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Single-ion Quantum Lock-in Amplifier

Shlomi Kotler Nitzan Akerman Yinnon Glickman Anna Kesselman Roee Ozeri. The Weizmann Institute of Science. FRISNO2011. Single-ion Quantum Lock-in Amplifier. Information is Physical. Information getters Measurement probe Couples to its environment. Information carriers

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Single-ion Quantum Lock-in Amplifier

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

  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, 253003 (2010)

  6. Quantum two-level probe |­ñ w L -w 0 = d(B) The Bloch sphere Z w 0 = w0(B) 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 Bloch sphere 2nd Ramsey pulse 1st Ramsey pulse |­ñ q = p/2 q = p/2 j = 0 j = 0→p |­ñ -|¯ñ T f |­ñ + i |¯ñ |­ñ - i |¯ñ f |­ñ +|¯ñ |¯ñ • Noise reduces fringe contrast • Repeat the experiment many times • Reduced contrast = more experiments

  8. N Echo-pulses 1st Ramsey pulse q = p/2 f = 0 q = p f = 0 q = p/2 f = 0,p q = p f = 0 q = p f = 0 2nd Ramsey pulse techo 2techo Quantum Lock-in T S. Kotler et. al. arXiv:1101.4885[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 5P3/2 Optical pumping 5P1/2 Fidelity > 0.9999 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 Fidelity = 0.9989 dark bright 2P3/2 2P1/2 Detection 1092nm 2D5/2 g = 0.4 Hz 2D3/2 422nm 674nm Shelving  2.8 MHz/G  2S1/2

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

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

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

  17. N Echo-pulses 1st Ramsey pulse q = p/2 f = 0 q = p f = 0 q = p/2 f = 0,p q = p f = p/2 q = p f = p/2 2nd Ramsey pulse Fast Lock-in Modulation Modulation at 312.5 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 3720sec

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

  20. Echo pulses 1st Ramsey pulse q = p/2 f = 0 q = p f = 0 q = p/2 f = 0,p q = p f = p/2 q = p f = p/2 2nd Ramsey pulse Light shift Detection 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. 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:1101.4885[quant-ph] (2011); accepted in Nature.

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

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