single-ion quantum lock-in amplifier shlomi kotler nitzan akerman yinnon glickman anna kesselman...
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![Page 1: Single-ion Quantum Lock-in Amplifier Shlomi Kotler Nitzan Akerman Yinnon Glickman Anna Kesselman Roee Ozeri The Weizmann Institute of Science FRISNO2011](https://reader035.vdocuments.mx/reader035/viewer/2022062518/56649d4e5503460f94a2cfe8/html5/thumbnails/1.jpg)
Single-ion Quantum Lock-in Amplifier
Shlomi KotlerNitzan AkermanYinnon GlickmanAnna Kesselman
Roee Ozeri
The Weizmann Institute of Science
FRISNO2011
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measurement
coherence
Information carriers• Physical memory• transmission channels• Weak coupling to the environment
Information getters• Measurement probe• Couples to its environment
Information is Physical
Noise as a common enemy.
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Radio transmission
• Transfer an audio-frequency electro-magnetic signal, f(t), over a noisy medium.• AM: modulate f(t) with a frequency m , outside the noise bandwidth:
• At the receiver, mix the recieved signal with and low-pass filter
• Recover at base-band frequencies the signal
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Lock-in amplifier and measurement
• Modulate Y at a frequency m outside the noise bandwidth:
• Invented in the 50’s by Princeton physicist, Robert Dicke
• Electronically mix the detected Y signal with:and low-pass filter
• Want to measure a (noisy) physical quantity Y
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“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.
Sagi, Almog and Davidson, Phys. Rev. Lett., 104, 253003 (2010)Gordon, Erez and Kurizki, J. of Phys. B, 40, S75 (2007)
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Y = (i 2Y = (i 2
X = ( 2X = ( 2
ZZ =
Z
Y
X
The Bloch sphere
Quantum two-level probe
0 = 0(B)
L 0 = (B)
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1st Ramsey pulse 2nd Ramsey pulse
Quantum phase estimation
T
i i
Bloch sphere
→
0 1 2 3 4 5 60.0
0.2
0.4
0.6
0.8
1.0
P
phase
• Noise reduces fringe contrast• Repeat the experiment many times• Reduced contrast = more experiments
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1st Ramsey pulse 2nd Ramsey pulse
echoecho
N Echo-pulses
Quantum Lock-in
T
J. R. Mae et. al. Nature, 455, 644, (2008)
S. Kotler et. al. arXiv:1101.4885[quant-ph] (2011); accepted in Nature
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A single trapped ion
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Electronic levels in 88Sr+
5 2P1/2
5 2P3/2
5 2S1/2
5 2P Fine structure
Turn on small B field2.8 MHz/G
4 2D3/2
4 2D5/2
4 2D
422 nm
408 nm
1092 nm
1033 nm
674 nm
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Probe initialization
5P1/2
5P3/2
5S1/2
2.8 MHz/G
Optical pumping
Fidelity > 0.9999
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Coherent probe rotations
i i
Bloch sphere
Pulse time RF phase
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Qubit Detection
0 10 20 30 40 500
50
100
150
200
250
2P1/2
2P3/2
2S1/2
Detection
422nm
2D5/2
674nm Shelving
2D3/2
0 10 20 30 40 500
50
100
150
200
250
= 0.4 Hz
dark bright
1092nm
2.8 MHz/G
Fidelity = 0.9989
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0 1 2 3 4 5 6 7 8 9 10 11 12
-20
0
20
40
60
80
100
Pha
se c
ontr
ast
%
arm (ms)
1
0 1 2 3 4 5 6 7 8 9 10 11 12
-20
0
20
40
60
80
100
Pha
se c
ontr
ast
%
arm (ms)
1
5
0 1 2 3 4 5 6 7 8 9 10 11 12
-20
0
20
40
60
80
100
Pha
se c
ontr
ast
%
arm (ms)
1
5
9
0 1 2 3 4 5 6 7 8 9 10 11 12
-20
0
20
40
60
80
100
Pha
se c
ontr
ast
%
arm (ms)
1
5
9
13
1st Ramsey pulse 2nd Ramsey pulse
echoecho
N Echo-pulses
0 1 2 3 4 5 6 7 8 9 10 11 12
-20
0
20
40
60
80
100
Pha
se c
ontr
ast
%
arm (ms)
1
5
9
13
17
Echo Pulse Train
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17 Echo-pulses
Long Coherence time and Measurement Sensitivity
A = contrast
2.6 G3.9 G 5.4 G
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Long Coherence time and Measurement Sensitivity
A=1; Standard Quantum Limit
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Coherence time = 1.4 Sec
Fast Lock-in Modulation
Modulation at 312.5 Hz
1st Ramsey pulse 2nd Ramsey pulse
N Echo-pulses
Sensitivity= 0.4 Hz/Hz1/2 =0.15 G/Hz1/2
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Allen deviation analysis
Minimum uncertainty: 9 mHz (3 nG) after 3720 sec
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100
101
102
103
104
105
106
10710
-2
100
102
104
106
108
1010
1012
Resolution (nm)
Se
nsi
tivity
(fT
/Hz1
/2)
NV DiamondHarvard 2008
Single ionWeizmann 2010
BECBerkeley 2006
CommercialSQUID's
SERFPrinceton 2003
SQUID
Magnetometer Performance
100
101
102
103
104
105
106
10710
-2
100
102
104
106
108
1010
1012
Resolution (nm)
Se
nsi
tivity
(fT
/Hz1
/2)
NV DiamondHarvard 2008
Single ionWeizmann 2010
BECBerkeley 2006
CommercialSQUID's
SERFPrinceton 2003
SQUID
1/(resolution)3/2
100
101
102
103
104
105
106
10710
-2
100
102
104
106
108
1010
1012
Resolution (nm)
Se
nsi
tivity
(fT
/Hz1
/2)
NV DiamondHarvard 2008
Single ionWeizmann 2010
BECBerkeley 2006
CommercialSQUID's
SERFPrinceton 2003
SQUID
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Light shift Detection
1st Ramsey pulse 2nd Ramsey pulse
Echo pulses
Off-resonance 674 nm beam(Line-width ≤ 80 Hz)
5 2S1/2
4 2D5/217 kHz
674 nm
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Small Signal Lock-in Detection
Measured light shift: 9.7(4) Hz
Calculated: 9.9(4) Hz
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Light shift Spectroscopy
5 2S1/2
4 2D5/2
674 nm
• Scan the laser frequency across the S →D transition
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Light shift Spectroscopy
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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.
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Thank you
Roee
Yinnon
Anna
ShlomiNitzan
Yoni Ziv Elad