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