Transcript
An Extremely Brief Overview of the State of the Art of
Maxwell Gregoire
Atom Interferometer Gyroscopes
What is a gyroscope
A device for measuring the rotation rate (or any time derivatives thereof) of its own reference frame
Applications Navigation
Compare satellites to a drag-free test mass
ndash Solar wind atmospheric drag
ndash Important for experiments that reference trajectories Submarines
ndash Cannot access GPS
ndash Less detectable if they
dont have to ping Aircraft and ships
(manned and unmanned)
ndash Not vulnerable to cyber
attack if they dont need GPS
Applications Geophysics
Measure wobble in Earths rotation rate due to
ndash Precession and nutation
ndash Lunar and solar tides Measure tidal drag
ndash Earths rotation causes tidal bulge to ldquoleadrdquo the moon moon pulls back on tidal bulge causes torque on Earth opposite rotation vector
ndash Earths rotation slows
ndash Moons revolution slows moon orbits further away (Virial Thm 2T = -V)
Applications General Relativity
Geodetic effect
ndash A vector (ex angular momentum of gyroscope on a satellite) is affected by space-time curvature created by a nearby massive body (ex Earth)
Lense-Thirring rotation aka gravitomagnetic frame-dragging
ndash An object (ex gyroscope on a satellite) rotates due to the rotation of a nearby massive body (ex Earth)
Together these effects predict precession of a gyroscope on a satellite that classically should not happen
Applications and Figure of MeritSensitivity Quick
ResponsePortability
Geodetic effect 10-8 ΩE absolute X
Frame-dragging 10-10 ΩE absolute X
ΩE wobble 10-8 Ω
E change in Ω
E per day
Tidal drag 10-13 ΩE change in Ω
E per year
Navigation 10-3 ΩE absolute X X
Earths rotation rate ΩE = 73∙10-5
Polarizability Measurements
In our lab the Earths rotation
changes measured static polarizability by up to 1
ndash Target accuracy is 02 changes measured magic zero wavelength by 200 pm
ndash Target accuracy is lt 1 pm
E
d
valence electron cloud
nucleus
U = -α E22
Atom Interferometer
L T = Lv L T = Lv
Interference pattern forms at position of 3rd grating
Sweep 3rd grating in +- x direction grating bars either block or admit ldquobright spotsrdquo
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
Atom Interferometer
L T = Lv L T = Lv
Measure phase and contrast of interference pattern
Contrast = (max-min) (max+min)
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
max
min
phase
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
What is a gyroscope
A device for measuring the rotation rate (or any time derivatives thereof) of its own reference frame
Applications Navigation
Compare satellites to a drag-free test mass
ndash Solar wind atmospheric drag
ndash Important for experiments that reference trajectories Submarines
ndash Cannot access GPS
ndash Less detectable if they
dont have to ping Aircraft and ships
(manned and unmanned)
ndash Not vulnerable to cyber
attack if they dont need GPS
Applications Geophysics
Measure wobble in Earths rotation rate due to
ndash Precession and nutation
ndash Lunar and solar tides Measure tidal drag
ndash Earths rotation causes tidal bulge to ldquoleadrdquo the moon moon pulls back on tidal bulge causes torque on Earth opposite rotation vector
ndash Earths rotation slows
ndash Moons revolution slows moon orbits further away (Virial Thm 2T = -V)
Applications General Relativity
Geodetic effect
ndash A vector (ex angular momentum of gyroscope on a satellite) is affected by space-time curvature created by a nearby massive body (ex Earth)
Lense-Thirring rotation aka gravitomagnetic frame-dragging
ndash An object (ex gyroscope on a satellite) rotates due to the rotation of a nearby massive body (ex Earth)
Together these effects predict precession of a gyroscope on a satellite that classically should not happen
Applications and Figure of MeritSensitivity Quick
ResponsePortability
Geodetic effect 10-8 ΩE absolute X
Frame-dragging 10-10 ΩE absolute X
ΩE wobble 10-8 Ω
E change in Ω
E per day
Tidal drag 10-13 ΩE change in Ω
E per year
Navigation 10-3 ΩE absolute X X
Earths rotation rate ΩE = 73∙10-5
Polarizability Measurements
In our lab the Earths rotation
changes measured static polarizability by up to 1
ndash Target accuracy is 02 changes measured magic zero wavelength by 200 pm
ndash Target accuracy is lt 1 pm
E
d
valence electron cloud
nucleus
U = -α E22
Atom Interferometer
L T = Lv L T = Lv
Interference pattern forms at position of 3rd grating
Sweep 3rd grating in +- x direction grating bars either block or admit ldquobright spotsrdquo
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
Atom Interferometer
L T = Lv L T = Lv
Measure phase and contrast of interference pattern
Contrast = (max-min) (max+min)
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
max
min
phase
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Applications Navigation
Compare satellites to a drag-free test mass
ndash Solar wind atmospheric drag
ndash Important for experiments that reference trajectories Submarines
ndash Cannot access GPS
ndash Less detectable if they
dont have to ping Aircraft and ships
(manned and unmanned)
ndash Not vulnerable to cyber
attack if they dont need GPS
Applications Geophysics
Measure wobble in Earths rotation rate due to
ndash Precession and nutation
ndash Lunar and solar tides Measure tidal drag
ndash Earths rotation causes tidal bulge to ldquoleadrdquo the moon moon pulls back on tidal bulge causes torque on Earth opposite rotation vector
ndash Earths rotation slows
ndash Moons revolution slows moon orbits further away (Virial Thm 2T = -V)
Applications General Relativity
Geodetic effect
ndash A vector (ex angular momentum of gyroscope on a satellite) is affected by space-time curvature created by a nearby massive body (ex Earth)
Lense-Thirring rotation aka gravitomagnetic frame-dragging
ndash An object (ex gyroscope on a satellite) rotates due to the rotation of a nearby massive body (ex Earth)
Together these effects predict precession of a gyroscope on a satellite that classically should not happen
Applications and Figure of MeritSensitivity Quick
ResponsePortability
Geodetic effect 10-8 ΩE absolute X
Frame-dragging 10-10 ΩE absolute X
ΩE wobble 10-8 Ω
E change in Ω
E per day
Tidal drag 10-13 ΩE change in Ω
E per year
Navigation 10-3 ΩE absolute X X
Earths rotation rate ΩE = 73∙10-5
Polarizability Measurements
In our lab the Earths rotation
changes measured static polarizability by up to 1
ndash Target accuracy is 02 changes measured magic zero wavelength by 200 pm
ndash Target accuracy is lt 1 pm
E
d
valence electron cloud
nucleus
U = -α E22
Atom Interferometer
L T = Lv L T = Lv
Interference pattern forms at position of 3rd grating
Sweep 3rd grating in +- x direction grating bars either block or admit ldquobright spotsrdquo
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
Atom Interferometer
L T = Lv L T = Lv
Measure phase and contrast of interference pattern
Contrast = (max-min) (max+min)
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
max
min
phase
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Applications Geophysics
Measure wobble in Earths rotation rate due to
ndash Precession and nutation
ndash Lunar and solar tides Measure tidal drag
ndash Earths rotation causes tidal bulge to ldquoleadrdquo the moon moon pulls back on tidal bulge causes torque on Earth opposite rotation vector
ndash Earths rotation slows
ndash Moons revolution slows moon orbits further away (Virial Thm 2T = -V)
Applications General Relativity
Geodetic effect
ndash A vector (ex angular momentum of gyroscope on a satellite) is affected by space-time curvature created by a nearby massive body (ex Earth)
Lense-Thirring rotation aka gravitomagnetic frame-dragging
ndash An object (ex gyroscope on a satellite) rotates due to the rotation of a nearby massive body (ex Earth)
Together these effects predict precession of a gyroscope on a satellite that classically should not happen
Applications and Figure of MeritSensitivity Quick
ResponsePortability
Geodetic effect 10-8 ΩE absolute X
Frame-dragging 10-10 ΩE absolute X
ΩE wobble 10-8 Ω
E change in Ω
E per day
Tidal drag 10-13 ΩE change in Ω
E per year
Navigation 10-3 ΩE absolute X X
Earths rotation rate ΩE = 73∙10-5
Polarizability Measurements
In our lab the Earths rotation
changes measured static polarizability by up to 1
ndash Target accuracy is 02 changes measured magic zero wavelength by 200 pm
ndash Target accuracy is lt 1 pm
E
d
valence electron cloud
nucleus
U = -α E22
Atom Interferometer
L T = Lv L T = Lv
Interference pattern forms at position of 3rd grating
Sweep 3rd grating in +- x direction grating bars either block or admit ldquobright spotsrdquo
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
Atom Interferometer
L T = Lv L T = Lv
Measure phase and contrast of interference pattern
Contrast = (max-min) (max+min)
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
max
min
phase
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Applications General Relativity
Geodetic effect
ndash A vector (ex angular momentum of gyroscope on a satellite) is affected by space-time curvature created by a nearby massive body (ex Earth)
Lense-Thirring rotation aka gravitomagnetic frame-dragging
ndash An object (ex gyroscope on a satellite) rotates due to the rotation of a nearby massive body (ex Earth)
Together these effects predict precession of a gyroscope on a satellite that classically should not happen
Applications and Figure of MeritSensitivity Quick
ResponsePortability
Geodetic effect 10-8 ΩE absolute X
Frame-dragging 10-10 ΩE absolute X
ΩE wobble 10-8 Ω
E change in Ω
E per day
Tidal drag 10-13 ΩE change in Ω
E per year
Navigation 10-3 ΩE absolute X X
Earths rotation rate ΩE = 73∙10-5
Polarizability Measurements
In our lab the Earths rotation
changes measured static polarizability by up to 1
ndash Target accuracy is 02 changes measured magic zero wavelength by 200 pm
ndash Target accuracy is lt 1 pm
E
d
valence electron cloud
nucleus
U = -α E22
Atom Interferometer
L T = Lv L T = Lv
Interference pattern forms at position of 3rd grating
Sweep 3rd grating in +- x direction grating bars either block or admit ldquobright spotsrdquo
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
Atom Interferometer
L T = Lv L T = Lv
Measure phase and contrast of interference pattern
Contrast = (max-min) (max+min)
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
max
min
phase
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Applications and Figure of MeritSensitivity Quick
ResponsePortability
Geodetic effect 10-8 ΩE absolute X
Frame-dragging 10-10 ΩE absolute X
ΩE wobble 10-8 Ω
E change in Ω
E per day
Tidal drag 10-13 ΩE change in Ω
E per year
Navigation 10-3 ΩE absolute X X
Earths rotation rate ΩE = 73∙10-5
Polarizability Measurements
In our lab the Earths rotation
changes measured static polarizability by up to 1
ndash Target accuracy is 02 changes measured magic zero wavelength by 200 pm
ndash Target accuracy is lt 1 pm
E
d
valence electron cloud
nucleus
U = -α E22
Atom Interferometer
L T = Lv L T = Lv
Interference pattern forms at position of 3rd grating
Sweep 3rd grating in +- x direction grating bars either block or admit ldquobright spotsrdquo
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
Atom Interferometer
L T = Lv L T = Lv
Measure phase and contrast of interference pattern
Contrast = (max-min) (max+min)
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
max
min
phase
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Polarizability Measurements
In our lab the Earths rotation
changes measured static polarizability by up to 1
ndash Target accuracy is 02 changes measured magic zero wavelength by 200 pm
ndash Target accuracy is lt 1 pm
E
d
valence electron cloud
nucleus
U = -α E22
Atom Interferometer
L T = Lv L T = Lv
Interference pattern forms at position of 3rd grating
Sweep 3rd grating in +- x direction grating bars either block or admit ldquobright spotsrdquo
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
Atom Interferometer
L T = Lv L T = Lv
Measure phase and contrast of interference pattern
Contrast = (max-min) (max+min)
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
max
min
phase
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Atom Interferometer
L T = Lv L T = Lv
Interference pattern forms at position of 3rd grating
Sweep 3rd grating in +- x direction grating bars either block or admit ldquobright spotsrdquo
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
Atom Interferometer
L T = Lv L T = Lv
Measure phase and contrast of interference pattern
Contrast = (max-min) (max+min)
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
max
min
phase
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Atom Interferometer
L T = Lv L T = Lv
Measure phase and contrast of interference pattern
Contrast = (max-min) (max+min)
area Av λ
dB
z
x
(not all diffraction orders are shown)
P
Detec tor
max
min
phase
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Atom Interferometer
phase Φ = k [ndash 2Δx2(T) + Δx3(2T)]
L T = Lv L T = Lv
k grating ldquoreciprocal lattice vectorrdquo aka kx given to atom in 1st order diffraction
Δxi how much grating i has moved since atom hit first grating
area Av λ
dB
z
xD
etec tor
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Atom Interferometer
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
L T = Lv L T = Lv
d grating period
Δxi how much grating i has moved (in x direction) since atom hit first grating
area Av λ
dB
z
xD
etec tor
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
The Sagnac Effect
grating period d
Φsag = (2πd) [0 ndash 0 + (ΩL)(2Lv)] = hellip = 4πΩA λdBv
L T = Lv L T = Lv
phase Φ = (2πd) [ndash 2Δx2(T)+ Δx3(2T)]
area Av λ
dB
Ω
z
xD
etec tor
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Atoms vs Light response factor matters Response factor ΦsagΩ
In general ΦsagΩ = 4πA λv
Φsagatom = λlightc = mc2 asymp 1011
Φsaglight λdBv ħv
That said number of atoms matters In shot-noise limit δΩ = δΦ = Ω
ΦsagΩ ΦsagCradicN
When statistics are Gaussian
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Nano-grating Interferometer
PROS Works with any atomic
species High dynamic range
CONS Gratings only transmit 01 of
atoms Contrast asymp 30
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Light Grating Interferometer
ω1
ω2
|ggt
|egt
|igtΔ
effective ωeff
g ω2 k
2ω
1 k
1
Kapitza-Dirac diffraction
Bragg diffraction
Raman diffraction
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Dynamic rangeWith no Sagnac shift
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Dynamic rangeWith Sagnac shift
Sagnac shift is v-dependent
ndash Atoms disperse in x
ndash Causes contrast loss
ndash Oh no Whatever shall we do
P
x position along 3rd grating
slowfast
slowfast
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
Dynamic rangeWith Sagnac shift apply static non-uniform E
Field pulls slower atoms more in opposite direction of Sagnac shift
Recovers contrast
Measure Ω by maximizing contrast
+
P
x position along 3rd grating
cylinder axis into page
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
top related