1. A Predictive Correction Technique in a
Yb+
Trapped Ion Frequency Standard
J. Sastrawan, A. Soare, M.C. Jarratt, C. Jones
S. Dona, N. Nand, M.J. Biercuk
Quantum Control Laboratory
University of Sydney

2. Outline
Frequency standards and their performance limitations
Software technique: predictive correction
Experimental platform: trapped Yb+ ions
Stability improvements with predictive correction
Figure : Fluorescence of neutral Yb in a linear Paul trap

3. Introduction to frequency standards
Frequency standards are essential for timekeeping, space-based
applications, global positioning, geodesy and tests of fundamental
physics
Figure : NIST-F1, the atomic fountain clock that maintains US time.
NIST: Time and Frequency Division. http://tf.nist.gov/general/museum/nist-f1.jpg

4. Passive frequency standards: closed-loop feedback
Local
Oscillator
Reference
(extremely stable)
Signal
Processor
Δf MeasurementCorrection
f0
Interrogation
Project’s aim: to devise a software technique for predicting noise
trajectories for improved frequency stability

5. Our technique: linear predictive correction
In all feedback control, we seek to reduce frequency variance
1
0
g(t)
-50
0
50
y(t)(a.u.) 543210
Measurement number
1
0
g(t)
t (a.u.)
C
(n)
k
C
(n)
k+1
Tc
TR TD
ts
1 ts
2 ts
3 ts
4 ts
5 te
5te
4te
3te
2te
1
C
(n)
k+2
y
(LO)
k y
(LLO)
k
y(LO)
(t) y(LLO)
(t)
Feedback
Hybrid Feedforward
(a)
(b)
(c)
Predictive scheme exploits non-Markovian character of LO noise
Cov(Mi , Mj ) =
∞
0
S(ω)G2
(ω)dω (1)

6. Experimental platform: trapped ions
Engineered noise with tailored power spectrum applied to VSG

7. Experimental verification of predictive control
0.40
0.35
0.30
0.25
0.20
SampleVariance(Hz
2
)
10008006004002000
Number of Samples
Traditional
Predictive
10
0
10
1
10
2
10
3
10
4
PowerSpectralDensity(a.u.)
2 4 6 8
0.1
2 4 6 8
1
2 4 6 8
10
Frequency (Hz)
Non-Markovian
LO Noise
Average stability improvement ≈ 10% @ 1000 measurements

8. Next steps
Scope out parameter space of LO noise and measurement
Analyse real clock data to calculate potential benefits
Develop an adaptive implementation to combat intrinsic noise
Reconstruct time-domain noise traces using prediction

9. References
Sastrawan, J. et al. arXiv: 1407.3902
Hinkley, N. et al. Science, 341, 1215-1218 (2013)
Hartnett, J.G. et al. Appl. Phys. Lett., 100, 183501 (2012)
Cacciapuoti, L. and Salomon, C. J. Phys, 327, 012049 (2011)
Jiang, Y.Y. et al. Nat. Photon., 5, 158-161 (2011)
Rutman, J. Proceedings of the IEEE, 66, 9 (1978).
Soare, A. et al. Physical Review A, 89, 042329 (2014)
With thanks to H. Ball, K. Pyka, T. McRae and T.J. Green