FRISNO 2011 Singleion Quantum Lockin Amplifier The Weizmann
- Slides: 25
FRISNO 2011 Single-ion Quantum Lock-in Amplifier The Weizmann Institute of Science Shlomi Kotler Nitzan Akerman Yinnon Glickman Anna Kesselman Roee Ozeri
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.
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
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
“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, S 75 (2007) Sagi, Almog and Davidson, Phys. Rev. Lett. , 104, 253003 (2010)
Quantum two-level probe w L -w 0 = d(B) The Bloch sphere Z w 0 = w 0(B) X Y Z+ = Z- = X- = ( + ) /Ö 2 X- = ( - )/Ö 2 Y+ = ( +i )/Ö 2 Y- = ( -i )/Ö 2
Quantum phase estimation 1 st Ramsey pulse Bloch sphere 2 nd Ramsey pulse q = p/2 j=0 j = 0→p T f - +i -i + f • Noise reduces fringe contrast • Repeat the experiment many times • Reduced contrast = more experiments
Quantum Lock-in N Echo-pulses 1 st Ramsey pulse q = p/2 f=0 2 nd Ramsey pulse q=p f=0 techo 2 techo q=p f=0 T S. Kotler et. al. ar. Xiv: 1101. 4885[quant-ph] (2011); accepted in Nature J. R. Mae et. al. Nature, 455, 644, (2008) q = p/2 f = 0, p
A single trapped ion
Electronic levels in 88 Sr+ 5 2 P 3/2 Fine structure 5 2 P 1033 nm 5 2 P 1/2 1092 nm 4 2 D 5/2 4 2 D 408 nm 4 2 D 3/2 422 nm 674 nm 5 2 S 1/2 Turn on small B field 2. 8 MHz/G
Probe initialization 5 P 3/2 5 P Optical pumping 1/2 Fidelity > 0. 9999 s+ 2. 8 MHz/G 5 S 1/2
Coherent probe rotations Pulse time RF phase Bloch sphere - +i -i +
Qubit Detection Fidelity = 0. 9989 2 P 2 P dark 3/2 bright 1/2 Detection 1092 nm 422 nm 2 D 5/2 2 D 3/2 g = 0. 4 Hz 674 nm 2 S 1/2 2. 8 MHz/G Shelving
Echo Pulse Train N Echo-pulses 1 st Ramsey pulse q = p/2 f=0 2 nd Ramsey pulse q=p f=0 techo 2 techo q=p f=0 q = p/2 f = 0, p
Long Coherence time and Measurement Sensitivity 2. 6 m. G 17 Echo-pulses 3. 9 m. G 5. 4 m. G A = contrast
Long Coherence time and Measurement Sensitivity A=1; Standard Quantum Limit
Fast Lock-in Modulation N Echo-pulses 1 st Ramsey pulse q = p/2 f=0 2 nd Ramsey pulse q=p f = p/2 q=p f=0 Modulation at 312. 5 Hz 1/2 =0. 15 Sensitivity= Coherence 0. 4 Hz/Hztime = 1. 4 m. G/Hz Sec 1/2 q=p f = p/2 q = p/2 f = 0, p
Allen deviation analysis Minimum uncertainty: 9 m. Hz (3 n. G) after 3720 sec
Magnetometer Performance 1/(resolution)3/2
Light shift Detection Echo pulses 1 st Ramsey pulse q = p/2 f=0 2 nd Ramsey pulse q=p f=0 q=p f = p/2 q = p/2 f = 0, p Off-resonance 674 nm beam (Line-width ≤ 80 Hz) 4 2 D 5/2 17 k. Hz 674 nm 5 2 S 1/2
Small Signal Lock-in Detection Measured light shift: 9. 7(4) Hz Calculated: 9. 9(4) Hz
Light shift Spectroscopy 4 2 D 5/2 • Scan the laser frequency across the S →D transition 674 nm 5 2 S 1/2
Light shift Spectroscopy
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/Hz 1/2 (15 p. T/Hz 1/2) • Frequency shift measurement uncertainty: 9 m. Hz (300 f. T) after 1 hour integration time • Applications: magnetometery; direct magnetic spin-spin coupling • Applications: Precision measurements; frequency metrology. S. Kotler et. al. ar. Xiv: 1101. 4885[quant-ph] (2011); accepted in Nature.
Yinnon Roee Shlomi Anna Yoni Ziv Elad Thank you Nitzan
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