atomic gravitational wave inertial sensor (agis)atomic gravitational wave inertial sensor (agis)...

Atomic Gravitational wave Inertial Sensor

(AGIS)

Surjeet Rajendran, Stanford/SLACwith

Savas Dimopoulos, Peter Graham, Jason Hogan,

Mark KasevicharXiv:0712.1250arXiv:0806.2125

Gravitational Wave Detection Distance between objects oscillates due to gravitational

wave.LDetect oscillation and observe gravitational wave.

Gravitational Wave Detection Distance between objects oscillates due to gravitational

wave.L

Objects need to be well isolated from environment.(vibrational noise for LIGO, acceleration noise for

LISA)

Simultaneously need high sensitivity and low noise

Detect oscillation and observe gravitational wave.

Outline

1. Atom Interferometry

2. Terrestrial Experiment (1 Hz - 10 Hz)

3. Satellite Setup (10-2 Hz - 1 Hz)

4. AGIS Sensitivities

Atom Interferometry

• Established technology (Kasevich and Chu, 1991)

• High precision sensors, e.g. 16 digit atomic clock synchronization, accelerometers with 12 digit sensitivity.

• Rapidly evolving field. Several future advances possible e.g. atom cooling techniques etc.

r

0

T

2T

t

What is an atom interferometer?

|atom〉 = |p〉

r

0

T

2T

t

beamsplitter


|atom〉 = |p〉

1√2(|p〉+ ei∆φ|p + k〉)

r

0

T

2T

t

mirrormirror

beamsplitter


|atom〉 = |p〉

1√2(|p〉+ ei∆φ|p + k〉)

1√2(|p + k〉+ ei∆φ|p〉)

r

0

T

2T

t

mirrormirror

beamsplitter

beamsplitter


1√2(|p + k〉+ ei∆φ|p〉)

1√2(|p + k〉 − |p〉)

1√2(|p〉+ |p + k〉)

r

0

T

2T

t

mirrormirror

beamsplitter

beamsplitter


Final State

1√2(|p + k〉+ ei∆φ|p〉)

1√2(|p + k〉 − |p〉)

1√2(|p〉+ |p + k〉)

12((1 + ei∆φ)|p〉+ ((1− ei∆φ))|p + k〉)

r

0

T

2T

t output ports

mirrormirror

beamsplitter

beamsplitter


Final State12((1 + ei∆φ)|p〉+ ((1− ei∆φ))|p + k〉)

Probability in State |p〉 = cos2(

∆φ2

)

Probability in State |p + k〉 = sin2(

∆φ2

)

Light Pulse Atom Interferometry(Kasevich and Chu, 1991)

Beamsplitter and mirror must transfer momentum to the atom.



|1, p〉


ω2ω1


|1, p〉


ω2ω1


|1, p〉|2, p + k〉

Atom undergoes coherent Raman Scattering with momentum transfer

|3〉

keff = ω1 − ω2 ≈ 2 ω1 ∼ 1eV

Beamsplitter and Mirror Pulses

pulse is a beamsplitterpulse is a mirrorπ

π/2

Π""""2

Π 3 Π""""""""2

2 Πt !#Rabi$1"

1""""2

1

,#c1#2 #c2#2

#1,p$#2,p%k$

!1,p" !2,p!k"

Ω1 Ω2

ψ = c1|p〉 + c2|p + k〉

|p〉

|p〉

|p + k〉|p + k〉

Spacetime Diagram of the Atom Interferometer

Control Laser Passive Laserx

0

T

2T

Time

Τa

Τb

Τc

Τd

Spacetime Diagram of the Atom Interferometer


0

T

2T

Time

Τa

Τb

Τc

Τd

Typical Terrestrial Interferometer

∼ 107 atoms launched with velocities ~ 10 m/s

Atoms are in free fall during interferometer.

T ~ 1 s sets interferometer length to ~ 10 m.

Phase Shift in the Interferometer

• Differences in the trajectories of the wavepackets.


0

T

2T

Time

Τa

Τb

Τc

Τd

Phase Shift in the Interferometer

• Differences in the trajectories of the wavepackets.

• The laser phase imprinted on the atom during the atom laser interaction.


0

T

2T

Time

Τa

Τb

Τc

Τd

What can cause a phase shift?


0

T

2T

Time

Τa

Τb

Τc

Τd



0

T

2T

Time

Τa

Τb

Τc

Τd

Interferometer symmetric about the mirror pulse at T.



0

T

2T

Time

Τa

Τb

Τc

Τd


Need to break symmetry to cause phase shift.



0

T

2T

Time

Τa

Τb

Τc

Τd



Interferometer is an accelerometer.



0

T

2T

Time

Τa

Τb

Τc

Τd



Interferometer is an accelerometer.

Acceleration causes phase shift

a∼ keff a T 2

The Gravitational Wave Signal in the Interferometer

ds2 = −dt2 + (1 + h sin(ω(t− z)))dx2 + (1− h sin(ω(t− z)))dy2 + dz2



Control Laser Passive LaserL

0

T

2T

Time

!L!hL

T!L"hL

2T!L!hL




0

T

2T

Time

!L!hL

T!L"hL

2T!L!hL

Gravitational wave causes acceleration

∼ h Lω2




0

T

2T

Time

!L!hL

T!L"hL

2T!L!hL


Phase shift

∼ h Lω2

∼ keff(h Lω2

)T 2




0

T

2T

Time

!L!hL

T!L"hL

2T!L!hL


Phase shift

∼ h Lω2

∼ keff(h Lω2

)T 2

sin (ωt)

sin (ωt)


Phase difference maximal when



0

T

2T

Time

!L!hL

T!L"hL

2T!L!hL


T ∼ 1ω

Phase shift

∼ h Lω2

∼ keff(h Lω2

)T 2

sin (ωt)

sin (ωt)

Laser ranging atom in the presence of gravitational wave.


Phase difference maximal when



0

T

2T

Time

!L!hL

T!L"hL

2T!L!hL


T ∼ 1ω

Phase shift

∼ h Lω2

∼ keff(h Lω2

)T 2

sin (ωt)

sin (ωt)

What about vibrational noise?

The atoms are in free fall during the course of the interferometry.

Atoms coupled to vibrations only gravitationally. A much smaller effect!

What about vibrational noise?

The atoms are in free fall during the course of the interferometry.

Atoms coupled to vibrations only gravitationally. A much smaller effect!

BUT

The lasers are not in free fall.

Laser phase noise?

Differential Measurement

Run two, widely separated atom interferometers using common lasers.

Measure differential phase shift.

Control Laser Passive LaserLDistance

0

T

2T

Time

Τa1

Τa2

Τb1

Τb2Τc1

Τc2

Τd1

Τd2



Laser vibration and phase noise cancels (up to finite light travel time effects).

Measure differential phase shift.

Gravitational wave signal is retained ~

keff hL


0

T

2T

Time

Τa1

Τa2

Τb1

Τb2Τc1

Τc2

Τd1

Τd2

Take LIGO’s mirrors, drop them

and measure relative acceleration during

free fall.




0

T

2T

Time

Τa1

Τa2

Τb1

Τb2Τc1

Τc2

Τd1

Τd2

Take LIGO’s mirrors, drop them

and measure relative acceleration during

free fall.




0

T

2T

Time

Τa1

Τa2

Τb1

Τb2Τc1

Τc2

Τd1

Τd2

Atoms are LIGO’s mirrors.

Role of laser similar to LIGO’s laser.

Terrestrial Configuration

Two 10 m atom interferometers at either ends of a vertical mine shaft (e.g. DUSEL)

Both interferometers are operated by common lasers.

I1

I2

~10 m

~ 1 km

~10 m




Allows free fall time ~ 1s. Maximally sensitive in the 1 Hz band.

Signal scales with the length ~ 1 km between interferometers.

I1

I2

~10 m

~ 1 km

~10 m




Allows free fall time ~ 1s. Maximally sensitive in the 1 Hz band.

Time varying gravity gradient noise cuts off sensitivity below ~ 0.3 Hz.

Signal scales with the length ~ 1 km between interferometers.

I1

I2

~10 m

~ 1 km

~10 m

Gravity gradient noise in Space

LISA Satellite Mirror is inside a satellite of mass of a fewhundred kg.

Free floating mirror gravitationally coupled to vibrations of the satellite.

Gravity gradient noise in Space

LISA Satellite Mirror is inside a satellite of mass of a fewhundred kg.

Free floating mirror gravitationally coupled to vibrations of the satellite.

Requires position control of the satellite ~ 1nm√Hz

at 10−2 Hz(LISA Pre Phase A Report)

Major hurdle for LISA

Satellite Experiment Setup

IL~100 md~30 m

S1

IL~100 m d~30 m

S2

L ~ 1000 km

Two widely separated atom interferometers run by common lasers.


IL~100 md~30 m

S1

IL~100 m d~30 m

S2

L ~ 1000 km

Atoms brought d ~ 30 m from satellites through laser manipulations. Run interferometer over region IL ~ 100 m.



IL~100 md~30 m

S1

IL~100 m d~30 m

S2

L ~ 1000 km


Satellite Position fluctuation δr causes acceleration ∼(

GMsatd2

) (δr

d

)



IL~100 md~30 m

S1

IL~100 m d~30 m

S2

L ~ 1000 km


Satellite Position fluctuation δr causes acceleration ∼(

GMsatd2

) (δr

d

)


Signal again scales with the distance L between interferometers. Distance limited by laser power. With One Watt, L ~ 1000 km.

Backgrounds

For gravitational wave sensitivity similar to LISA, the atom interferometer requires position control of the satellite at

∼ 104 nm√Hz

at 10−2 Hz for d ∼ 30 m.

Backgrounds


LISA Requirement: 1nm√Hz

at 10−2 Hz

∼ 104 nm√Hz

at 10−2 Hz for d ∼ 30 m.

Backgrounds



at 10−2 Hz

Stray electrostatic forces are a problem for LISA

∼ 104 nm√Hz

at 10−2 Hz for d ∼ 30 m.

Backgrounds



at 10−2 Hz

Stray electrostatic forces are a problem for LISA

Background absent for atom interferometer. Neutral atoms in magnetically insensitive states.

∼ 104 nm√Hz

at 10−2 Hz for d ∼ 30 m.

Laser Requirements

S1 S2

S3

L ~ 1000 km

Phase noise cancellation up to knowledge of arm length.

Laser Requirements

S1 S2

S3

L ~ 1000 km

Phase noise cancellation up to knowledge of arm length.1m arm length resolution, need laser frequency stability

∼ 104 Hz√Hz

@ 10−2 Hz

Laser Requirements

S1 S2

S3

L ~ 1000 km

Phase noise cancellation up to knowledge of arm length.1m arm length resolution, need laser frequency stability

∼ 104 Hz√Hz

@ 10−2 Hz

LISA ∼ 10 Hz√Hz

@ 10−2 Hz

Laser Requirements

S1 S2

S3

L ~ 1000 km

A lot of other backgrounds. While non-trivial, they all seem controllable.

Status of atom technology?

The Stanford 10 m Atom Interferometer

drop colocated 85Rb and 87Rb clouds to test Principle of Equivalence

10 m atom drop tower.

10 m

(Hogan, Johnson and Kasevich)

10 m




10 m

Test equivalence principle to 10-15in controlled (lab) conditions. Improves current

bounds by ~ 300.

Goal


10 m




10 m

Test equivalence principle to 10-15in controlled (lab) conditions. Improves current

bounds by ~ 300.

Goal


Results expected within the end of the year!

10 m

Projected AGIS Terrestrial Sensitivity

L= 1 km and 4 km

10!5 Hz 10!4 Hz 10!3 Hz 10!2 Hz 10!1 Hz 1 Hz 10 Hz 102 Hz 103 Hz 104 Hz

f

10!14

10!15

10!16

10!17

10!18

10!19

10!20

10!21

10!22

10!23

h ! Hz10!5 Hz 10!4 Hz 10!3 Hz 10!2 Hz 10!1 Hz 1 Hz 10 Hz 102 Hz 103 Hz 104 Hz

10!14

10!15

10!16

10!17

10!18

10!19

10!20

10!21

10!22

10!23

LIGO

LISA

WhiteDwarf

Binaryat

10kpc

10 3Ms,

1Ms

BHbinary

at10

kpc

10 3Ms ,

1Ms BH

binaryat

10Mpc

WhiteDwarf

Binaryat

10Mpc

Projected AGIS Satellite Sensitivity

L= 100 km, 103 km, and 104 km

10!5 Hz 10!4 Hz 10!3 Hz 10!2 Hz 10!1 Hz 1 Hz 10 Hz 102 Hz 103 Hz 104 Hzf

10!14

10!15

10!16

10!17

10!18

10!19

10!20

10!21

10!22

10!23

h ! Hz10!5 Hz 10!4 Hz 10!3 Hz 10!2 Hz 10!1 Hz 1 Hz 10 Hz 102 Hz 103 Hz 104 Hz

10!14

10!15

10!16

10!17

10!18

10!19

10!20

10!21

10!22

10!23

LIGO

LISA

10 3Ms , 1 Ms BH binary at 10 Mpc10 5 Ms, 1 Ms BH binary at 10 Gpc

White Dwarf Binary at 10 MpcWhite Dwarf Binary at 3 Gpc

Conclusions

• Atom interferometer configuration allows for large signal enhancements with suppressed backgrounds.

• Frequency band complementary to LIGO on Earth• Satellite experiment probes same spectrum as LISA

with comparable sensitivity

• Potentially easier systematics than conventional light interferometers.

atomic gravitational wave inertial sensor (agis)atomic gravitational wave inertial sensor (agis)...

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