Searches for Lorentz violation in 3 He/ 129 Xe clock comparison experiments Outline:  Features of frequency standards and clocks  3 He/ 129 Xe „spin“-clock  Conclusion and outlook  3 He/ 129 Xe clock-comparison experiments W.Heil SSP2012, Groningen

Current accuracy: Microwave: 6 x Optical : 3 x Stable frequency Local oscillator sensitivity (absolute scale):  mHz  1 ns / day  „nuclear spin -clock“ better: reference transition at f  1 Hz with  f /f  second = 9,192, 631,770 cycles

detector Clock based on nuclear spin precession „ spin-clock“ (ms ) signal (a.u.) (G. D. Cates, et al., Phys. Rev. A 37, 2877)

Spin-clock: Detection of free spin precession :  long spin coherence times T 2 * > 1  f/f ~  free spin precession: no induced frequency shifts due to feedback phase error, light shift, etc. (Maser, Cs-M )  use of LT c -SQUIDs to detect the spin precession signal - intrinsic noise of SQUID:  1 fT/  Hz  no feedback coupling between detector and spin sample

Accuracy of frequency determination: # data points Fourier width If the noise w[n] is Gaussian distributed, the Cramer-Rao Lower Bound (CRLB) sets the lower limit on the variance example: SNR = 10000:1, = 1 Hz, T= 1 day  < >  x  0.1  m /day D=10 cm T

 n =  K  He =  K J  Xe 129 He 3  Xe =  K 3 He/ 129 Xe „spin“-clock OP-techniques: MEOP SEOP Schmidt-model:

BMSR 2, PTB Berlin 6 cm 3 He (4.5 mbar ) J. Bork, et al., Proc. Biomag 2000, 970 (2000). The 7-layered magnetically shielded room (residual field < 2 nT) LT c - SQUID magnetic guiding field  0.4  T (Helmholtz-coils)

3 He free spin-precession signal R d SQUID parameters: p He = 1-3 mbar ; P = 10-50% R =2.9 cm; d = 6cm   B = pT Signal: Note: At present, the Xe spin coherence time T 2 * is limited to due to wall relaxation 3 h < T 2 * < 4 h system noise inside BMSR-2 ~ 2 fT/  Hz

Test of CRLB via Allan Standard Deviation (ASD) Non-gaussian noise: magnetic field drifts intrinsic noise … 2  [s] ii+1 

B [nT] t [h] drift ~ 1pT/h 3 He / 129 Xe clock comparison to get rid of magnetic field drifts 129 Xe 3 He (4,7 Hz) (13 Hz) !    Hz/h B0B0

I. Earth‘s rotation II.  =  He -  He /  Xe   Xe  rem =  -  Earth  rem Subtraction of deterministic phase shifts  uncertainties in subtraction of  Earth  chemical shift: BoBo non-ideal spherical cell: Ramsey-Bloch-Siegert shift (self shift) Phase residuals +  (t) spin-coupling

ASD of phase residuals

The detection of the free precession of co-located 3 He/ 129 Xe sample spins can be used as ultra-sensitive probe for non-magnetic spin interactions of type:  Search for a Lorentz violating sidereal modulation of the Larmor frequency  Search for spin-dependent short-range interactions  Search for EDM of Xenon  … Observable:

Search for a Lorentz violating sidereal modulation preferred direction in space-time

SM: relativistic quantum field theory electromagnetic force weak force strong force gravitation General relativity is a classical theory, i.e., non-quantum Standard Model (SM) of particle physics Unification theories: string theory, loop quantum gravity,.. Planck scale: energy scale where gravity meets quantum physics M p ~ GeV Courtesy of C. Lämmerzahl A closer look…

Kostelecký, Perry, Pot, Samuel ’89; ’90; ’91; ’95; '00 Spontaneous Lorentz symmetry breaking in string theory e.g. Lorentz vector field makes non zero vacuum expectation value low-energy world Planck scale  GeV Background fields (tensor fields) give preferred direction e.g. rest frame of CMB D. Colladay and V.A. Kostelecky, Phys. Rev. D 55, 6760 (1997); Phys.Rev. D 58, (1998)  talk of Ralf Lehnert

Michelson (1881,Potsdam) Michelson&Morley (1887,Cleveland) c(  ) = c photon sector: Traditional tests of Lorentz symmetry & special relativity 19 independent parameters Li + - ions C.Novotny et al., PR A 80 (2009) ESR at GSI relativistic Doppler effect c(v) = c

Test of constancy of c Kennedy,Thorndike 1932 Hils,Hall 1990 Braxmaier 2002 Wolf 2004 Herrmann 2009 Resonators Interferometers Year

Topics: searches for CPT and Lorentz violations involving -birefringence and dispersion from cosmological sources -clock-comparison measurements -CMB polarization -collider experiments -electromagnetic resonant cavities -equivalence principle -gauge and Higgs particles -high-energy astrophysical observations -laboratory and gravimetric tests of gravity -matter interferometry -neutrino oscillations -oscillations and decays of K, B, D mesons -particle-antiparticle comparisons -space-based missions -spectroscopy of hydrogen and antihydrogen -spin-polarized matter * Theoretical studies of CPT and Lorentz biviolation involving -physical effects at the level of the SM, General Relativity, and beyond -origins and mechanisms for violations classical and quantum issues in field theory, particle physics, gravity, and strings Modern Tests of Lorentz violation

Modified Dirac equation for a free spin ½ particle (w=e,p,n) standard DECPT violatingCPT preserving terms A. Kostelecky and C. Lane: Phys. Rev. D 60, (1999) Lorentz violating terms Standard-Model Extension Experimental access: Cs- fountain Torsion pendulum Antihydrogen spectroscopy Astrophysics Hg/Cs comparison UCN/Hg comparison He/Xe maser K/He co-magnetometer coupling strength  clock comparison experiments Wolf et al., B.Heckel et al. PRD 78 (2008) matter sector -

C Coupling of spin to background field: Zeeman LV  LAB cosmic microwave background v = 368 km/s  T dip  3.3 mK

Search for a sidereal modulation of the weighted phase difference  rem  rem =  He -  He /  Xe   Xe -  Earth  s = 2  /T SD = 2  /(23 h :56 m :4.091 s ). expect strong correlated error for total data-taking time:  90 h March 2009 run:

Results of  2 -fit for the sidereal phase amplitudes a c and a s together with their correlated and uncorrelated 1  -errors. a c mrad a s mrad To demonstrate the strong dependence of the correlated error on  s, corresponding fit results are shown for multiples of  s :  ’ s = g  s Phase residuals with fit-results for Phaseamplitude of the sidereal modulation:

Kostelecky et al., Phys. Rev. D 60, (1999) 3 He: µ = µ K 129 Xe: µ = µ K n : µ = µ K Schmidt-Model free neutron: (X,Y,Z) non-rotating frame with Z along Earth‘s rotation axis Lab-frame with quantization axis z In terms of frequency: (95% C.L.) PTB Berlin:  = 52, north  = 28 0 (north-south) PRD 82 (2010)

Coefficient Proton Neutron Electron < < < <  Torsion pendulum B.R.Heckel et al., PRD 78 (2008) K- 3 He co-magnetometer J. M. Brown et al. Phys. Rev. Lett., 105, (2010). Spin maser experiments with 3 He and 129 Xe ( D.Bear et al., PRL 85 (2000) 5038 ) (95% C.L.) = e Tightest constrains on SME parameters on neutron sector: our result:

March 2012 run at PTB (1) conventional runs with B-field fixed (2) active rotation of B-field (2 h / turn)

T 2 * - improvements: FID-Amplitude ( fT ) pure 3 p=2.5 mbar : Gas mixture: p He = 2.7 mbar, p Xe = 4.9 mbar, p N2 = 24.8 mbar

Phase residuals: March 2009 subrun for comparison (shifted by 0.04 rad)  gain in SNR: 2-3  gain due to CRLB power law (~1/T 3/2 ) : 2.8  reduction of correlated error: ~ 7  total data taking time: 165 h (90 h March 2009 ) ~1.8 overall gain in sensitivity: ~ 100

(2) rotation of B-field (quantization axis) 5 subruns (~ 14 h each) BMSR-2 N S expected LV-signal: … field rotation (45 0 ) : 2.5 min measurement (static): 12.5 min … Sequence:

Change of the absolute field gradient during rotation and its effect on T 2 * data analysis ongoing

Conclusion and Outlook  3 He, 129 Xe spin clock based on free spin precession  long spin coherence times (, March 2012 run ) Search for neutron spin coupling to a Lorentz and CPT-violating background field K- 3 He and 3 He/ 129 Xe co-magnetometer set the tightest limits on SME-parameters K- 3 He co-magnetometer : 3 He- 129 Xe co-magnetometer : PRL 105, (2010) PRD 82, (2010) March 2012 run: expected gain in sensitivity ~ 100 to trace LV interactions

Short range spin-dependent interaction: J.E.Moody, F.Wilczek PRD 30 (1984) 130 September 2010 run 129 Xe electric dipole moment (Groningen-Heidelberg-Mainz collaboration): Proposal: present sensitivity of 3 He/ 129 Xe-comagnetometer: < 0.1 nHz per day Rosenberry and Chupp, PRL 86,22 (2001) ecm  Magnetometry ( 3 He)magnetometer for nEDM experiment at PSI high field : > 1 Tesla low field :  1  Tesla beat signal (a.u.) time 1.5 T ultra-high sensitive magnetometer to monitor relative field changes of 

Institut für Physik, Universität Mainz: C. Gemmel, W. Heil, H.Hofsetz, S. Karpuk, Y. Sobolev, K. T. Physikalisch-Technische-Bundesanstalt, Berlin: M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg: F. Allendinger, U. Schmidt 3 He/ 129 Xe clock comparison probing fundamental symmetries K.Tullney Thank you for your attention

Search for a new pseudoscalar boson (Axion-like particle) Original proposal for Axion ( R. Peccei, H.Quinn PRL 38(1977),1440) as possible solution to the „Strong CP Problem“ that cancels the CP violating term in the QCD Lagrangian from neutron EDM we get : Modern interest: Dark Matter candidate. All couplings to matter are weak Axions, if they exist, will be very light and will mediate a macroscopic CP- force energy scale P.Q.-symmetry is spontaneously broken Gerardus 't Hooft,: QCD has a non-trivial vacuum structure that in Gerardus 't Hooft principle permits CP-violation

Galactic axions Tunable resonant cavity in magnetic field coupled to a ultra low noise microwave receiver ADMX, CARRACK 8 Tesla Axions generated in the sun Laboratory axions Polarised laser through vacuum in a strong magnetic field (PVLAS) AXION SEARCHES using the Primakoff Effect ** ** 1GHz: 4  eV E a  4 KeV “Light shines through the wall”

If axions are dark matter, they are a relic of the early universe. A particular scenario coupled with the requirement that the axion mass density not severely overclose the universe results in a lower bound to the axion mass. CAST Current Axion Search Experiments  Solar Axion Telescope – „CAST“  Dark Matter Axion Search – „ADMX“  Vacuum Optical Properties –“PVLAS“ etc.  Photon Disappearance Experiments  New Force Search – Torsion Pendulums, etc.

Short range interaction of the axion (Moody and Wilczek PRD (1984)) Yukawa-type potential with monopole-dipole coupling: axion gsgs gpgp N N nn nn F axion polarized matter unpolarized matter N n N

How to measure? 3 He Position: Close unpolarized matter (Pb-glass, BGO) 3 He Position: Far Requirement:

3 He/ 129 Xe cell Pb-glass (2009 run) BGO crystal (2010 run) Dewar housing the LT c -SQUIDs

Data processing for extraction of short-range interaction effect: 1.To cancel magnetic field influence we calculate the weighted phase difference: 2. Temporal dependence can be described by: CloseFar t0t0 Earth rotation chemical shift short range  Ramsey-Bloch-Siegert-Shift f(t)= c+(a ER +a CS +a SR )  t+a He  e -t/T2,He +a Xe  e -t/T2,Xe  SR =(a SR,close - a SR,far )   He  Xe  

Results Analysis: Average potential was calculated numerically for our cells ( Ø = 6 cm, l = 6 cm), a gap of 2.2 mm between cell inner volume and BGO crystal ( Ø = 57 mm, l = 81 mm). Due to the inequation /h < Δ(  ) the sensitivity level of g S g P can be determined by: g S g P ) B0B0 September 2010: 11 measurements (~9 hours) gap = 2.2 mm Mass sample: BGO crystal with density ρ=7.13 g/cm³ =>  SR = (-0.78 ± 1.22 ± 0.15) nHz  SR [nHz]  corr. [nHz]  uncorr. [nHz] C53-R C54-R C55-L C60-L C63-L C65-L C67-R C68-R C71-R C80-L C82-L LR

Exclusion Plot for new spin-dependent forces Adelberger 2011 our result 2010 our result 2009 Youdin 1996 Ni 1999 Hammond 1993 gap of 0.5 mm

Search for a Xe EDM I I I 129 Xe Xe EDM search short range int. CKM-C ̷ P too small to produce observed baryon asymmetry Standard-model: P,T transformation of spin and EDM

particle EDM hadron EDM nuclear EDM atomic EDM observable EDM

3   

Atomic EDM‘s  L.I.Schiff ( PR ,1963): System of non-relativistic charged point particles that interact electrostatically can not have an EDM  Heavy atoms (relativistic treatment):  d e  0  d atom  0 ~ Z 3  2 d e  P,T-odd eN interaction Tensor-Pseudotensor ~Z 2 G F C T Scalar- Pseudoscalar ~Z 3 G F C S  Nuclear EDM – finite size Schiff moment induced by P,T-odd N-N interaction ~  [ecm] Ginges & Flambaum, Phys. Rep. 397 (04) 63. Dzuba, Flambaum, Ginges, Phys. Rev. A 66 (02)  Diamagnetic atoms: [ecm] Parameter 199 HgBest alternate limit d e (e cm) 3.0  YbF:1.0  d n (e cm) 5.8  n: 2.9  CSCS 5.2  Tl:2.4  CTCT 1.5  TlF:4.5  C PS 5.1  TiF: 3   8.0  Xe: 5   less sensitive to CP violating interactions E ext E int - ++ E ext +E int =0 PRL 102, (2009)

Measurement sensitivity: 129 Xe electric dipole moment EoEo  E   E  BoBo E E Then we will reach … after 100 days of data taking: from 2010 run:  = day assume : E=2 kV/cm Observable: weighted frequency difference sensitivity limit: Rosenberry and Chupp, PRL 86,22 (2001) ecm

Xe/3He polarizer Dewar with SQUIDs 5 layer  -metal shield eddy current shield 3D field compensation University of Mainz KVI Groningen University of Heidelberg PTB Berlin Collaboration: Proposed setup  Lorentz-invariance tests  short range interations There is room for improvements:  Increase of SNR of Xe (P xe : 10%  70%)  Increase of T 2,Xe 5h (at present)  h   d Xe < ecm …new sensitivity levels for

Optical Pumping LASER absorption … …reemission of fluorescence light …transfer of angular momentum Rb-pumping 5 s 1/2 5 p 1/2 2/3 1/3 m = -1/2m = +1/2 T1T1 P = N( 1/2 ) – N( -1/2 ) N( 1/2 ) + N( -1/2 ) = 1 – (2/3) n rate equation: ++ BoBo

Optical Pumping of 3 He history : ● Spin exchange with optically pumped Rb-vapour ( SEOP ) ( Bouchiat et al., Phys. Rev. Lett. 5 (1960) 373 ) ● Optical pumping of metastable 3 He * -atoms ( MEOP ) ( Colegrove et al., Phys. Rev. 132 (1963) 2561 ) Rb 3 He p He  1 mbar p He  1-10 bar 3 He * 3 He 3 He *

MEOP: Metastabilty Exchange Optical Pumping 3 He *  1ppm L.D. Schearer 3 He : 1 mbar

Kostelecky et al., Phys. Rev. D 60, (1999) 3 He: µ = µ K 129 Xe: µ = µ K n : µ = µ K Schmidt-Model free neutron: (X,Y,Z) non-rotating frame with Z along Earth‘s rotation axis Lab-frame with quantization axis z In terms of frequency: (95% C.L.) PTB Berlin:  = 52, north  = 28 0 (north-south)

Feedback loop to get long coherence times … ( Cs-Magnetometer, Maser, … ) but …  frequency shifts due to feedback phase error  light shift  …

TSR (HD) : ß = ESR(GSI) : ß = 0.34 Ch.D.Lane, PRD 72 (2005) β (moving clock) Laser P Laser A metastable 7 Li + - ions Lamb dip

Clock-comparison experiments Kostelecky et al., arXiv: v2

Antihydrogen Spectroscopy (  J. Walz ) Torsion pendulum B.R.Heckel et al., PRD 78 (2008) spin-coupled interactions

Fundamental physics tests using Rb and Cs fountains Observable free of 1st order Zeeman-effect Wolf et al.,

  : Earth‘s rotation frequency       : Earth‘s orbital motion

Relaxation of 129 Xe (measured)

Magnetic field (measured via the He spin precession signal ) in presence of a conductor ( aluminium cylinder : diameter 56 mm, length 70 mm) removal of aluminium block Johnson noise paramagnetic effects

(l, b) = (264 o.31±0 o.04±0 o.16, +48 o.05±0 o.02±0 o.09) galactic coordinate system horizon coordinate system (observer's local horizon) PTB-Berlin (52° 31´ north, 13° 25´ east) measurement on at CMB dipole v = 368 km/s  T dip  3.3 mK

Prototype of cylindrical  -metal shield no elevated system noise inside inner shield made out of metglas (amorphous metal alloy ribbon)

Lead glass samples Ø 57 mm H = 81 mm Density = 3.9 g/cm 3

1083 nm MEOP Polarizer Mainz: 3 He SEOP Polarizer PTB: Xe He Xe N2N2

(Cohen-Tannoudji et al., PRL 22 (1969),758) Detection of magnetic field produced by oriented nuclei Results:  3 He spin precession: T 2 * = 2h 20min  sensitivity of Rb-magnetometer: BW 0.3 Hz  P He  4 mbar Improvement of measurement sensitivity:  fT/  Hz  laser for OP of 3 P> 70%  longer T 2 *-times (needed !!!) tesla tesla

False effects : Barometric formula : assume: S He S Xe x x h B0B0  = ½ ( Δ right sample - Δ left sample ) = (4.8 ± 7.0 ± 0.4) nHz drops out in From the measured value of  we get: g S g P )

1 day Gain in sensitivity compared to measurements with short coherence times: Example „short spin coherence time“:  T = 5 min   300  less sensitive ! arbitrary phase