wr = 1.93 and 2.02
secular frequencies with tickler
170MHz detuning seems to work (but see note on Rb-lock!), see rise in fluorescence at resonance
DDS attenuation 4dB for radial modes, 10 dB for z-mode
At -5.5 V12cm, RF 70mVpp, seculars (0.936125, 0.9805, 1.8918) MHz. Radial modes split by 44 kHz
overnight fluorescence monitor, gate time 1000ms, n_pts = 46800 (13 hours)
NOTE all beams ABC on!
256x speedup stream: https://www.youtube.com/watch?v=bSQgo7BL8f4
slow stream: https://www.youtube.com/watch?v=Ey-IkPURY4o
overnight scans, variations in probe length and attenuation.
5kHz span, 10 Hz resolution, 499 pts/scan, ca 1 hour/scan
'center' scans, not randomized (seems to scan outwards from center?)
scan1: 20 dB, 5 ms
scan2: 20 dB, 10 ms
scan3: 20 dB, 20 ms
scan4: 20 dB, 40 ms
scan5: 22 dB, 10 ms
scan6: 22 dB, 20 ms
scan7: 22 dB, 40 ms
scan8: 22 dB, 80 ms
scan9: 18 dB, 10 ms
scan10: 18 dB, 20 ms
scan11: 18 dB, 40 ms
scan12: 18 dB, 80 ms
scan13: 18 dB, 5 ms
run5: same scan as run4, longer 20ms probe
run6: longer 40ms probe
run4: try to zoom in on left peak (-C1?)
center 75.9474 MHz, span 1 kHz, resolution 10 Hz, 101 points. Probe 10ms, attenuation 20 dB
run3: try I3=0mA, to separate Zeeman-components? Coil currents (-5, 0, 0) mA
center 75.9484 MHz, span 4 kHz, resolution 100 Hz, 41 points. DDS att 20 dB (from rabi-osc attempts 20 dB seems fine?)
run2: center 75.9484 MHz, narrower span 4 kHz, lower resolution 25 Hz, 161 points, DDS att 5 dB, 10ms probe, 20ms detection, 500/50 bright/dark.
run1: center 75.948 MHz, span 12 kHz, resolution 100Hz, 121 points. DDS att 5 dB. 10ms probe. 20ms detection 500/50 bright/dark.
ca 7s per 100 pulses
record-high 48% excitation!?
B-field seems low, peaks overlap
f_beat = 23.150
estimated f_corrected -330.396 MHz
NPL-optimization gives (0.2668, 26.719, 43.503) voltages. Here contrasts are (0.3, 0.5, 0.7)%. n_photons=300k
With no changes to bias-voltages, get contrasts of (5.5, 8.7, 13.3) %, detuning 210 MHz
The old voltages were (?) (0.246, 26.57, 44.2) V
2019-12-17 13:40Z Loading 1.60A, 6min 20s
setup changes: metglas 3rd layer. Toptica clock-laser (lock servo might not be optimal)
Simulation: how many photons to collect into the correlation histogram?
<1% stdev in the S-contrast requires more than 2e4 photons.
ca 0.5% stdev in S expected with 1e5 photons.
<0.1% stdev requires >1e6 photons
Number of bins in the histogram is not important
15:00Z: ion was dark from 23-local y-day evening. 405 or 422-re-lock doesn't help. shut down lasers.
2019-12-06 Independence Ion
128x speedup: https://www.youtube.com/watch?v=f3edhdwqXgc
scan1 Lorentzian fits to data, based on f_corr estimate -330.3895 MHz
lorentzian(x) = height*(width)/(pow(x - center,2) +pow(width,2))
Estimated AHM3 vs UTC is -2.5194e-12 or 1121 Hz @ SRS
|Component||height||width / Hz||center-SRS / Hz|
Estimate of B-field based on scan1 pairs is ~0.363(1) uT
|Pair||peak-separation / Hz||Zeeman shift / Hz/uT||B = sep/(2*shift) / uT|
from livestream, ion lost 20:59:30Z. It was loaded 2019-12-04 13:37Z.
leave longer ca 1h scans running
center 75.9455, range 12 kHz, resolution 25 Hz, 481 points
probe 10ms, attenuation 20 dB
seem to detect C1 through C4 (not C5)
B ~0.36 uT with I = (-5, 0, -1) mA applied
data file e.g. "2019-12-06-scan1.txt"
scan1 (4794) through scan7 (4800) contain good data. scan8 (4801) has both a 5min dark period and the ion loss event.
scan9 through scan24 are invalid data
12:15Z suddenly lost ion??... and then it returned at 12:20z after 5 min!?
try I3 = 3 mA
-C1 at 75.9412
+C1 at ?
Run with a few different currents and plot in same figure
orange (0, 0, +3) run4: I3 = +3 mA
red (0, 0, +1) run4-1mA: I3 = +1 mA
pink (0, 0, -1) run4-minus1mA: I3 = -1 mA
blue (I1, I2, I3) = (+1, 0, -1) (did not move -C1 closer to line-center)
green (-1, 0 , -1) - now closer!
cyan (-2, 0, -1) - best so far
yellow (-3, 0, -1) - we now se also -C2 in the 3kHz scan? excitation-P for -C1 is lower? ex-P for -C2 is record-high!? run also the +side
tab:blue (-4, 0, -1)
tab:brown (-5, 0, 1)
change I-driver state from "#" (edit mode?) to "^" (actual current-drive?) - maybe this will move C1?
same centers and ranges as before
+C1 at 75.94895 (moved only -100Hz?)
-C1 at 75.9415 (did not move much)
search wider for C1
old (1mA) predicted center at 75.9416 (-C1) and 75.9486 (+C1)
observed at 75.94145 (25 jumps) and 75.94905 (26 jumps)
seems like the 2mA value is not in use? (repeat?)
center 75.9451 (no change)
range 7 kHz (should see C1 peaks, they were at +/-3.5 kHz previously)
step 100 Hz, 71 points
Increase I3=2mA - prediction is that this further decreases B.
interrupt run8 from y-day, it is taking too long...
Clock transition run
longer run, leave overnight
win-machine spontaneously rebooted in the evening (~21 local) !?! live-stream cut
4753 26dB attenuation rabi-flop
4752 rabi-flopping on -C2, DDS att 23 dB, range 1ms to 20ms
zoom in on -C2 and get a linewidth (with first B-shield 2019-11-05 linewidth was ~800Hz )
Zeeman model predicts -C2 at AOM=75.9381 MHz
peaks fit a B-field of 1.25 uT (but the prediction was 0.2uT from 1mA of current?)
try to get a wider view
back to calculated center (+2800Hz from run5)
wider range 30kHz, resolution 200Hz, probe 10ms, 151 points
Zeeman peaks offset +1.1 kHz from scan-center, with B=1.25 uT
add 1mA of I3 coil current. ca 200uT/A -> B=0.2 uT
This should split C5 by 7.8kHz and C1 by 1.12kHz
larger range 10kHz but lower resolution 100Hz -> 101 points
double range to 1kHz. 40ms probe, more attenuation 20 dB (seems OK from rabi-flopping)
10Hz resolution, 101 points
Now see high excitation probabilities, around 30% at best.
(4743) Rabi-flop, DDS_att = 5dB. Rises from 1ms to 4ms - then flat
(4744) Rabi-flop 10 dB att, rises until 8ms then flat
(4745) Rabi-flop 20 dB att, intially quadratic - good(!?) - from 0 to 6ms
(4746) Rabi-flop 30 dB att, narrower range 1ms to 30ms. too much attenuation - not much excitation.
(4747) 23 dB att.
shift down center -2800 Hz
longer 40ms probe, 10 Hz resolution 1 kHz range
longer probe 20ms, lower resolution 25Hz, larger range 2*6 kHz. 241 points. N_probe=100
tau_probe=10ms, DDS_att=5dB, N_pulses=100, tau_det=20ms, N_bright=500, N_dark=50
6th run of NPL, over lunch, gave (0.258, 26.594, 43.829)
contrasts(300 kphotons, 35 bins) are (A, B, C) = (0.94%, 1.3%, 0.79%)
300 kphoton measurement takes (16, 23, 25) s to perform, depending on fluorescence amount from each beam
NPL-algorithm with 3 variables now seems to converge
detuning AOM 210MHz, V12cm = -5.5V (NOTE: this is FIXED in the v2 NPL-script!)
ABC-optimal point, 1st run: (0.250 , 26.573 , 43.814 ) (V12dif, V34cm, V34dif)
Here ABC-contrasts (2, 2, 2) %
60 k photons/histogram, 3 points scanned per voltage (27 points)
ABC-optimal point, 2nd run: small changes to optimum (-1 mV, +5 mV, +8 mV)
voltages = (0.249, 26.578, 43.822)
100 k photons/histogram, 5 points per voltage (125 points total)
here ABC-contrasts (2.5, 2.5, 2.5) % - not any better than previous optimum
NPL-algorithm modified to only have 3 scanned parameters (V12dif, V34cm, V34dif)
Dashed lines show A-optimal and B-optimal voltages. Dash-dotted lines are shifted versions (2020-04) - probably not useful
pa = -1.5009 85.1762
pb = 1.6786 2.3214
For example a change of (V34cm, V34diff) = (+1, -1.5) should be along the A-optimal line.
These should be compared to the planes found in the 2019-12-19 data
AB-contrast optimal point found in (V34cm, V34dif) plane. C-contrast not optimal.
V-shaped bias-sweep plots, sine-shaped correlation histograms.
Micromotion minimization, need to move both ABC beams and ASE as bias-voltages change
Using V12cm = -5.5V to get axial/radial ~2
13:37Z Ion loaded 1.60A / 1.25 W and 6min 35s
Filter-boards removed from clock-laser prestabilizer - now seems to stay locked for >8h.
Cavity drift from 8h of data: +18.093 mHz/s
OHDEV(drift-corrected) reaches 1e-15 at around 200s.
f_cavity = -490.2075 MHz (SRS) (morning 2019-12-03)
Ion loaded 1456Z (1.60A and 8min 10s) - but lost 22:xxZ the same day
By scanning, found voltages that minimize A-contrast (but B/C beams do not cool in this state?)
Vbias = (-5.5, +1, 0, 80.4) V
A-contrast (repeats, n_photon = 60k or 80k): 0.9%, 0.45%, 1.2%, 0.58%
Clear minimum with pi-phase change at V34diff 80.4V. Sine-shaped correlation histogram
Secular frequencies: could not find radial splitting, see only one peak. why? (using A-beam)
70mVpp from agilent, and the usual 1.65Vpp monitor.
ARTIQ DDS as tickler, 4 dB attenuation for Radial, 10 dB attenuation for Axial.
Fluorescence dips or peaks, depending on cooling laser detuning.
Siglent siggen+bias-amp connected for DC-modulation (try this later also with shorting N-connector on helical-resonator!)
|V12common / V
||Axial / MHz
||Radial / MHz
abs(qz)=0.32, trap voltage V0 = 390 V (assumes 0.75 trap efficiency)
az = 0 at V12common = -5.319 V
Loading at 1.70A gave two (or more?) ions
Estimated cavity mode spacing 501.305 MHz
Note that comb measures drift-corrected IR, not cavity frequency.
If cavity mode-numbers and abs-frequencies correct, mode spacing is 501 304 565 Hz
|f_cavity - SRS / MHz
||sign, f_beat / MHz
||Wavemeter / nm
||Cabity mode nr
||2 223 894
||2 223 896
||2 223 899
(measured against AHM3, with estimated frequency of -2.51e-12 wrt UTC(MIKE), maser is slow)
Observed drift in 4h run: +24.733 mHz/s
Increase drift-correction by +4.49 mHz/s (single-pass), based on 4-hour run 2019-11-28 evening.
ion lost 2019-11-26 at 17:24:52Z, storage time was ca 29 hours
Clock laser (briefly) locked to cavity
F_corrected = -330.386205 MHz
f_beat = 23.145390(50) MHz
With fixed 178.5 MHz AOM this gives line-center at AOM_Zeeman = 75.943103 MHz
P_674_A-beam = 44 nW (5dB att. on Zeeman AOM)
20 ms detection window, bright=230, dark=30
Drift-correction was not updated recently, still runs with AOM-drifts of k0 + k1 = (6.532e-3 + 2.728e-3) Hz/s = 0.5 * 18.52 mHz/s
Try to optimize micromotion - but no clear minimum found
Longer NPL-algorithm run gives V12diff, V34common, V34diff = (+2.22, +23.138, +105.991)
This gives photon-correlation contrasts A/B/C = 18% 4% 14%
About 60 000 photons in one histogram seems necessary for good statistics
New RF-drive 16.716 MHz. 70mVpp gives 1.65 Vpp monitor as before.
2019-11-25 12:21Z Ion loaded with I_disp = 1.60 A after 4min 45s.
Bias-voltage source improved range to +/-168 V on V3 and V4
After tuning impedance match (New RigExpert AA-55 Zoom)
- SWR 1.03 @ 16.7188 MHz
- Z=48.9 Ohm, R= 48.9, X= -0.96
- Q ~730...770
pulse data from wide scan of 2019-11-05
Overnight results in Technicolor 3D:
(07:38) ion lost, tried 405nm but no change, checked 422nm Rb-lines - seems OK
from video, lost around 2019-11-07 21:39Z (was trapped at 2019-11-04 09:52Z)
camera intensifier battery-box needs a new 9V battery..
(07:33Z) clock-laser has unlocked at some point. when?
Observed line is ca.800Hz (optical) wide - what B-field changes does this correspond to?
C2 sensitivity 11.190 kHz/uT, so 400Hz shift by 0.036 uT.
this is 2% of the assumed 1.56uT field at the ion
If we have a 36 nT peak AC-field (frequency?), can this be measured with a probe+meter?
How? Outside the shield, close to ion, and assume some AC attenuation?
(14:55Z) new center for scan: 75.93805 MHz
schedule overnight runs, 8pcs a 2hours = 16 hours.
all scans have same AOM range 1200Hz and AOM step 5Hz, 239 frequency-points per scan.
3rd run 50ms
5th run 40ms
1st run 30ms
7th run 20ms
2nd run 10ms
4th run 5ms
8th run 2.5ms
6th run 1ms
(14:40Z) New drift-compensation = [6.523 (old) + 2.728 (new) ]*2 = 18.52 mHz/s, from 58794.611
(13:17Z) combined plot, run1 and run2
(13:01Z) What effect does cavity-drift have? We currently compensate 2*6.532 mHz/s = 13 mHz/s
Measured overnight drift is 18.5 mHz/s
During 1h we have uncompensated drift of 3600s*5 mHz/s = 20 Hz
During 1 day, 470 Hz!
(11:54Z) start run2: same 60ms probe, range 1500Hz (down from 2kHz), AOM step 5 Hz (down from 10Hz). 200 shots/freq.
301 points, 25s/pt, expected duration 2h, will finish at ca.13:54Z
re-lock clock laser
(values are 15 min averages, from Chronograf)
f_beat= 23.148089 (37) MHz (12:01Z)
f_cavity = -490.255964 MHz
f_corrected = -330.391669 MHz
cavity_drift = 0.024 Hz/s
Clock-laser unlocked during lunch-break scan...(11:21UTC)
Use only A beam, P_674 = 105 nW, try 200 pulses per frequency
Same -C2 center-frequency (75.9383 MHz), 2kHz range (down from 7kHz), 10 Hz resolution (down from 20Hz).
200 frequency points, 25-26s/point, duration 1.5 hours
overnight cavity frequency: 2019-11-07_fcavity.csv
NOTE: all three beams ABC ON for cooling and probe
Scan area around -C2, with different probe pulse lengths= 30ms, 40ms, 50ms, 60ms, 70ms....
7200 Hz AOM scan range, 20Hz AOM resolution, 360 points per scan. (1 hour per scan?)
shorter detection window 10ms, collects ~350 photons in 10 ms.
-C2_fcenter = 75.9383 MHz
Fcavity = -490.257406 MHz
Fcorrected = -330.392137 MHz
f_beat = 23.148357 MHz
clock-cycle configuration (clearout, cool, detect, repum)=(10, 50, 10, 60)
bright=350, dark=25. threshold is geometric mean
run1 (note randomized order of frequencies!)
Clock laser unlocked at some point during morning? (was unlocked at 0740 UTC)
Some of the later data in the overnight run is bad.
Overnight scheduled runs for 30, 26, 22, 18, 14, 9, 6, 3 ms probe pulses. Approx 10 nW in A-beam to ion.
Scan is 75.947MHz +/- 35 kHz (assumes B=50uT/b_att=1.56 uT is correct...?).
1000 points, approx 70 Hz AOM resolution, 140 Hz optical.
30ms lin scale
22ms lin sale
all scans, log scale:
Zeeman-split at 50uT is +/- 281, 560, 1121, 1400, 1961 kHz (for C1, C2, C3, C4, C5 components)
sensitivities 5.6124, 11.190, 22.415, 27.992, 39.217 kHz/uT (NRC email 26.5.2013)
Corresponding to gS=2.00248 gD=1.200486 and gS/gD = 1.66806
Barwood2012b reports gS/gD = 1.668057
Normalized by C1 sensitivity ratios are approx: (1, 2, 4, 5, 7) and differ from integers by about 0.02 at most.
Ratios for zeeman-split from above sensitivities are (1, 1.9938, 3.9938, 4.9875, 6.9876)
- F_cavity -490.259 MHz SRS
- F_IR_comb = f0 + ncomb * frep - fbeat
- ncomb = 2 223 894
- f0 = -20e6, NOTE negative f0!
- frep = 100e6
- fbeat = 23.148 MHz
- F_red_comb = 2*F_IR_comb
- F_cavity = F_red_comb - 2*AOM_drift
- Fcorrected -330.392 MHz SRS (shifted up by 2*AOM_drift=2*79.933 MHz)
- fixed single pass AOM_fix= +178.5 MHz (28dB attenuation on DDS, for 674nm P-control)
- line-center estimate from 2019-11-04 was AOM_Zeeman = 75.9465 MHz
- Check: -490.259 + 2*79.933 + 178.5 + 2*75.9465 = 0 MHz SRS
try minimizing micromotion, without much success... need higher Vbias voltages?
lower 674 intensity 10-fold, to around 10nW at ion (28dB attenuation on 178.5MHz DDS AOM, ca 2uW at 674-launch).
use 3ms probe pulse
scan range around inner two Zeeman-components (from -C2 to +C2) from 2019-11-04.
1000 frequency points (ca 100Hz AOM-step), ca 2 hours.
Fit to data!?
center_freq = 75.947000 (+2 kHz SRS)
C5-shift = 0.030641
+C5 = 75.977641
-C5 = 75.916359
B_eff = 50uT/b_att = 1.56 uT
from 75.85 to 76.05 (200 kHz) in 5000 steps (~10 hours)
40 Hz AOM step, 80 Hz optical
try 16 ms probe pulse (?)
2019-11-04 run1: from 75.8465 to 76.0465 (200 kHz) in 1000 steps (~2 hours)
200Hz AOM step, 400 Hz optical step
first half of data is bad, ASE-overrides were ON...
8 ms probe pulse, maybe 100nW in A-beam.
Cooling laser detuning scan
Micromotion minimization with the Baynham-matrix was successful (?).
Measured contrasts before scans (A/B/C) = (1.0 % / 1.6 % / 5.3 %)
However only A and B beam scans were successful, data from C-beam looks strange?
Measured power (A/B/C) = (0.38 / 0.35 / 0.27) uW
Theory curve has detuning shifted by -1 MHz, background counts 1700 cps estimated, fluorescence collection efficiency 1/218
Canon EOS 60D, 5 s exposure, f/2.8 105mm Sigma Macro, ISO-3200. 13mm extension tube.
The 8ms results were interpreted as due to either 33uT or 66uT ambient B-field.
2019-07.13 ca 17:00+03 re-locked cooling laser - strange noise on Rb-signal!?
8ms pulses: sat-13-8ms.txt
Ion trapped on wednesday (after lunch?) was lost friday 19:50+03. 405nm did not help (H-Sr molecule??), A/B/C beams did not help.
Better diagnostics for cooling-laser needed - not sure if servo was at limit or not..
New ion trapped sat 2019-07-13 ca 10:30+03
New longer probe-time runs scheduled
2.0 ms, 4.0 ms, 8.0 ms
8000 frequency-points in 2 MHz span -> AOM step 250 Hz -> optical step 500 Hz.
100 pulses per frequency, ca 7 s per frequency or 16 hours per 8000 frequency-points.
674nm ca 100nW, 422nm ca 1.1 uW detuning_AOM=200MHz, beam A.
run1: probe 0.5 ms
run2: probe 1.0 ms
run3: probe 2.0 ms
run4: probe 4.0 ms
1ms, lower power
Zeeman AOM att. 21 dB (was 15dB) - now approx 50 nW to ion
longer 4 ms pulse
A beam, ca 100 nW
longer 2ms pulse
A beam, ca 100 nW
one beam, the A beam
cooling ca 1.5 uW
clock ca 100nW, 1ms pulses
detection window longer (was 20 ms), now 34 ms
AOM-scan-batch is 250 kHz / 1001 points. 8 batches = 8008 points in total
Optical frequencies denoted SRS are offsets from BIPM SRS value.
All three cooling beams, AOM = 200 MHz detuning.
All three clock beams, ca 100 nW in total, 1 ms pulse.
Estimate of drift-corrected cavity-light: -330.486522 MHz SRS.
AOM-shift from this is AOM_fixed +178.5 MHz + 2*AOM_Zeeman
So the high peaks are centered at +0.854 MHz SRS and split by +/-0.617 MHz
Jumps (more than 2/100):
- 4 jumps AOM_Z = 75.882 MHz
- 45 jumps AOM_Z = 76.1118 MHz -> optical +0.237078 MHz SRS
- 3 jumps 76.6245
- 3 jumps 76.716
- 46 jumps at AOM_Z = 76.7286 MHz -> optical +1.470678 MHz SRS
- 3 jumps at 76.8894
Canon 60D, Sigma f/2.8 105mm macro + XX mm extension tube, ISO-1000, 8 s exposure
Secular frequencies measured with tickler (on one outer electrode)
Here -6 VDC is applied to both outer electrodes in order to get an axial/radial ratio of ~2.005.
The common mode lowers the radial frequency and raises the axial frequency
Radial splitting ~43 kHz.
Without common-mode voltage on the outer electrodes the axial/radial ratio is ~1.54.
Radial splitting ~37 kHz.