quantum enhanced magnetometer and squeezed state of light

Quantum enhanced magnetometer and squeezedstate of light tunable filter

Eugeniy E. Mikhailov

The College of William & Mary

October 5, 2012

Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 1 / 42

Transition from classical to quantum field

Classical analogField amplitude aField real partX1 = (a∗ + a)/2Field imaginary partX2 = i(a∗ − a)/2

E(φ) = |a|e−iφ = X1 + iX2

X2

X1

φ

Quantum approachField operator aAmplitude quadratureX1 = (a† + a)/2Phase quadratureX2 = i(a† − a)/2

E(φ) = X1 + i X2

X2

X1

φ


Squeezed quantum states zooX

2

X1

φ

Notice ∆X1∆X2 ≥ 14

Unsqueezedcoherent

X2

X1

φ

Amplitudesqueezed

X2

X1

φ

Phasesqueezed

X2

X1

φ

Vacuumsqueezed

X2

X1

θ


Squeezed quantum states zooX

2

X1

θ

Notice ∆X1∆X2 ≥ 14

Unsqueezedcoherent

X2

X1

φ

Amplitudesqueezed

X2

X1

φ

Phasesqueezed

X2

X1

φ

Vacuumsqueezed

X2

X1

θ


Self-rotation of elliptical polarization in atomic medium

SR

∆

Ω+ Ω-

A.B. Matsko et al., PRA 66, 043815 (2002): theoretically prediction of4-6 dB noise suppression

aout = ain +igL2

(a†in − ain) (1)


Simplified setup

PBSPBSRB87

LOV.Sq


Setup


Noise contrast vs detuning in hot 87Rb vacuum cell

Fg = 2→ Fe = 1,2

-2 0 2 4 6 8

10 12

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

Noi

se (

dB)

Frequency (GHz)

Noise vs detuning

Transmission PSR noise

-1 0 1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8 9 10

Noi

se (

dB)

Quadrature angle (Arb.Units)

Noise vs quadrature angle

Fg = 1→ Fe = 1,2

-1-0.5

0 0.5

1 1.5

2 2.5

3 3.5

4 4.5

6.6 6.8 7 7.2 7.4 7.6 7.8

Noi

se (

dB)

Frequency (GHz)

Noise vs detuning

Transmission PSR noise

-2-1 0 1 2 3 4 5 6 7 8

2 4 6 8 10 12

Noi

se (

dB)

Quadrature angle (Arb.Units)

Noise vs quadrature angle


Atomic low frequency squeezing source

-86

-84

-82

-80

-78

-76

-74

-72

-70

-68

0 250 500 750 1000

Nois

espectr

aldensity

(dB

m/H

z)

Noise Frequency (kHz)

(a)

(b)

-85

-80

-75

-70

-65

-60

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

(a)

(b)


Optical magnetometer based on Faraday effect87Rb D1 line

F=1

F=2

F'=1

F'=2

m=0

m'=0

m=1

m=-1

-+

Susceptibility vs B

-1

-0.5

0

0.5

1

-10 -5 0 5 10

detuning

χ′′

χ′

Polarization rotation vs B

-1

-0.5

0

0.5

1

-10 -5 0 5 10

B field

∆χ′


Optical magnetometer based on Faraday effect87Rb D1 line

F=1

F=2

F'=1

F'=2

m=0

m'=0

m=1

m=-1

-+

Susceptibility vs B

-1

-0.5

0

0.5

1

-10 -5 0 5 10

detuning

χ′′(+∆)χ′′(−∆)χ′(+∆)χ′(−∆)

Polarization rotation vs B

-1

-0.5

0

0.5

1

-10 -5 0 5 10

B field

∆χ′


Optical magnetometer and non linear Faraday effect

Naive model of rotation

-1

-0.5

0

0.5

1

-10 -5 0 5 10

B field

∆χ′

Rb Cell Rb Cell

λ/2λ/2

SMPMFIBER

GPLENSMAGNETIC

SHIELDING

LENS

PBS

BPD

SCOPE

LASER

Rb87

B

Experiment


Optical magnetometer and non linear Faraday effectNaive model of rotation

-1

-0.5

0

0.5

1

-10 -5 0 5 10

B field

∆χ′

Rb Cell Rb Cell

λ/2λ/2

SMPMFIBER

GPLENSMAGNETIC

SHIELDING

LENS

PBS

BPD

SCOPE

LASER

Rb87

B

Experiment


Magnetometer response vs atomic density

1010

1011

1012

0

0.05

0.1

0.15

0.2

0.25

Atomic density (atoms/cm3)

Slo

pe o

f ro

tation s

ignal (V

/µT

)

1010

1011

10120.75

0.8

0.85

0.9

0.95

1

Norm

aliz

ed tra

nsm

issio

n


Shot noise limit of the magnetometer

Rb Cell Rb Cell

λ/2λ/2

SMPMFIBER

GPLENSMAGNETIC

SHIELDING

LENS

PBS

BPD

SCOPE

LASER

Rb87

B

S = |Ep + Ev |2 − |Ep − Ev |2S = 4EpEv

< ∆S > ∼ Ep < ∆Ev >

Scope

Ep

Ev


Squeezed enhanced magnetometer setup

Rb Cell Rb Cell

PhR λ/2λ/2

SMPM

FIBER

GPLENS

PBS

LENS

PBS

BPD

SCOPE SQUEEZER MAGNETOMETER

LENS

y

x

zk

Laser

Field

Sq.

Vac

yx

zk

y

x Laser

Field

Sq.

Vac

(a)

(b)

Note: Squeezed enhanced magnetometer was first demonstrated byWolfgramm et. al Phys. Rev. Lett, 105, 053601, 2010.


Magnetometer noise floor improvements

-86

-84

-82

-80

-78

-76

-74

-72

-70

-68

0 250 500 750 1000

Nois

espectr

aldensity

(dB

m/H

z)

Noise Frequency (kHz)

(a)

(b)

-85

-80

-75

-70

-65

-60

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

(a)

(b)


Magnetometer noise spectra


Noise suppression and response vs atomic density

Noise suppression

1010

1011

1012

−6

−4

−2

0

2


Nois

e s

uppre

ssio

n (

dB

)

5 kHz

100 kHz

500 kHz

1 MHz

Response

1010

1011

1012

0

0.05

0.1

0.15

0.2

0.25


Slo

pe

of

rota

tio

n s

ign

al (V

/µT

)

1010

1011

10120.75

0.8

0.85

0.9

0.95

1

No

rma

lize

d tra

nsm

issio

n


Magnetometer with squeezing enhancement

Rb Cell Rb Cell

λ/4 λ/2λ/2

SMPMFIBER

GPLENS

PBS

MAGNETIC

SHIELDING

MAGNETIC

SHIELDING

LENS

PBS

BPD

SCOPE SQUEEZER MAGNETOMETER

LASER

Rb87Rb87

1

10

100

1010 1011 1012

Sensitiv

ity

pT

/√H

z


(a)

(b)

coherent probesqueezed probe


Light group velocity expression

Group velocity vg = cω ∂n

∂ω

Susceptibility

-1

-0.5

0

0.5

1

-10 -5 0 5 10

detuning

χ′′

χ′ Rotation vs B field


Light group velocity expression


∂ω

Susceptibility

-1

-0.5

0

0.5

1

-10 -5 0 5 10

detuning

χ′′

χ′

Rotation vs B field

-1

-0.5

0

0.5

1

-10 -5 0 5 10

B field

∆χ′


Light group velocity estimate


∂ω

Delay τ = Lvg∼ ∂n

∂ω ∼ ∂R∂B


Squeezing vs magnetic field

Spectrum analyzer settings: Central frequency = 1 MHz, VBW =3 MHz, RBW = 100 kHz

Rb Cell Rb Cell

λ/2λ/2

SMPMFIBER

GPLENSMAGNETIC

SHIELDING

LENS

PBS

BPD

SCOPE

LASER

Rb87

B

0 0.2 0.4 0.6 0.8 1 1.2−5

0

5

10

15

Magnetic field (G)

No

ise

po

we

r (d

B)

0 0.05 0.1

−2.5

−2

−1.5

−1

−0.5

0

(b) squeezed

(a) antisqueezed


Squeezing vs magnetic fieldSpectrum analyzer settings: Central frequency = 1 MHz, VBW =3 MHz, RBW = 100 kHz

0

0.1

B−

fie

ld(G

)

−100 0 100

−2

−1

0

No

ise

(dB

)

0

0.1

B−

fie

ld(G

)

−100 0 100

−2

−1

0

No

ise

(dB

)

0

0.1

B−

fie

ld(G

)

−200 0 200

−2

−1

0

time (µs)

No

ise

(dB

)

−1 −0.5 0 0.5 1

−1 −0.5 0 0.5 1

−1 −0.5 0 0.5 1time (ms)

(d)

(e)

(f)

(a)

(b)

(c)

SNL

SNL

SNL

0 0.2 0.4 0.6 0.8 1 1.2−5

0

5

10

15

Magnetic field (G)

No

ise

po

we

r (d

B)

0 0.05 0.1

−2.5

−2

−1.5

−1

−0.5

0

(b) squeezed

(a) antisqueezed


Time advancement setup


Squeezing modulation and time advancement


Squeezing after advancement cell


Advancement vs power


Quantum limited interferometers revisited

Vacuum input

laser

Squeezed input

laser


Limiting noise - Quantum Optical noise

Next generation of LIGO will bequantum optical noise limited at almost all detection frequencies.

shot noiseUncertainty in number ofphotons

h ∼√

1P

(2)

radiation pressure noisePhotons impart momentum tomirrors

h ∼√

PM2f 4 (3)

There is no optimal light power to suit all detection frequency.Optimal power depends on desired detection frequency.


Interferometer sensitivity improvement with squeezing

Projected advanced LIGO sensitivity

F. Ya. Khalili Phys. Rev. D 81, 122002 (2010)Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 29 / 42

EIT filter

0

0.2

0.4

0.6

0.8

1

-100 -50 0 50 100

Tra

nspa

renc

y [A

rb. U

nit]

Probe detuning [Arb. Unit]

Probe transparency dependence on its detuning.

|b〉

|c〉

ωbc

|a〉

ωp


EIT filter

0

0.2

0.4

0.6

0.8

1

-100 -50 0 50 100

Tra

nspa

renc

y [A

rb. U

nit]



|b〉

|c〉

ωbc

ωd

|a〉

ωp

0

0.2

0.4

0.6

0.8

1

-100 -50 0 50 100

Tra

nspa

renc

y [A

rb. U

nit]




Squeezing and EIT filter

(V out

1V out

2

)=

(A2+ A2

−A2− A2

+

)(V in

1V in

2

)+[1−

(A2+ + A2

−

)]( 11

)

ϕ± =12

(Θ+ ±Θ−)

A± =12

(T+ ± T−)

|b〉

|c〉

ωbc

ωd

|a〉

ωp


Squeezing and EIT filter setup


EIT filter and measurements without light

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Tra

nsm

issio

n (

Arb

. U

nits)

Noise Frequency (MHz)

Coherent signal

|b〉

|c〉

ωbc

ωd

|a〉

ωp

Signal in the noise quadratures

-4

-2

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2

No

ise

po

we

r (d

Bm

)


-4

-2

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2

No

ise

po

we

r (d

Bm

)



Squeezing angle rotationX

2

X1

θ

X2

X1

θ

(V out

1V out

2

)=

(cos2 ϕ+ sin2 ϕ+

sin2 ϕ+ cos2 ϕ+

)(A2+ A2

−A2− A2

+

)(V in

1V in

2

)+[1−

(A2+ + A2

−

)]( 11

)Locked at 300kHz Locked at 1200kHz


Narrower filter

T=35C, no controltransmission 42%

0 0.2 0.4 0.6 0.8 1−2

0

2

4

6

8

10Noise vs frequency through atoms: control off (35 degrees)

Frequency (MHz)

Noi

se(d

B)

output

Input


0 0.2 0.4 0.6 0.8 1−2

0

2

4

6

8

10

Frequency (MHz)

Noi

se(d

B)

Noise vs frequency through atoms: control off (40 degrees)

Input

output


Narrower filter


0 0.2 0.4 0.6 0.8 1−2

0

2

4

6

8

10

Noise frequency (MHz)

Noi

se (

dB)

Noise vs frequency through EIT (35 degrees)

Input

output


0 0.2 0.4 0.6 0.8 1−2

0

2

4

6

8

10

Frequency (MHz)

Noi

se (

dB)

Noise vs frequency through EIT (40 degrees)

Input

output


Excess noise and leakage

0 0.5 1 1.5 2−2

0

2

4

6

8

10

12

14

16

Effect of leakage photons

MHz

dB

Shot noiseOutput noise, 1 mV leakageOutput noise, 20 mV leakage


Theoretical prediction for MOT squeezing with 87Rb

Fg = 2→ Fe = 1,2 high optical density is very important

-1000 -500 0 500 1000 1500

-8

-4

0

4

8

12

16

20

24

-1000 -500 0 500 1000 1500

-8

-4

0

4

8

12

16

20

24

-1000 -500 0 500 1000 1500

-8

-4

0

4

8

12

16

20

24

-1000 -500 0 500 1000 1500

-8

-4

0

4

8

12

16

20

24

Laser detuning (MHz)

γ = 10-4 Γ

F=2 to F'=2F=2 to F'=1

87Rb D1Rabi = 30 Γ

squeezing antisqueezing

γ = 10-2 Γ

F=2 to F'=2F=2 to F'=1

Optical density: 100 500 900 1300 1700

γ = 10-1 Γ

F=2 to F'=2F=2 to F'=1

Nor

mal

ized

noi

se p

ower

(dB

)

γ = 10-3 Γ

F=2 to F'=2F=2 to F'=1


MOT squeezer

Cloud size =1 mm, T = 200 µK, N = 7× 109 1/cm3,OD = 2, beam size = 0.1 mm, 105 interacting atoms

PBSPBS

V.Sq LO


Noise contrast in MOT with 87Rb Fg = 2→ Fe = 1

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9N

ois

e (

dB

)

Quadrature angle (Arb. Units)

(a)

(b)


Squeezing in MOT with 87Rb Fg = 2→ Fe = 1

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12N

ois

e (

dB

)

Quadrature angle (Arb. Units)

(a)

(b)


People

Travis Horrom and Gleb Romanov

Irina Novikova

Robinjeet Singh, LSU

Jonathan P. Dowling, LSU


Summary

We demonstrate fully atomic squeezed enhanced magnetometerMagnetometer noise floor lowered in the range from several kHzto several MHzDemonstrated sensitivity as low as 1 pT/

√Hz in our particular

setupFirst demonstration of superluminal squeezing propagation withvg = c/2000 or time advancement of 0.5 µS

For more details:T. Horrom, et al. “Quantum Enhanced Magnetometer with LowFrequency Squeezing”, PRA, 86, 023803, (2012).T. Horrom, et al. “All-atomic generation and noise-quadraturefiltering of squeezed vacuum in hot Rb vapor”, arXiv:1204.3967.

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quantum enhanced magnetometer and squeezed state of light

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