fundamental physics with atomic interferometry · 2020. 4. 8. · prd 78 (2008) prd 78 (2008) plb...

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Fundamental Physics with Atomic Interferometry Peter Graham Stanford Savas Dimopoulos Jason Hogan Mark Kasevich Surjeet Rajendran with PRL 98 (2007) PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691

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Page 1: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Fundamental Physics with Atomic Interferometry

Peter GrahamStanford

Savas DimopoulosJason Hogan

Mark KasevichSurjeet Rajendran

with

PRL 98 (2007)PRD 78 (2008)PRD 78 (2008)PLB 678 (2009)arXiv:1009.2702arXiv:1101.2691

Page 2: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Outline

1. Atomic Interferometry

2. Gravitational Wave Detection

3. Axion Dark Matter Detection

Page 3: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atomic Interferometry

Page 4: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atom Interferometry

• established technology

• rapidly advancingdriven by progress in atom cooling (BEC), atomic clocks, ...

1991 - Kasevich & Chu - 3 x 10-6 1998 - A. Peters - 10-10 2011? - 10-15

• high precision already reached 10-11 gearth, 17 digit clock synchronization

path to future improvements (increased atom flux, entangled atoms...)

can test e.g. time variation of fundamental constants

There must be more fundamental physics to be done with it

Page 5: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atomic Clock|atom〉 = |1〉

1

2∆E

Page 6: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atomic Clock|atom〉 = |1〉

beamsplitter1√2

(|1〉+ |2〉) 1

2∆E

Page 7: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atomic Clock|atom〉 = |1〉

beamsplitter1√2

(|1〉+ |2〉) 1

2∆E

1√2

(|1〉+ ei(∆E)t|2〉

)wait time t

Page 8: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atomic Clock|atom〉 = |1〉

beamsplitter1√2

(|1〉+ |2〉) 1

2∆E

1√2

(|1〉+ ei(∆E)t|2〉

)wait time t

beamsplitter

12

[(1− ei(∆E)t

)|1〉+

(1 + ei(∆E)t

)|2〉

]

Page 9: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atomic Clock|atom〉 = |1〉

beamsplitter1√2

(|1〉+ |2〉) 1

2∆E

1√2

(|1〉+ ei(∆E)t|2〉

)wait time t

beamsplitter

12

[(1− ei(∆E)t

)|1〉+

(1 + ei(∆E)t

)|2〉

]

N1 N2

output ports

can measure times t ∼ 1∆E ∼ 10−10 s

Page 10: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

pulse is a beamsplitterpulse is a mirrorπ

π/2

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

Ω1 Ω2

Π""""2

Π 3 Π""""""""2

2 Πt !#Rabi$1"

1""""2

1

,#c1#2 #c2#2

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

ψ = c1|1, p〉+ c2|2, p+ k〉

Raman Transition

Page 11: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

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

Ω1 Ω2

ke f f = ω1 +ω2 ∼ 1 eV

ωe f f = ω1−ω2 ∼ 10−5 eV

ke f f

ω1 ω2

ω2

Raman Transition

Page 12: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Light Pulse Atom Interferometry

r

0

T

2T

t

π

π

2

π

2

beamsplitter

beamsplitter

mirror

Page 13: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Light Pulse Atom Interferometry

a constant gravitational field produces a phase shift:

the interferometer can be as long as T ~ 1 sec ~ earth-moon distance!

sensitivity ~ 10-7 rad∆φ ∼ mg(∆h)T ∼ mg

(k

mT

)T = kgT 2 ∼ 108 rad

∆φ =∫

Ldt =∫

mdτ =∫

pµdxµ

r

0

T

2T

t

π

π

2

π

2

beamsplitter

beamsplitter

mirror

Page 14: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Stanford 10m Interferometer

colocated 85Rb and 87Rb clouds test Principle of

Equivalence initially to 10-15

in controlled (lab) conditions

10 m atom drop tower.

10 m

Page 15: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atomic Gravitational Wave

Interferometric Sensor (AGIS)

PRD 78 (2008)PLB 678 (2009)arXiv:1009.2702

Page 16: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

• provide unique astrophysical informationcompact object binariesblack holes, strong field GR tests

• Every new band opened has revealed unexpected discoveries

Gravitational waves open a new window to the universe

sourced by mass, not chargeuniverse is transparent to gravity waves

Motivation

Page 17: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

• rare opportunity to study cosmology before last scattering

inflation and reheatingearly universe phase transitionscosmic strings ...

CosmologyGravitational waves open a new window to the universe

sourced by mass, not chargeuniverse is transparent to gravity waves

Page 18: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Gravitational Wave Signal

laser ranging an atom (or mirror) from a starting distance L sees a position:

and an acceleration

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

x ∼ L(1 + h sin(ωt))

a ∼ hLω2 sin(ωt)

For GR calculation see PRD 78 (2008)

Page 19: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Gravitational Wave Signal

laser ranging an atom (or mirror) from a starting distance L sees a position:

and an acceleration

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

x ∼ L(1 + h sin(ωt))

a ∼ hLω2 sin(ωt)

gives a phase shift

actual answer

∆φ = kaT 2 ∼ khLω2 sin(ωt)T 2

∆φtot = 4hk

ωsin2

(ωT

2

)sin (ωL) sin (ωt)

For GR calculation see PRD 78 (2008)

Page 20: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

0 LHeight

0

T

2T

Time

L~1 km

10 m

Experiment Design

Page 21: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

L~1 km

10 m

0 LHeight

0

T

2T

Time

Differential Measurement

similar to comparing two clocks separated by L

Page 22: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

• A differential measurement cancels vibrations and laser phase noise (at least to leading order)

allows GW detection down to ω ~ 0.3 Hz (Hughes and Thorne ‘98)

earth vibrations naturally at 1 Hz ! 10−7 m√Hz

• Time-varying gravity gradient noise due to nearby motions of earth

Terrestrial Backgrounds

possible site: DUSEL, Homestake mine (~ 2 km shaft)

Page 23: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

• A differential measurement cancels vibrations and laser phase noise (at least to leading order)

allows GW detection down to ω ~ 0.3 Hz (Hughes and Thorne ‘98)

earth vibrations naturally at 1 Hz ! 10−7 m√Hz

• Time-varying gravity gradient noise due to nearby motions of earth

Terrestrial Backgrounds

• All other backgrounds including timing errors, launch position uncertainty, Coriolis effects, and magnetic fields seem controllable to below shot noise

laser vibration control: 10−7 m√Hz

(1 Hz

f

) 32

(1 km

L

)

−140dBcHz

@ 3× 105Hzlaser phase noise control:

δf

f∼ 10−15 over time scales of 1 slaser frequency stability:

already demonstrated by high finesse cavity-locked lasers

possible site: DUSEL, Homestake mine (~ 2 km shaft)

Page 24: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

!"#"$%&"'(

$%%"(&%"(

)$

$%%"( &%"(

)*

Possible Satellite Configuration

interferometer regionsatellite

space allows a longer interferometer time and sensitivity to lower ω

• ambient B-field (~ nT), vacuum, etc. in space sufficient for interferometer region

• laser power sufficient for atomic transitions

• the time-varying gravitational fields, vibrations, etc. naturally much smaller than for LISA

Page 25: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Satellite Experiment

Atom Interferometry (AGIS)

baseline L ~ 103 km

requires satellite control (at 10-2 Hz) to

atoms provide inertial proof mass, neutral

gas collisions remove atoms, not a noise source

10µm√Hz

LISA

baseline L = 5×106 km

satellite control to

large EM force on charged proof mass

collisions with background gas are noise

1nm√Hz

motivates more careful consideration of engineering details

several backgrounds and technical requirements may be easier with AI

!"#"$%&"'(

$%%"(&%"(

)$

$%%"( &%"(

)*

interferometer regionsatellite

Page 26: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Projected 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 3

Ms,1Ms

BHbinary

at10

kpc

10 3

Ms ,

1Ms BH

binaryat

10Mpc

WhiteDwarf

Binaryat

10Mpc

Page 27: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Projected 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 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

10kpc10 3

Ms ,

1Ms BH

binaryat

10Mpc

10 5

Ms,1Ms

BHbinary

at10

Gpc

WhiteDwarf

Binaryat

10Mpc

Page 28: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Stochastic GW’s - Phase Transitions

RS1

also get observable gravitational waves from some SUSY models (NMSSM)

10!3Hz 10!2Hz 10!1Hz 1 Hz 10 Hz 102 Hz 103 Hz

f

10!17

10!16

10!15

10!14

10!13

10!12

10!11

10!10

10!9

10!8

10!7

10!6

10!5

10!4

10!3

10!2

10!1

1

"GW

10!3Hz 10!2Hz 10!1Hz 1 Hz 10 Hz 102 Hz 103 Hz

10!17

10!16

10!15

10!14

10!13

10!12

10!11

10!10

10!9

10!8

10!7

10!6

10!5

10!4

10!3

10!2

10!1

1

LIGO S4

LISA

inflation

Initial LIGO

Advanced LIGO

BBN # CMB

10!3Hz 10!2Hz 10!1Hz 1 Hz 10 Hz 102 Hz 103 Hz

f

10!17

10!16

10!15

10!14

10!13

10!12

10!11

10!10

10!9

10!8

10!7

10!6

10!5

10!4

10!3

10!2

10!1

1

"GW

10!3Hz 10!2Hz 10!1Hz 1 Hz 10 Hz 102 Hz 103 Hz

10!17

10!16

10!15

10!14

10!13

10!12

10!11

10!10

10!9

10!8

10!7

10!6

10!5

10!4

10!3

10!2

10!1

1

Page 29: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

10!3Hz 10!2Hz 10!1Hz 1 Hz 10 Hz 102 Hz 103 Hz

f

10!17

10!16

10!15

10!14

10!13

10!12

10!11

10!10

10!9

10!8

10!7

10!6

10!5

10!4

10!3

10!2

10!1

1

"GW

10!3Hz 10!2Hz 10!1Hz 1 Hz 10 Hz 102 Hz 103 Hz

10!17

10!16

10!15

10!14

10!13

10!12

10!11

10!10

10!9

10!8

10!7

10!6

10!5

10!4

10!3

10!2

10!1

1

LIGO S4

LISA

inflation

Initial LIGO

Advanced LIGO

BBN # CMB

10!3Hz 10!2Hz 10!1Hz 1 Hz 10 Hz 102 Hz 103 Hz

f

10!17

10!16

10!15

10!14

10!13

10!12

10!11

10!10

10!9

10!8

10!7

10!6

10!5

10!4

10!3

10!2

10!1

1

"GW

10!3Hz 10!2Hz 10!1Hz 1 Hz 10 Hz 102 Hz 103 Hz

10!17

10!16

10!15

10!14

10!13

10!12

10!11

10!10

10!9

10!8

10!7

10!6

10!5

10!4

10!3

10!2

10!1

1

Cosmic Strings

Gμ=10-10

DePies & Hogan PRD 75 125006

Gμ=10-16

Page 30: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

7

LIGO

LISA

Adv LIGO

c

a

d

b AGIS!LEO

10!5Hz 10

!4Hz 10

!3Hz 10

!2Hz 10

!1Hz 1 Hz 10 Hz 10

2Hz 10

3Hz 10

4Hz

10!14

10!15

10!16

10!17

10!18

10!19

10!20

10!21

10!22

10!23

10!24

f

h Hz

FIG. 4: The thick (red) curve shows the enveloped strain sensitivity versus gravitational wave frequency of a five-pulse inter-ferometer sequence for a single arm of the proposed AGIS-LEO instrument. Analogous plots for LIGO [31], Advanced LIGO[32], and LISA [33] are included for comparison. Curves a-d show gravitational wave source strengths after integrating over thelifetime of the source or one year, whichever is shorter: (a) represents inspirals of 103M!, 1M! intermediate mass black holebinaries at 10 kpc, (b) inspirals of 105M!, 1M! massive black hole binaries at 10 Mpc, (c) white dwarf binaries at 10 kpc, and(d) inspirals of 103M!, 1M! intermediate mass black hole binaries at 10 Mpc.

(1), the interferometer is maximally sensitive to GW frequencies at and above the corner frequency ωc =2T cos−1

√38 ≈

2π · 0.29/T at which point ∆φGW = (125/16)keffhL sin θGW. For lower frequencies ω < ωc, the 3 dB point occurs atω3dB = 2

T csc−1[4/√5] ≈ 2π · 0.19/T and sensitivity falls off as ω4. At higher frequencies ω > ωc, the envelope of

the sensitivity curve is constant and the periodic anti-resonant frequencies that are present in (Eq. 1) can easily beavoided by varying T [26].In order to observe a gravitational wave, the phase shift∆φGW must be sampled repeatedly as it oscillates in time due

to the evolution of θGW. To avoid aliasing, the sampling rate fr must be at least twice the frequency of the gravitationalwave. The sampling rate can be increased (without decreasing T ) by operating multiple concurrent interferometersusing the same hardware [26]. In these multiplexed interferometers, atom clouds with different velocities would beaddressed via Doppler shifts of the laser light.

C. Gravitational Wave Sensitivity

The phase sensitivity of an atom interferometer is limited by quantum projection noise δφ = 1/SNR = 1/√Na,

where Na is the number of detected atoms per second. For shot-noise limited atom detection, the resulting strain

sensitivity to gravitational waves becomes h = δφ8keffL

csc4(ωT/2)(

27+8 cosωT

). Figure 4 shows the AGIS-LEO mission

strain sensitivity (enveloped) for a single pair of satellites using the five-pulse interferometer sequence from Fig. 3with !keff = 200!k beamsplitters, an L = 30 km baseline, a T = 4 s interrogation time, and a phase sensitivity of

AGIS-LEOlow Earth orbit may be simpler

White paper with detailed proposal, backgrounds, etc: arXiv:1009.2702

a: IMBH@ 10 kpc

103M!

b: BH@ 10 Mpc105M!

c: WD binary@ 10 kpc

d: IMBH@ 10 Mpc

103M!

Page 31: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Axion Dark Matter Detection

arXiv:1101.2691

Page 32: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Strong CP problem:

Cosmic Axions

measurements ⇒ θ ! 3× 10−10

creates a nucleon EDM d ∼ 3× 10−16 θ e cmL ⊃ θ GG

Page 33: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Strong CP problem:

Cosmic Axions

measurements ⇒ θ ! 3× 10−10

creates a nucleon EDM d ∼ 3× 10−16 θ e cmL ⊃ θ GG

the axion is a simple solution:

withL ⊃ a

faGG + m2

aa2 ma ∼(200 MeV)2

fa∼ MHz

(1016 GeV

fa

)

Page 34: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Strong CP problem:

Cosmic Axions

measurements ⇒ θ ! 3× 10−10

creates a nucleon EDM d ∼ 3× 10−16 θ e cmL ⊃ θ GG

the axion is a simple solution:

withL ⊃ a

faGG + m2

aa2 ma ∼(200 MeV)2

fa∼ MHz

(1016 GeV

fa

)

a

Va(t) ∼ a0 cos (mat)

cosmic expansion reduces amplitude a0

Page 35: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Strong CP problem:

Cosmic Axions

measurements ⇒ θ ! 3× 10−10

creates a nucleon EDM d ∼ 3× 10−16 θ e cmL ⊃ θ GG

the axion is a simple solution:

withL ⊃ a

faGG + m2

aa2 ma ∼(200 MeV)2

fa∼ MHz

(1016 GeV

fa

)

the axion is a good cold dark matter candidate

this field has momentum = 0 ⇒ it is non-relativistic matter

a

Va(t) ∼ a0 cos (mat)

cosmic expansion reduces amplitude a0

Page 36: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Axions From High Energy Physics

Easy to generate axions from high energy theories

have a global symmetry broken at a high scale fa

string theory or extra dimensions naturally have axions from non-trivial topology

naturally gives large fa ~ GUT (1016 GeV) or Planck (1019 GeV) scales

Axions and WIMPs are the best motivated cold dark matter candidates

Page 37: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Constraints and Searches

1014

1018

1016

fa (GeV)

1012

1010

108

Page 38: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Constraints and Searches

1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter

Page 39: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Constraints and Searches

a γ

B

L ⊃ a

faFF =

a

fa

!E · !B

in most models also have:

microwave cavity (ADMX)

1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter

Page 40: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Constraints and Searches

a γ

B

L ⊃ a

faFF =

a

fa

!E · !B

in most models also have:

microwave cavity (ADMX)

1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter

axion-photon conversion suppressed by fa

size of cavity increases with fa

signal ∝1f4

a

Page 41: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Constraints and Searches

a γ

B

L ⊃ a

faFF =

a

fa

!E · !B

in most models also have:

microwave cavity (ADMX)

1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter

axion emission affects SN1987A, White Dwarfs, other astrophysical objects

axion-photon conversion suppressed by fa

size of cavity increases with fa

signal ∝1f4

a

Page 42: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Constraints and Searches

a γ

B

L ⊃ a

faFF =

a

fa

!E · !B

in most models also have:

microwave cavity (ADMX)

1014

1018

1016

fa (GeV)

1012

1010

108

How search for high fa axions?

Axion dark matter

axion emission affects SN1987A, White Dwarfs, other astrophysical objects

axion-photon conversion suppressed by fa

size of cavity increases with fa

signal ∝1f4

a

Page 43: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Strong CP problem:

Axion Dark Mattercreates a nucleon EDM d ∼ 3× 10−16 θ e cmL ⊃ θ GG

witha(t) ∼ a0 cos (mat) ma ∼(200 MeV)2

fa∼ MHz

(1016 GeV

fa

)

the axion: L ⊃ a

faGG + m2

aa2 creates a nucleon EDM d ∼ 3× 10−16 a

fae cm

Page 44: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Strong CP problem:

Axion Dark Mattercreates a nucleon EDM d ∼ 3× 10−16 θ e cmL ⊃ θ GG

witha(t) ∼ a0 cos (mat) ma ∼(200 MeV)2

fa∼ MHz

(1016 GeV

fa

)

the axion: L ⊃ a

faGG + m2

aa2 creates a nucleon EDM d ∼ 3× 10−16 a

fae cm

the axion gives all nucleons a rapidly oscillating EDM

axion dark matter is the biggest BEC ρDM ∼ m2aa2

0 ∼ 0.3GeVcm3

Page 45: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Strong CP problem:

Axion Dark Mattercreates a nucleon EDM d ∼ 3× 10−16 θ e cmL ⊃ θ GG

witha(t) ∼ a0 cos (mat) ma ∼(200 MeV)2

fa∼ MHz

(1016 GeV

fa

)

the axion: L ⊃ a

faGG + m2

aa2 creates a nucleon EDM d ∼ 3× 10−16 a

fae cm

the axion gives all nucleons a rapidly oscillating EDM

axion dark matter is the biggest BEC ρDM ∼ m2aa2

0 ∼ 0.3GeVcm3

thus all (free) nucleons radiate

Axion is more observable through its effects on atomic energy levels(significantly different from standard EDM searches)

Page 46: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atomic Axion SearchesUnlike a normal EDM search, can look directly for the axion,

without external EM fields to modulate the signal

Eint ∼eA

2 ∼ 1012 Vm

instead use internal fields, much larger:

induces a shift to the energy levels: δω ∼ #Eint · #dn ∼ 10−24 eV

Page 47: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Atomic Axion SearchesUnlike a normal EDM search, can look directly for the axion,

without external EM fields to modulate the signal

Eint ∼eA

2 ∼ 1012 Vm

instead use internal fields, much larger:

induces a shift to the energy levels: δω ∼ #Eint · #dn ∼ 10−24 eV

if cool 108 atoms per sec, interferometer lasts ~ 1 sec, and take 106 trials

then shot noise limit is δω ∼(1 s ·

√1014 atoms

)−1∼ 7× 10−23 eV

There are two important caveats: Parity and Schiff’s Theorem

Page 48: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Parity Breaking

Atomic states have very little parity breaking

thus !Eint · !dn ≈ 0

Axion breaks parity (CP)

Page 49: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Parity Breaking

Atomic states have very little parity breaking

thus !Eint · !dn ≈ 0

Axion breaks parity (CP)

!dnmolecules can naturally break parity at O(1), though more difficult to work with due to low-lying modes

One possible solution:

Must control molecular rotation with applied E field (~ 106 V/m)

Use applied B field (< 0.1 T) to rotate nuclear spin with axion’s frequency (easily scanned)

Page 50: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Schiff’s TheoremSchiff’s theorem: in electrostatic equilibrium the E field on any point charge is zero

thus !Eint · !dn ≈ 0

Page 51: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Schiff’s TheoremSchiff’s theorem: in electrostatic equilibrium the E field on any point charge is zero

thus !Eint · !dn ≈ 0

higher moments take into account corrections to this (e.g. finite size of nucleus...)

Schiff moment: δω ∼ Eint dS ∼(10−9 Z3

)Eint dn

δω ∼ 10−3 Eint dn ∼ 10−27 eVoften use Hg or Tl

Page 52: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Schiff’s TheoremSchiff’s theorem: in electrostatic equilibrium the E field on any point charge is zero

thus !Eint · !dn ≈ 0

higher moments take into account corrections to this (e.g. finite size of nucleus...)

Schiff moment: δω ∼ Eint dS ∼(10−9 Z3

)Eint dn

δω ∼ 10−3 Eint dn ∼ 10−27 eVoften use Hg or Tl225Ra

223Fr

225Ac

229Pa

0.2

0.4

0.6

9

2× 10−25 eV

4× 10−25 eV

6× 10−25 eV

9× 10−24 eV

239Pu 3× 10−25 eV0.3

Page 53: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Schiff’s TheoremSchiff’s theorem: in electrostatic equilibrium the E field on any point charge is zero

thus !Eint · !dn ≈ 0

higher moments take into account corrections to this (e.g. finite size of nucleus...)

Schiff moment: δω ∼ Eint dS ∼(10−9 Z3

)Eint dn

δω ∼ 10−3 Eint dn ∼ 10−27 eVoften use Hg or Tl225Ra

223Fr

225Ac

229Pa

0.2

0.4

0.6

9

2× 10−25 eV

4× 10−25 eV

6× 10−25 eV

9× 10−24 eV

239Pu 3× 10−25 eV0.3

22 min

10 d

1.4 d

2.4×104 y

15 d

half-life

Page 54: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Schiff’s TheoremSchiff’s theorem: in electrostatic equilibrium the E field on any point charge is zero

thus !Eint · !dn ≈ 0

higher moments take into account corrections to this (e.g. finite size of nucleus...)

Schiff moment: δω ∼ Eint dS ∼(10−9 Z3

)Eint dn

δω ∼ 10−3 Eint dn ∼ 10−27 eVoften use Hg or Tl225Ra

223Fr

225Ac

229Pa

0.2

0.4

0.6

9

2× 10−25 eV

4× 10−25 eV

6× 10−25 eV

9× 10−24 eV

239Pu 3× 10−25 eV0.3

22 min

10 d

1.4 d

2.4×104 y

15 d

half-life

Argonne

Stony Brook

NIST cooled polar 40K87Rb to < µK

Page 55: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

microwave cavity (ADMX)

1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter

astrophysical constraints

Molecular Axion Searches

GUT

Planck

Page 56: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

microwave cavity (ADMX)

1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter

astrophysical constraints

Molecular Axion Searches

molecular interferometry

can most easily search in kHz - MHz frequencies high fa

GUT

Planck

Page 57: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

microwave cavity (ADMX)

1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter

astrophysical constraints

Molecular Axion Searches

molecular interferometry

can most easily search in kHz - MHz frequencies high fa

GUT

Planck

difficult technological challenges, similar to early stages of WIMP detection

axion dark matter is very well-motivated, no other way to search for at high fa

would be both the discovery of dark matter and a glimpse into physics at very high energies

Page 58: Fundamental Physics with Atomic Interferometry · 2020. 4. 8. · PRD 78 (2008) PRD 78 (2008) PLB 678 (2009) arXiv:1009.2702 arXiv:1101.2691. Outline 1. Atomic Interferometry 2. Gravitational

Summary

1. Considered the use of molecular interferometry to detect Axion dark matter

• Axion dark matter is well motivated

• unlike WIMPs, currently no way to detect over most of parameter space

2. Proposed an Atomic Gravitational Wave Interferometric Sensor (AGIS)

• both terrestrial and satellite versions

• AGIS-LEO in low Earth orbit

3. Proposed laboratory tests of General Relativity

• including test of Equivalence Principle to 10-15 under construction @ Stanford

4. New ideas?