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