Fundamental Physics with Atomic Interferometry

Transcription

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

2 Outline 1. Atomic Interferometry 2. Gravitational Wave Detection 3. Axion Dark Matter Detection

3 Atomic Interferometry

4 Atom Interferometry established technology rapidly advancing driven by progress in atom cooling (BEC), atomic clocks, Kasevich & Chu - 3 x A. Peters ? high precision already reached 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

5 Atomic Clock atom = } E

6 Atomic Clock beamsplitter atom = ( ) 1 2 } E

7 Atomic Clock beamsplitter wait time t atom = ( ) ) ( 1 + e i( E)t 2 2 } E

8 Atomic Clock beamsplitter atom = ( ) 1 2 } E wait time t beamsplitter ) ( 1 + e i( E)t 2 2 [( 1 e i( E)t) 1 + ( 1 + e i( E)t) ] 2

9 Atomic Clock beamsplitter atom = ( ) 1 2 } E wait time t beamsplitter 1 2 output ports 1 ) ( 1 + e i( E)t 2 2 [( 1 e i( E)t) 1 + } N1 N2 ( 1 + e i( E)t) ] 2 } can measure times t 1 E s

10 Raman Transition ψ = c 1 1, p + c 2 2, p + k c 1 2, c Ω 1 Ω ,p 2,p k 1,p 2,p k Π 2 Π 3 Π 2 2 Π t Rabi 1 π/2 pulse is a beamsplitter π pulse is a mirror

11 Raman Transition ω 1 ω 2 Ω 1 Ω 2 k e f f ω 2 1,p 2,p k k e f f = ω 1 + ω 2 1 ev ω e f f = ω 1 ω ev

12 Light Pulse Atom Interferometry t π 2 beamsplitter 2T T π π 2 mirror beamsplitter 0 r

13 Light Pulse Atom Interferometry t π 2 beamsplitter 2T T π π 2 mirror beamsplitter 0 φ = Ldt = mdτ = r p µ dx µ φ mg( h)t mg a constant gravitational field produces a phase shift: ( k m T ) T = kgt rad sensitivity ~ 10-7 rad the interferometer can be as long as T ~ 1 sec ~ earth-moon distance!

14 Stanford 10m Interferometer 10 m 10 m atom drop tower. colocated 85 Rb and 87 Rb clouds test Principle of Equivalence initially to in controlled (lab) conditions

15 Atomic Gravitational Wave Interferometric Sensor (AGIS) PRD 78 (2008) PLB 678 (2009) arxiv:

16 Motivation Gravitational waves open a new window to the universe sourced by mass, not charge universe is transparent to gravity waves provide unique astrophysical information compact object binaries black holes, strong field GR tests Every new band opened has revealed unexpected discoveries

17 rare opportunity to study cosmology before last scattering inflation and reheating early universe phase transitions cosmic strings... Cosmology Gravitational waves open a new window to the universe sourced by mass, not charge universe is transparent to gravity waves

18 Gravitational Wave Signal ds 2 = dt 2 (1 + h sin(ω(t z)))dx 2 (1 h sin(ω(t z)))dy 2 dz 2 For GR calculation see PRD 78 (2008) laser ranging an atom (or mirror) from a starting distance L sees a position: x L(1 + h sin(ωt)) and an acceleration a hlω 2 sin(ωt)

19 Gravitational Wave Signal ds 2 = dt 2 (1 + h sin(ω(t z)))dx 2 (1 h sin(ω(t z)))dy 2 dz 2 For GR calculation see PRD 78 (2008) laser ranging an atom (or mirror) from a starting distance L sees a position: x L(1 + h sin(ωt)) and an acceleration a hlω 2 sin(ωt) gives a phase shift φ = kat 2 khlω 2 sin(ωt)t 2 actual answer φ tot = 4 hk ω sin2 ( ωt 2 ) sin (ωl) sin (ωt)

20 Experiment Design 2T 10 m Time T L~1 km 0 0 L Height

21 Differential Measurement 2T 10 m Time T L~1 km 0 0 L Height similar to comparing two clocks separated by L

22 Terrestrial Backgrounds A differential measurement cancels vibrations and laser phase noise (at least to leading order) Time-varying gravity gradient noise due to nearby motions of earth earth vibrations naturally 10 7 m Hz at 1 Hz allows GW detection down to ω ~ 0.3 Hz (Hughes and Thorne 98) possible site: DUSEL, Homestake mine (~ 2 km shaft)

23 Terrestrial Backgrounds A differential measurement cancels vibrations and laser phase noise (at least to leading order) Time-varying gravity gradient noise due to nearby motions of earth earth vibrations naturally 10 7 m Hz at 1 Hz allows GW detection down to ω ~ 0.3 Hz (Hughes and Thorne 98) 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 1 Hz Hz f laser phase noise control: laser frequency stability: possible site: DUSEL, Homestake mine (~ 2 km shaft) ) 3 ( ) 2 1 km 140 dbc 105 Hz δf f over time scales of 1 s L already demonstrated by high finesse cavity-locked lasers

24 Possible Satellite Configuration satellite ) $ interferometer region ) * &%"( $%%"( $%%"( &%"(!"#"$% & "'( 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

25 satellite ) $ Satellite Experiment interferometer region ) * &%"( $%%"( $%%"( &%"(!"#"$% & "'( Atom Interferometry (AGIS) baseline L ~ 10 3 km LISA baseline L = km requires satellite control (at 10-2 Hz) to 10 µm Hz satellite control to 1 nm Hz atoms provide inertial proof mass, neutral gas collisions remove atoms, not a noise source large EM force on charged proof mass collisions with background gas are noise several backgrounds and technical requirements may be easier with AI motivates more careful consideration of engineering details

26 Projected Terrestrial Sensitivity Hz 10 4 Hz 10 3 Hz 10 2 Hz 10 1 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz 10 4 Hz Ms, 1 Ms BH binary at 10 kpc White Dwarf Binary at 10 kpc LISA 10 3 M s, 1 M s BH binary at 10 Mpc White Dwarf Binary at 10 Mpc h Hz LIGO Hz 10 4 Hz 10 3 Hz 10 2 Hz 10 1 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz 10 4 Hz f L= 1 km and 4 km 10 23

27 Projected Satellite Sensitivity Hz 10 4 Hz 10 3 Hz 10 2 Hz 10 1 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz 10 4 Hz White Dwarf Binary at 10 kpc LISA 10 3 M s, 1 M s BH binary at 10 Mpc White Dwarf Binary at 10 Mpc h Hz Ms, 1 Ms BH binary at 10 Gpc LIGO Hz 10 4 Hz 10 3 Hz 10 2 Hz 10 1 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz 10 4 Hz f L= 100 km, 10 3 km, and 10 4 km 10 23

28 Stochastic GW s - Phase Transitions GW 10 3 Hz 10 2 Hz 10 1 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz Initial LIGO LISA Advanced LIGO RS1 inflation BBN CMB LIGO S Hz 10 2 Hz 10 1 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz f also get observable gravitational waves from some SUSY models (NMSSM)

29 Cosmic Strings GW 10 3 Hz 10 2 Hz 10 1 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz LISA inflation Gμ=10-10 Gμ=10-16 BBN CMB Initial LIGO Advanced LIGO LIGO S Hz 10 2 Hz 10 1 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz f DePies & Hogan PRD

30 AGIS-LEO low Earth orbit may be simpler White paper with detailed proposal, backgrounds, etc: arxiv: a: 10 3 M 10 kpc b: 10 5 M 10 Mpc h Hz a LISA b c AGIS LEO c: WD 10 kpc d LIGO d: 10 3 M 10 Mpc Adv LIGO 10 5 Hz 10 4 Hz 10 3 Hz 10 2 Hz 10 1 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz 10 4 Hz f

31 Axion Dark Matter Detection arxiv:

32 Cosmic Axions Strong CP problem: L θ G G creates a nucleon EDM d θ e cm measurements θ

33 Cosmic Axions Strong CP problem: L θ G G creates a nucleon EDM d θ e cm measurements θ the axion is a simple solution: L a f a G G + m 2 aa 2 with m a (200 MeV)2 f a ( ) GeV MHz f a

34 Cosmic Axions Strong CP problem: L θ G G creates a nucleon EDM d θ e cm measurements θ the axion is a simple solution: L a G with f G + m 2 aa 2 a V m a (200 MeV)2 f a ( ) GeV MHz a(t) a 0 cos (m a t) f a a cosmic expansion reduces amplitude a0

35 Cosmic Axions Strong CP problem: L θ G G creates a nucleon EDM d θ e cm measurements θ the axion is a simple solution: L a G with f G + m 2 aa 2 a V m a (200 MeV)2 f a ( ) GeV MHz a(t) a 0 cos (m a t) f a a cosmic expansion reduces amplitude a0 this field has momentum = 0 it is non-relativistic matter the axion is a good cold dark matter candidate

36 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 (10 16 GeV) or Planck (10 19 GeV) scales Axions and WIMPs are the best motivated cold dark matter candidates

37 f a (GeV) Constraints and Searches

38 f a (GeV) Constraints and Searches Axion dark matter

39 f a (GeV) Constraints and Searches Axion dark matter in most models also have: a γ L a f a F F = a f a E B B microwave cavity (ADMX) 10 8

40 f a (GeV) Constraints and Searches Axion dark matter in most models also have: a γ L a f a F F = a f a E B axion-photon conversion suppressed by fa B microwave cavity (ADMX) size of cavity increases with fa signal 1 f 4 a 10 8

41 f a (GeV) Constraints and Searches Axion dark matter in most models also have: a γ L a f a F F = a f a E B axion-photon conversion suppressed by fa B microwave cavity (ADMX) size of cavity increases with fa signal 1 f 4 a 10 8 axion emission affects SN1987A, White Dwarfs, other astrophysical objects

42 f a (GeV) Constraints and Searches Axion dark matter in most models also have: a γ L a f a F F = a f a E B axion-photon conversion suppressed by fa B microwave cavity (ADMX) size of cavity increases with fa signal 1 f 4 a 10 8 axion emission affects SN1987A, White Dwarfs, other astrophysical objects How search for high fa axions?

43 Axion Dark Matter Strong CP problem: L θ G G creates a nucleon EDM d θ e cm the axion: L a f a G G + m 2 aa 2 creates a nucleon EDM d a f a e cm a(t) a 0 cos (m a t) with m a (200 MeV)2 f a ( ) GeV MHz f a

44 Axion Dark Matter Strong CP problem: L θ G G creates a nucleon EDM d θ e cm the axion: L a f a G G + m 2 aa 2 creates a nucleon EDM d a f a e cm a(t) a 0 cos (m a t) with m a axion dark matter is the biggest BEC (200 MeV)2 f a ( ) GeV MHz ρ DM m 2 aa GeV cm 3 f a the axion gives all nucleons a rapidly oscillating EDM

45 Axion Dark Matter Strong CP problem: L θ G G creates a nucleon EDM d θ e cm the axion: L a f a G G + m 2 aa 2 creates a nucleon EDM d a f a e cm a(t) a 0 cos (m a t) with m a axion dark matter is the biggest BEC (200 MeV)2 f a ( ) GeV MHz ρ DM m 2 aa GeV cm 3 f a the axion gives all nucleons a rapidly oscillating EDM thus all (free) nucleons radiate Axion is more observable through its effects on atomic energy levels (significantly different from standard EDM searches)

46 Atomic Axion Searches Unlike a normal EDM search, can look directly for the axion, without external EM fields to modulate the signal instead use internal fields, much larger: E int e A 2 V 1012 m induces a shift to the energy levels: δω E int d n ev

47 Atomic Axion Searches Unlike a normal EDM search, can look directly for the axion, without external EM fields to modulate the signal instead use internal fields, much larger: E int e A 2 V 1012 m induces a shift to the energy levels: δω E int d n ev if cool 10 8 atoms per sec, interferometer lasts ~ 1 sec, and take 10 6 trials ( then shot noise limit is δω 1s 10 1 atoms) ev There are two important caveats: Parity and Schiff s Theorem

48 Parity Breaking Axion breaks parity (CP) Atomic states have very little parity breaking thus Eint d n 0

49 Parity Breaking Axion breaks parity (CP) Atomic states have very little parity breaking thus Eint d n 0 One possible solution: molecules can naturally break parity at O(1), though more difficult to work with due to low-lying modes d n Must control molecular rotation with applied E field (~ 10 6 V/m) Use applied B field (< 0.1 T) to rotate nuclear spin with axion s frequency (easily scanned)

50 Schiff s Theorem Schiff s theorem: in electrostatic equilibrium the E field on any point charge is zero thus Eint d n 0

51 Schiff s Theorem Schiff s theorem: in electrostatic equilibrium the E field on any point charge is zero thus Eint d n 0 higher moments take into account corrections to this (e.g. finite size of nucleus...) Schiff moment: often use Hg or Tl δω E int d S ( 10 9 Z 3) E int d n δω 10 3 E int d n ev

52 Schiff s Theorem Schiff s theorem: in electrostatic equilibrium the E field on any point charge is zero thus Eint d n 0 higher moments take into account corrections to this (e.g. finite size of nucleus...) Schiff moment: δω E int d S ( 10 9 Z 3) E int d n often use Hg or Tl 225 Ra 223 Fr 225 Ac 229 Pa δω 10 3 E int d n ev ev 239 Pu ev ev ev ev

53 Schiff s Theorem Schiff s theorem: in electrostatic equilibrium the E field on any point charge is zero thus Eint d n 0 higher moments take into account corrections to this (e.g. finite size of nucleus...) Schiff moment: δω E int d S ( 10 9 Z 3) E int d n often use Hg or Tl 225 Ra 223 Fr 225 Ac 229 Pa δω 10 3 E int d n ev ev 239 Pu ev ev ev ev half-life 15 d y 22 min 10 d 1.4 d

54 Schiff s Theorem Schiff s theorem: in electrostatic equilibrium the E field on any point charge is zero thus Eint d n 0 higher moments take into account corrections to this (e.g. finite size of nucleus...) Schiff moment: δω E int d S ( 10 9 Z 3) E int d n often use Hg or Tl Argonne Stony Brook 225 Ra 223 Fr 225 Ac 229 Pa δω 10 3 E int d n ev ev 239 Pu ev ev ev ev half-life 15 d y 22 min 10 d 1.4 d NIST cooled polar 40 K 87 Rb to < µk

55 f a (GeV) Molecular Axion Searches Planck GUT Axion dark matter microwave cavity (ADMX) astrophysical constraints

56 f a (GeV) Molecular Axion Searches Planck molecular interferometry can most easily search in khz - MHz frequencies high fa GUT Axion dark matter microwave cavity (ADMX) astrophysical constraints

57 f a (GeV) Molecular Axion Searches Planck molecular interferometry can most easily search in khz - MHz frequencies high fa GUT Axion dark matter microwave cavity (ADMX) 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 astrophysical constraints would be both the discovery of dark matter and a glimpse into physics at very high energies

58 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 under Stanford 4. New ideas?