1. Single-ion Quantum Lock-in Amplifier
FRISNO2011
Single-ion Quantum Lock-in Amplifier
Shlomi Kotler
Nitzan Akerman
Yinnon Glickman
Anna Kesselman
Roee Ozeri
The Weizmann Institute of Science

2. Information is Physical
Information getters
Measurement probe
Couples to its environment
Information carriers
Physical memory
transmission channels
Weak coupling to the environment
measurement
coherence
Noise as a common enemy.

3. Radio transmission
Transfer an audio-frequency electro-magnetic signal, f(t), over a noisy medium.
AM: modulate f(t) with a frequency wm , outside the noise bandwidth:
At the receiver, mix the recieved signal with
and low-pass filter
Recover at base-band frequencies the signal

4. Lock-in amplifier and measurement
Invented in the 50’s by Princeton physicist, Robert Dicke
Want to measure a (noisy) physical quantity Y
Modulate Y at a frequency wm outside the noise bandwidth:
Electronically mix the detected Y signal with:
and low-pass filter

5. “Quantum Radio”: Dynamic de-coupling
Protect coherence in a quantum system (e.g. qubit) which is subject to a noisy environment or coupled to a non-Markovian bath
Engineer a time dependent system Hamiltonian: H(t)
Decoherence rate is proportional to the spectral overlap of the system time evolution with the noise/bath spectrum.
Gordon, Erez and Kurizki, J. of Phys. B, 40, S75 (2007)
Sagi, Almog and Davidson, Phys. Rev. Lett., 104, (2010)

6. Quantum two-level probe
|­ñ
w 0 = w0(B)
w L -w 0 = d(B)
The Bloch sphere Z X
|¯ñ Y
|Z+ñ = |­ñ
|Z-ñ = |¯ñ
|X-ñ = (|­ñ + |¯ñ) /Ö2
|X-ñ = (|­ñ - |¯ñ)/Ö2
|Y+ñ = (|­ñ + i |¯ñ)/Ö2
|Y-ñ = (|­ñ - i |¯ñ)/Ö2

7. Quantum phase estimation
q = p/2
j = 0
1st Ramsey pulse
2nd Ramsey pulse
Bloch sphere
q = p/2
|­ñ
j = 0→p
|­ñ - |¯ñ f T
|­ñ + i |¯ñ
|­ñ - i |¯ñ
|­ñ + |¯ñ f
|¯ñ
Noise reduces fringe contrast
Repeat the experiment many times
Reduced contrast = more experiments

8. Quantum Lock-in T q = p f = 0 2techo techo N Echo-pulses q = p/2 f = 0
f = 0,p
1st Ramsey pulse
2nd Ramsey pulse T
S. Kotler et. al. arXiv: [quant-ph] (2011); accepted in Nature
J. R. Mae et. al. Nature, 455, 644, (2008)

9. A single trapped ion

10. Electronic levels in 88Sr+
5 2P3/2
Fine structure
5 2P
1033 nm
5 2P1/2
4 2D5/2
1092 nm
4 2D
408 nm
4 2D3/2
422 nm
674 nm
5 2S1/2
Turn on small B field
2.8 MHz/G

11. Probe initialization Optical pumping Fidelity > 0.9999 5S1/2 s+

5S1/2
2.8 MHz/G


12. Coherent probe rotations
Pulse time
RF phase
Bloch sphere
|­ñ
|­ñ - |¯ñ
|­ñ + i |¯ñ
|­ñ - i |¯ñ
|­ñ + |¯ñ
|¯ñ

13. Qubit Detection 2S1/2 Fidelity = 0.9989 Detection Shelving  
2P3/2
dark
bright
2P1/2
Detection
1092nm
2D5/2
g = 0.4 Hz
2D3/2
422nm
674nm
Shelving


2.8 MHz/G
2S1/2

14. Echo Pulse Train q = p f = 0 2techo techo N Echo-pulses q = p/2 f = 0
f = 0,p
1st Ramsey pulse
2nd Ramsey pulse

15. Long Coherence time and Measurement Sensitivity
17 Echo-pulses
2.6 mG
3.9 mG
5.4 mG
A = contrast

16. Long Coherence time and Measurement Sensitivity
A=1; Standard Quantum Limit

17. Fast Lock-in Modulation
q = p
f = p/2
f = 0
N Echo-pulses
q = p/2
f = 0
f = 0,p
1st Ramsey pulse
2nd Ramsey pulse
Modulation at Hz
Sensitivity= 0.4 Hz/Hz1/2 =0.15 mG/Hz1/2
Coherence time = 1.4 Sec

18. Allen deviation analysis
Minimum uncertainty: 9 mHz (3 nG) after 3720 sec

19. Magnetometer Performance
1/(resolution)3/2

20. Light shift Detection 5 2S1/2   Echo pulses q = p/2 f = 0
f = 0,p
1st Ramsey pulse
2nd Ramsey pulse
q = p
f = p/2
f = 0
Off-resonance 674 nm beam
(Line-width ≤ 80 Hz)
4 2D5/2
17 kHz
674 nm


5 2S1/2

21. Small Signal Lock-in Detection
Measured light shift: 9.7(4) Hz
Calculated: 9.9(4) Hz

22. Light shift Spectroscopy
4 2D5/2
Scan the laser frequency across the S →D transition
674 nm


5 2S1/2

23. Light shift Spectroscopy

24. With a single trapped ion coupled to a magnetically noisy environment:
Summary
Quantum Lock-in amplifier: Dynamic coupling/de-coupling can improve on measurement SNR
With a single trapped ion coupled to a magnetically noisy environment:
A long coherence time: 1.4 sec.
Frequency shift measurement sensitivity : 0.4 Hz/Hz1/2 (15 pT/Hz1/2)
Frequency shift measurement uncertainty: 9 mHz (300 fT) after 1 hour integration time
Applications: magnetometery; direct magnetic spin-spin coupling
Applications: Precision measurements; frequency metrology.
S. Kotler et. al. arXiv: [quant-ph] (2011); accepted in Nature.

25. Yinnon
Roee
Shlomi
Nitzan
Anna
Thank you
Yoni
Ziv
Elad