quantum enhanced magnetometer and squeezed state of light
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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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 3 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 4 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 4 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 4 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 4 / 42
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)
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 5 / 42
Simplified setup
PBSPBSRB87
LOV.Sq
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 7 / 42
Setup
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 8 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 9 / 42
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)
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 10 / 42
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′
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 11 / 42
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′
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 11 / 42
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′
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 11 / 42
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′
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 11 / 42
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′
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 11 / 42
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′
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 11 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 12 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 12 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 13 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 14 / 42
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.
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 15 / 42
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)
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 16 / 42
Magnetometer noise spectra
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 17 / 42
Noise suppression and response vs atomic density
Noise suppression
1010
1011
1012
−6
−4
−2
0
2
Atomic density (atoms/cm3)
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
Atomic density (atoms/cm3)
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 18 / 42
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
Atomic density (atoms/cm3)
(a)
(b)
coherent probesqueezed probe
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 19 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 20 / 42
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
-1
-0.5
0
0.5
1
-10 -5 0 5 10
B field
∆χ′
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 20 / 42
Light group velocity estimate
Group velocity vg = cω ∂n
∂ω
Delay τ = Lvg∼ ∂n
∂ω ∼ ∂R∂B
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 21 / 42
Light group velocity estimate
Group velocity vg = cω ∂n
∂ω
Delay τ = Lvg∼ ∂n
∂ω ∼ ∂R∂B
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 21 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 22 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 22 / 42
Time advancement setup
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 23 / 42
Squeezing modulation and time advancement
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 24 / 42
Squeezing after advancement cell
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 25 / 42
Advancement vs power
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 26 / 42
Advancement vs power
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 26 / 42
Quantum limited interferometers revisited
Vacuum input
laser
Squeezed input
laser
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 27 / 42
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.
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 28 / 42
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.
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 28 / 42
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.
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 28 / 42
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.
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 28 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 30 / 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
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]
Probe detuning [Arb. Unit]
Probe transparency dependence on its detuning.
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 30 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 31 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 31 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 31 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 31 / 42
Squeezing and EIT filter setup
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 32 / 42
Squeezing and EIT filter setup
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 32 / 42
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
)
Noise Frequency (MHz)
-4
-2
0
2
4
6
8
10
12
14
0 0.5 1 1.5 2
No
ise
po
we
r (d
Bm
)
Noise Frequency (MHz)
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 33 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 34 / 42
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
T=40C, no controltransmission 17%
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 35 / 42
Narrower filter
T=35C, no controltransmission 42%
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
T=40C, no controltransmission 17%
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 35 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 36 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 37 / 42
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
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 38 / 42
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)
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 39 / 42
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)
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 40 / 42
People
Travis Horrom and Gleb Romanov
Irina Novikova
Robinjeet Singh, LSU
Jonathan P. Dowling, LSU
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 41 / 42
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.
Support from
Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 2012 42 / 42
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