single-ion quantum lock-in amplifier shlomi kotler nitzan akerman yinnon glickman anna kesselman...
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Single-ion Quantum Lock-in Amplifier
Shlomi KotlerNitzan AkermanYinnon GlickmanAnna Kesselman
Roee Ozeri
The Weizmann Institute of Science
FRISNO2011
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.
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
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
“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)
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)
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
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
A single trapped ion
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
Probe initialization
5P1/2
5P3/2
5S1/2
2.8 MHz/G
Optical pumping
Fidelity > 0.9999
Coherent probe rotations
i i
Bloch sphere
Pulse time RF phase
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
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
17 Echo-pulses
Long Coherence time and Measurement Sensitivity
A = contrast
2.6 G3.9 G 5.4 G
Long Coherence time and Measurement Sensitivity
A=1; Standard Quantum Limit
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
Allen deviation analysis
Minimum uncertainty: 9 mHz (3 nG) after 3720 sec
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
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
Small Signal Lock-in Detection
Measured light shift: 9.7(4) Hz
Calculated: 9.9(4) Hz
Light shift Spectroscopy
5 2S1/2
4 2D5/2
674 nm
• Scan the laser frequency across the S →D transition
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/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.
Thank you
Roee
Yinnon
Anna
ShlomiNitzan
Yoni Ziv Elad
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