Active optical gyroscope with controllabledispersion.
Eugeniy E. Mikhailov, Owen Wolfe, Irina Novikova1,Simon Rochester, Dmitry Budker2,
1
2
LPHYS, 14 July 2016
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 1 / 17
Sagnac effect and cavity response
Ω
beamsplitter
input
detector
output
E cw
E ccw
∆p = ±ΩRt = ±2AΩc
∆f = f0∆pp
1ng
= ∆fempty1ng
Group index
ng(f ) = n + f0∂n∂f
vg = c/ng
Cavity response enhanced if ng < 1 i.e. under the fast light conditionShahriar et al., PRA 75, 053807 (2007)
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 2 / 17
Sagnac effect and cavity response
Ω
beamsplitter
input
detector
output
E cw
E ccw
∆p = ±ΩRt = ±2AΩc
∆f = f0∆pp
1ng
= ∆fempty1ng
Group index
ng(f ) = n + f0∂n∂f
vg = c/ng
Cavity response enhanced if ng < 1 i.e. under the fast light conditionShahriar et al., PRA 75, 053807 (2007)
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 2 / 17
EIT - slow light
| 2 〉
| 1 〉
| 3 〉
δ
∆ HFS
| 4 〉
Ω 1Ω 2
∆ 1
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 3 / 17
N-bar with four-wave mixing - fast and with gain
| 2 〉
| 1 〉
| 3 〉
δ
∆ HFS
| 4 〉
Ω 1Ω 2
∆ 1Ω 3
∆ 3
γ 42
γ 41
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 5 / 17
N-bar with Doppler averaging
Refractive index Absorption
Stationary atoms
Room temperatureDoppler averaged
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 6 / 17
N-bar levels and fields diagram
Artificial atom 87Rb atom
F=2
F=1
F’=2
F’=1
m=1m=0m=-1m=-2 m=2
F’=2
F’=1
F’=3
F’=0
5P
5P
5S
3/2
1/2
1/2
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 7 / 17
The first gyro setup and its performance
Finesse = 20
→ Pulling 1/200
D1 tuned around Fg = 1→ Fe = 1,2
E. Mikhailov, et al. Optical Engineering, Issue 10, 53, 102709, (2014)
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 8 / 17
The first gyro setup and its performance
P.F . =∆fdispersive
∆fempty=
1ng
∆fempty = f0∆pp
Finesse = 20 → Pulling 1/200
E. Mikhailov, et al. Optical Engineering, Issue 10, 53, 102709, (2014)Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 8 / 17
Gyro lasing: theory vs. experiment
|2〉
|1〉
|3〉
δ
∆HFS
|4〉
Ω 1Ω 2
δ1Ω 3
δ 3Ω 4
δ 2 P
δ 4
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 9 / 17
Gyro pulling and amplitude vs. gyro cavity detuning
Cavity detuning span 150 MHz. Pulling ×100
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 10 / 17
Pulling factor with increased cavity finesse (20→ 70)
|2〉
|1〉
|3〉
δ
∆HFS
|4〉
Ω 1Ω 2
δ1Ω 3
δ 3Ω 4
δ 2 P
δ 4
λ/2
FIBER
LENS
PBSLENS
D1 LASER
Rb Cell
MAGNETIC
SHIELDING
Rb87
PBS
D2 LASER
CAMERA
FIBERBEAMSPLITTER
SCOPE
PD
SpectrumAnalyzer
FASTPD
P.F . =∆fdispersive
∆fempty
=1ng
∆fempty = f0∆pp
−600 −400 −200 0 200−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
20150803: Pulling factor vs. D2 laser detuning
D2 laser detuning from F
g=2 −> F
e=3, MHz
Pu
llin
g f
acto
r
−600 −400 −200 0 2000
0.05
0.1
0.15
0.2
20150803: Pulling factor averaged vs. D2 laser detuning
D2 laser detuning from F
g=2 −> F
e=3, MHz
Pu
llin
g f
acto
r
−600 −400 −200 0 200−100
−90
−80
−70
−60
−50
20150803: Beat−note span vs. D2 laser detuning
D2 laser detuning from F
g=2 −> F
e=3, MHz
Fre
qu
en
cy ,
MH
z
−600 −400 −200 0 200−90
−85
−80
−75
−70
20150803: Beat−note amplitude vs. D2 laser detuning
D2 laser detuning from F
g=2 −> F
e=3, MHz
Be
at−
no
te a
mp
litu
de
, d
Bm
0 1 2 3 4−0.1
0
0.1
0.2
0.3
0.4
20150804: Pulling factor vs. D2 power
D2 power, mW
Pu
llin
g f
acto
r
0 1 2 3 4−0.1
0
0.1
0.2
0.3
0.4
20150804: Pulling factor averaged vs. D2 power
D2 power, mW
Pu
llin
g f
acto
r
0 1 2 3 4−86
−84
−82
−80
−78
−76
−74
20150804: Beat−note span vs. D2 power
D2 power, mW
Fre
qu
en
cy ,
MH
z
0 1 2 3 4−90
−85
−80
−75
−70
20150804: Beat−note amplitude vs. D2 power
D2 power, mW
Be
at−
no
te a
mp
litu
de
, d
Bm
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 11 / 17
Dependence on total pumps power
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 12 / 17
Dependence on 87Rb vapor density
Low pumps power
1.5 2 2.5 3 3.5
x 1012
0.06
0.08
0.1
0.12
0.14
0.16
Vapor Density, (Nparticles
cm−3
)
Pu
llin
g f
acto
r
20151002: Pulling factor vs. Vapor Density
1.5 2 2.5 3 3.5
x 1012
0.06
0.08
0.1
0.12
0.14
0.16
Density, 1/cm3
Pu
llin
g f
acto
r
20151002: Pulling factor averaged vs. Vapor Density
1.5 2 2.5 3 3.5
x 1012
−440
−420
−400
−380
−360
−340
Vapor Density, (Nparticles
cm−3
)
Fre
qu
en
cy ,
MH
z
20151002: Beat−note span vs. Vapor Density
1.5 2 2.5 3 3.5
x 1012
−86
−84
−82
−80
−78
−76
Vapor Density, (Nparticles
cm−3
)B
ea
t−n
ote
am
plit
ud
e,
dB
m
20151002: Beat−note amplitude vs. Vapor DensityHigh pumps power
2 4 6 8 10 120.2
0.4
0.6
0.8
1
1.220160708: Pulling factor vs. Density
Density, 1012
/cm3
Pu
llin
g f
acto
r
2 4 6 8 10 12
0.7
0.8
0.9
1
1.120160708: Pulling factor averaged vs. Density
Density, 1012
/cm3
Pu
llin
g f
acto
r
2 4 6 8 10 12660
680
700
720
740
760
78020160708: Beat−note span vs. Density
Density, 1012
/cm3
Fre
qu
en
cy ,
MH
z
2 4 6 8 10 12−68
−66
−64
−62
−6020160708: Beat−note amplitude vs. Density
Density, 1012
/cm3
Be
at−
no
te a
mp
litu
de
, d
Bm
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 13 / 17
Gyroscope laser multi-mode structure
Gyro beatnote spectrum vs. empty cavity offset
Empty cavity detuning, MHz
Beatn
ote
fre
quency, M
Hz
0 20 40 60 80 100 120 140 160
−400
−300
−200
−100
0
−100 −80 −60
−400
−350
−300
−250
−200
−150
−100
−50
0
50
dBm
Fre
quency, M
Hz
Cell temperature 110◦C, total power 350 mW.Modes pulling factors are 0.54, 0.45, 0.04.
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 14 / 17
High power regime: dependence on D2 detuning
Pumps power ≈ 6 mW Pumps power ≈ 180 mW
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 15 / 17
People
Irina Novikova, ShuangLi Du, Owen Wolfe, Demetrious Kutzke (WM),Dmitry Budker, Simon Rochester (Rochester Scientific).
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 16 / 17
Summary
0 20 40 600
10
20
30
40
50
60
Empty cavity shift, MHz
Dis
pe
rsiv
e c
avity s
hift,
MH
z
−600 −400 −200 0 200−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
20150803: Pulling factor vs. D2 laser detuning
D2 laser detuning from F
g=2 −> F
e=3, MHz
Pulli
ng facto
r
−600 −400 −200 0 2000
0.05
0.1
0.15
0.2
20150803: Pulling factor averaged vs. D2 laser detuning
D2 laser detuning from F
g=2 −> F
e=3, MHz
Pulli
ng facto
r
−600 −400 −200 0 200−100
−90
−80
−70
−60
−50
20150803: Beat−note span vs. D2 laser detuning
D2 laser detuning from F
g=2 −> F
e=3, MHz
Fre
quency , M
Hz
−600 −400 −200 0 200−90
−85
−80
−75
−70
20150803: Beat−note amplitude vs. D2 laser detuning
D2 laser detuning from F
g=2 −> F
e=3, MHz
Beat−
note
am
plit
ude, dB
m
Improved puling factor: 0.005→ 0.3 withincreased finesse (20→ 70)Increased pump lasers power (6 mW→200 mW) pushed the pulling factor to 1Setup has widely tunable responseinfluenced by
pump lasers power and detuningdensity of 87Rb atomscavity finesse
This allows us to tune the response of thesystem on demand
We are grateful for financial support to
Eugeniy E. Mikhailov (W&M) Towards fast gyroscope LPHYS, 2016 17 / 17
Sagnac effectCavity responseModification of dispersionExperimental realizationGyro lasing simulationsGyro lasingPulling dependence on detunings, power, Rb densityPulling sensitivity at high power
People
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