Fundamental Symmetry Tests with Atoms Michael Romalis Princeton University

Atomic Parity Violation Limits on CP violation from Electric Dipole Moments Tests of CPT and Lorentz symmetries

Atomic parity violation 4/15/2017 Atomic parity violation Parity transformation: Electromagnetic forces in an atom conserve parity [Hatomic, P]=0 Atomic stationary states are eigenstates of Parity But weak interactions maximally violate Parity! Electromagnetic Weak Tiny virtual contribution of Z-boson exchange can be measured! 3

Atomic Parity Violation Experiments Early work: M.-A. Bouchiat, C. Bouchiat (Paris) Sandars (Oxford) Khriplovich, Barkov, Zolotorev (Novosibirsk) Fortson (Seattle) Current Best Measurement – Wieman (Bolder, 1999) Parity mixing on M1 transition 6S1/2  7S1/2 transition in Cs Experimental accuracy on PV amplitude EPV: 0.35%

Relation to Standard Model Parameters 4/15/2017 Relation to Standard Model Parameters Exchange of virtual Z0 boson: Weak charge Qw Nuclear (neutron) distribution Axial-vector electron current and vector current, the other way leads to a non-scalar contribution to Hw In electronic sector the operator reduces to gamma_5 provides parity violation, GF is a Fermi constant and rho_n is a neutron distribution One of the most accurate tests of the SM below Z-pole Best Atomic Calculation in Cs: 0.27% error - Derevianko (Reno, 2009) Phys. Rev. Lett. 102, 181601 (2009) 5

K. Tsigutkin et al, Phys. Rev. Lett. 103, 071601 (2009) Parity violation in Yb Parity violation is enhanced 100 times in Yb because of close opposite-parity states (DeMille, 1995) Atomic calculations will not be as accurate, but one can compare a string of isotopes and measure the anapole moment First observation by Budker with 14 % accuracy (2009) The experiment is improving, needs to reach ~ 1% K. Tsigutkin et al, Phys. Rev. Lett. 103, 071601 (2009) 

Impact on Electroweak Physics

T and CP violation by a permanent EDM Time Reversal: t ® – I d d = I Vector: d  0  violation of time reversal symmetry CPT theorem also implies violation of CP symmetry EDM  T violation  CP violation Relativistic form of interaction: Requires a complex phase

Fundamental Theory - Supersymmetry, Strings EDM Searches Experiments Nuclear Atomic Molecular Neutron n Diamagnetic Atoms Hg, Xe, Rn Paramagnetic Atoms Tl,Cs, Fr Molecules PbO, YbF, TlF Atomic Theory Atomic Theory Atomic Theory Atomic Nuclear Theory Nuclear QCD QCD Quark EDM Quark Chromo-EDM Electron EDM High Energy Theory Fundamental Theory - Supersymmetry, Strings

Discovery potential of EDMs In SM the only source of CP violation is a phase in CKM matrix The EDMs are extremely small, require high-order diagrams with all 3 generations of quarks Almost any extension of the Standard Model contains additional CP-violating phases that generally produce large EDMs. Raw energy sensitivity: Current experiments are already sensitive enough to constrain EDMs from Supersymmetry by a factor of 100 or more Baryogenesis scenarios: Electroweak baryogenesis: EDMs around the corner, somewhat unfavorable based on existing constraints Leptogenesis: No observable EDMs Other (GUT scale, CPT violation): No observable EDMs d ~ em 2 , 10 – 27 e cm ® =100 TeV

Experimental Detection of an EDM Measure spin-precession frequencies B E d m w1 B E d m w1 H = – m × B d E w 1 = 2 m B + dE h w 2 = m B - dE h w 1 – 2 = 4 dE h Statistical Sensitivity: Single atom with coherence time t: N uncorrelated atoms measured for time T >> : dw = 1 t d = h 2 E 1 t TN

Search for EDM of the neutron Historically, nEDM experiments eliminated many proposals for CP violation

ILL neutron EDM Experiment n, 199Hg 40 mHz

Recent nEDM result Complicated effects of motional magnetic field Bm = E  v/c Random motion results in persistent rotating magnetic field Dependance on field gradient dBz/dz  dBr/dr  r V Rotating field causes frequency shift dBz/dz E and B0 into page dn = 0.61.5(stat)0.8(syst) 10-26 ecm |dn| < 3.0  10-26 ecm (90% CL) Factor of 2 improvement C.A. Baker et al Phys. Rev. Lett. 97, 131801 (2006)

Cryogenic nEDM experiments Superthermal production in superfluid 4He N increased by 100 – 10000 He-4 good isolator, low temperature E increased by 5 Superconducting magnetic shields SQUID magnetometers 1m

Electron EDM Sandars, 1965 Thallium: Electron has a finite charge, cannot be at rest in an electric field For purely electrostatic interactions F = eE = 0 — Schiff shielding, 1963 Can be circumvented by magnetic interactions, extended nucleus F = eE+mB = 0, E  0 Enhanced in heavy atoms: Strong spin-orbit magnetic interaction Large Nuclear Coulomb field Relativistic electrons near the nucleus E = Sandars, 1965 Thallium: Cs: 114, Fr: 1150

Berkeley Tl EDM Experiment Mixing chamber Na detectors 590 nm laser beams RF 1 RF 2 Tl detectors Light pipe photodiodes Beam stop Collimating slits E-field (120 kV/cm) State Selector Analyzer 378 nm laser beams B Atomic beams Na (~350 C) Tl (~700 C) 1 m 70 Hz Na atoms used as a co-magnetometer de = (6.9 7.4)10-28 ecm |de| < 1.610-27 ecm (90% C.L.) B. Regan, E. Commins, C. Schmidt, D. DeMille, Phys. Rev. Lett. 88, 071805 (2002)

Only 20% better than Thallium YbF Experiment Polarized polar molecules have very high internal electric field It is hard to generate paramagnetic molecules New Result !!! de= (−2.4 ± 5.7 ± 1.5) × 10−28e cm Only 20% better than Thallium J. J. Hudson, D. M. Kara, I. J. Smallman, B. E. Sauer, M. R. Tarbutt, E. A. Hinds, Nature 473, 493, (2011)

199Hg EDM Experiment 100,000 hours of operation Solid-state Quadrupled UV laser 100,000 hours of operation High purity non-magnetic vessel Hg Vapor cells All materials tested with SQUID Spin coherence time: 300 sec Electrical Resistance: 21016 W 19

Recent improvements in 199Hg Experiment Use four 199Hg cells instead of two to reduce magnetic field noise and have better systematic checks Larger signal due to cell improvements Frequency uncertainty 0.1 nHz w1 w2 inner cells E outer cells w3 E w4 Magnetic Gradient Noise Cancellation Leakage Current Diagnostic S = (w2 - w3) - 1/3 (w1 - w4) L = (w2 + w3) - (w1 + w4) 20

New 199Hg EDM Result d(199Hg) = (0.49±1.29stat±0.76syst)×10−29 e cm About 1 year of data Changed all components of the system: d(199Hg) = (0.49±1.29stat±0.76syst)×10−29 e cm |d(199Hg)| < 3.1×10−29 e cm (95% C.L.) Factor of 7 improvement W. C. Griffith, M. D. Swallows, T. H. Loftus, M. V. Romalis, B. R. Heckel, E. N. Fortson Phys. Rev. Lett. 102, 101601 (2009)

Continued work on 199Hg Still a factor of 10-20 away from shot noise limit Limited by light shift noise, magnetic shield noise Need to find more precisely path of leakage currents Practical cell fabrication issues Steady improvement – factor of 3-5 improvement in ~3 years

Interpretation of nuclear EDM Limits No atomic EDM due to EDM of the nucleus - Schiff’s Theorem Electrons screen applied electric field d(Hg) is due to finite nuclear size nuclear Schiff moment S - Difference between mean square radius of the charge distribution and electric dipole moment distribution Schiff moment induces parity mixing of atomic states, giving an atomic EDM: RA - from atomic wavefunction calculations, uncertainty 50% E I Recent work by Haxton, Flambaum on form of Schiff moment operator B. P. Das et al, V. Dzuba et al. 23

Interpretation of nuclear EDMs gpNN p n The Schiff moment is induced by CP nucleon-nucleon interaction: Due to coherent interactions between the valence nucleon and the core Large uncertainties due to collective effects CP-odd pion exchange dominated by chromo-EDMs of quarks Factor of 2 uncertainty in overall coefficient due to approximate cancellation Other effects: nucleon EDMs, electron EDM, CP-violating nuclear-electron exchange NN N g R S p = Engel, Flambaum g q ) ~ ( 1 d u QCD NN R g - = p Pospelov et al. Sen’kov Oshima Flambaum 24

Jon Engel calculations for 199Hg(2010) isovector

Octupole Enhancement I I Slab ~ e Z A2/3 b2 b32/DE b2 , b3 ~0.1 |+ + = ((1+a)|+ +(1-a)|-)/2 - = ((1-a)|+ +(1+a)|-)/2 |+ + = (|+ + |-)/2 - = (|+ - |-)/2 P, T DE I |- Sintr ~ eZAb2b3 Slab ~ e Z A2/3 b2 b32/DE b2 , b3 ~0.1 Haxton & Henley; Auerbach, Flambaum & Spevak; Hayes, Friar & Engel; Dobaczewski & Engel 223Rn 223Ra 225Ra 223Fr 225Ac 229Pa 199Hg 129Xe t1/2 23.2 m 11.4 d 14.9 d 22 m 10.0 d 1.5 d I 7/2 3/2 1/2 3/2 3/2 5/2 1/2 1/2 Deth (keV) 37 170 47 75 49 5 DEexp (keV) -- 50.2 55.2 160.5 40.1 0.22 105 S (efm3) 1000 400 300 500 900 12000 -1.4 1.75 1028 dA (e cm) 2000 2700 2100 2800 -5.6 0.8

EDM measurement with 225Ra Transverse cooling Oven: 225Ra Zeeman Slower Magneto-optical trap Optical dipole trap EDM measurement EDM measurement with 225Ra Statistical uncertainty: 100 kV/cm 10 s 104 10% 10 days dd = 3 x 10-26 e cm 100 s 106 100 days dd = 3 x 10-28 e cm Phase II 225Ra / 199Hg enhance factor ~ 1,000 dd(199Hg) = 1.5 x 10-29 e cm 27

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Limits on EDMs of fundamental particles 199Hg Atom EDM: Neutron EDM: Electron EDM: 27 e d – d < 6 ´ 10 – e cm d u e ( d + . 5 d )+ 1 . 3 d – . 32 d < 3 ´ 1 – 26 e cm d u d u m d ~ m d < 3 ´ 10 – 26 e e cm e m d CMSSM m1/2 = 250 GeV m0 = 75 GeV tanb = 10 New 199Hg Limit New limits on qm,qA K.A. Olive, M. Pospelov, A. Ritz, and Y. Santoso, PRD 72, 075001 (2005)

More recent EDM Analysis Electron, neutron and Hg limits provide complimentary constraints for some, but not all, possible CP-violating phases Y. Li, S. Profumo, and M. Ramsey-Musolf, JHEP08(2010)062

On to breaking more symmetries … Started with P, C, T symmetries Each symmetry violation came as a surprise Parity violation  weak interactions CP violation  Three generations of quarks CPT symmetry is a unique signature of physics beyond quantum field theory. Provides one of few possible ways to access Quantum Gravity effects experimentally. In each case symmetry violations were found before corresponding particles could be produced directly

A theoretical framework for CPT and Lorentz violation Introduce an effective field theory with explicit Lorentz violation am,bm,cmn,dmn are vector fields in space with non-zero expectation value Vector and tensor analogues to the scalar Higgs vacuum expectation value Surprising bonus: incorporates CPT violation effects within field theory Greenberg: Cannot have CPT violation without Lorentz violation (PRL 89, 231602 (2002) CPT-violating interactions break Lorentz symmetry, give anisotropy signals Can search for CPT violation without the use of anti-particles In contrast, scalar properties of anti-particles (masses, magnetic moments) are likely to be the same L = – y ( m + a g b 5 ) i 2 n c mn d ¶ a,b - CPT-odd c,d - CPT-even Fermions: Alan Kostelecky Although see arXiv:1103.0168

Phenomenology of Lorentz/CPT violation Modified dispersion relations: E2 = m2 + p2 + h p3 Jacobson Amelino-Cameli nm - preferred direction, k ~ h/Mpl Applied to fermions: H = h m2/MPl S·n Non-commutativity of space-time: [xm,xn] = qmn Witten, Schwartz qmn - a tensor field in space, [q] = 1/E2 Interaction inside nucleus: NqmnsmnN  eijkqjkSi Pospelov,Carroll y ¶ k g = m 2 5 ) ( n L Dimention-5 operator: Myers, Pospelov, Sudarsky Spin coupling to preferred direction ) )( ( ab mn q = F L

Experimental Signatures Spin Lorentz violation Spin coupling: S B × - = m ge A e 2 y g L L = – b m y g 5 2b · S c.f. CPT-violating interaction Magnetic moment interaction b is a (four-)vector field permeating all space Experimental Signatures Vector interaction gives a sidereal signal in the lab frame Don’t need anti-particles to search for CPT violation Need a co-magnetometer to distinguish from regular magnetic fields Assume coupling is not in proportion to the magnetic moment bm hn1= 2m1 B + 2b1 (b·nS) hn2= 2m2 B + 2b2 (b·nS) ) ( 2 1 S h n b × ÷ ø ö ç è æ m - = nS – direction of spin sensitivity in the lab

Turn most-sensitive atomic magnetometer into a co-magnetometer! K-3He Co-magnetometer Optically pump potassium atoms at high density (1013-1014/cm3) 2. 3He nuclear spins are polarized by spin-exchange collisions with K vapor 3. Polarized 3He creates a magnetic field felt by K atoms 4. Apply external magnetic field Bz to cancel field BK K magnetometer operates near zero magnetic field 5. At zero field and high alkali density K-K spin-exchange relaxation is suppressed 6. Obtain high sensitivity of K to magnetic fields in spin-exchange relaxation free (SERF) regime Turn most-sensitive atomic magnetometer into a co-magnetometer! B K = 8 p 3 k M He J. C. Allred, R. N. Lyman, T. W. Kornack, and MVR, PRL 89, 130801 (2002) I. K. Kominis, T. W. Kornack, J. C. Allred and MVR, Nature 422, 596 (2003) T.W. Kornack and MVR, PRL 89, 253002 (2002) T. W. Kornack, R. K. Ghosh and MVR, PRL 95, 230801 (2005)

Magnetic field self-compensation

Co-magnetometer Setup Simple pump-probe arrangement Measure Faraday rotation of far-detuned probe beam Sensitive to spin coupling orthogonal to pump and probe Details: Ferrite inner-most shield 3 layers of m-metal Cell and beams in mtorr vacuum Polarization modulation of probe beam for polarimetry at 10-7rad/Hz1/2 Whole apparatus in vacuum at 1 Torr

Have we found Lorentz violation? Rotating K-3He co-magnetometer Rotate – stop – measure – rotate Fast transient response crucial Record signal as a function of magnetometer orientation Have we found Lorentz violation?

Recording Sidereal Signal Measure in North - South and East - West positions Rotation-correlated signal found from several 180° reversals Different systematic errors Any sidereal signal would appear out of phase in the two signals

Long-term operation of the experiment N-S signal riding on top of Earth rotation signal, Sensitive to calibration E-W signal is nominally zero Sensitive to alignment Fit to sine and cosine waves at the sidereal frequency Two independent determinations of b components in the equatorial plane 20 days of non-stop running with minimal intervention

Final results Previous limit |bnxy| = (6.4 ± 5.4) 10-32 GeV Anamolous magnetic field constrained: bxHe-bxe = 0.001 fT ± 0.019 fTstat ± 0.010 fTsys byHe-bye = 0.032 fT ± 0.019 fTstat ± 0.010 fTsys Systematic error determined from scatter under various fitting and data selection procedures Frequency resolution is 0.7 nHz Anamalous electron couplings be are constrained at the level of 0.002 fT by torsion pendulum experiments (B.R. Heckel et al, PRD 78, 092006 (2008).) 3He nuclear spin mostly comes from the neutron (87%) and some from proton (-5%) Friar et al, Phys. Rev. C 42, 2310 (1990) and V. Flambaum et al, Phys. Rev. D 80, 105021 (2009). bxn = (0.1 ± 1.6)10-33 GeV byn = (2.5 ± 1.6)10-33 GeV |bnxy| < 3.7 10-33 GeV at 68% CL J. M. Brown, S. J. Smullin, T. W. Kornack, and M. V. R., Phys. Rev. Lett. 105, 151604 (2010) Previous limit |bnxy| = (6.4 ± 5.4) 10-32 GeV D. Bear et al, PRL 85, 5038 (2000)

Improvement in spin anisotropy limits 199

Recent compilation of Lorentz-violation limits Many new limits in last 10 years 10-33 GeV pl M m b 2 ~ h m - fermion mass or SUSY breaking scale Existing limits: h ~ 10-9 - 10-12 1/Mpl effects are already quite excluded Natural size for CPT violation ? Fine-tuning ? V.A. Kostelecky and N. Russell arXiv:0801.0287v4

Possible explanation for lack Lorentz violation With Supersymmetry, dimension 3 and 4 Lorentz violating operators are not allowed Higher dimension operators are allowed Dimention-5 operators (e.g. ) are CPT- violating, suppressed by MSUSY/MPlanck and are already quite constrained If CPT is a good symmetry, then the dimention-6 operators are the lowest order allowed Dimention-6 operators suppressed by (MSUSY/MPlank)2 ~10-31-10-33, still not significantly constrained, could be the lowest order at which Lorentz violation appears y ¶ h g = m 2 5 ) ( n L Pospelov, Mattingly

CPT-even Lorentz violation = – y ( m + a g b 5 ) i 2 n c mn d ¶ a,b - CPT-odd c,d - CPT-even Maximum attainable particle velocity Implications for ultra-high energy cosmic rays, Cherenkov radiation, etc Many laboratory limits (optical cavities, cold atoms, etc) Models of Lorentz violation without breaking CPT: Doubly-special relativity Horava-Lifshitz gravity Coleman and Glashow Jacobson ) ˆ 1 ( 00 k j jk MAX v c - = Something special needs to happen when particle momentum reaches Plank scale!

Astrophysical Limits on Lorentz Violation Spectrum of Ultra-high energy cosmic rays at Auger: cp-cp < 6 ×10-23 Scully and Stecker Synchrotron radiation in the Crab Nebula: ce < 6 ×10-20 Brett Altschul Spin limits can do better….!

Search for CPT-even Lorentz violation with nuclear spin Need nuclei with orbital angular momentum and total spin >1/2 Quadrupole energy shift due to angular momentum of the valence nucleon: Previously has been searched for in two experiments using 201Hg and 21Ne with sensitivity of about 0.5 mHz Bounds on neutron cn<10-27 – already most stringent bound on c coefficient! I,L pn Suppressed by vEarth

21Ne-Rb-K co-magnetometer Replace 3He with 21Ne A factor of 10 smaller gyromagnetic ratio of 21Ne gives the co-magnetometer 10 times better energy resolution for anomalous interactions Use hybrid optical pumping KRb21Ne Allows control of optical absorption of pump beam, operation with 10 times higher Rb density, lower 21Ne pressure. Overcomes faster quadrupole spin relaxation of 21Ne Eventually expect a factor of 100 gain in sensitivity over K-3He co-magnetometer Overall, the experimental procedure is identical except the signal can be at either 1st or 2nd harmonic of Earth rotation rate

Search for CPT-even Lorentz violation with 21Ne-Rb-K co-magnetometer About 2 month of data collection Just completed preliminary analysis Sensitivity is about a factor of 100 higher than previous experiments Limited by systematic effects due to Earth rotation N-S E-W Tensor frequency shift resolution ~ 4 nHz Earth rotation signal is ~10 times larger in magnetic field units Causes extra drift of N-S signal due to changes in sensitivity

Results of Tensor Lorentz-Violation Search × 10-29 East-West North-South Comb. cxx-cyy 0.86 ±1.1 ±0.56 3.6 ±2.8 ±1.6 1.2 ±1.1 cxx+cyy 0.14 ±1.1 ±0.56 0.57 ±2.8 ±1.6 0.19 ±1.1 cyz+czy 5.2 ±3.9 ±2.1 -4.2 ±15 ±18 4.8 ±4.3 cxz+czx -4.1 ±2.2 ±2.4 17 ±14 ±13 -3.5 ±3.2 2 w 1 w Constrain 4 out of 5 spatial tensor components of cmn at 10-29 level Improve previous limits by 2 to 3 orders of magnitude Most stringent constrains on CPT-even Lorentz violation! Assume Schmidt nucleon wavefunction – not a good approximation for 21Ne – need a better wavefunction Assume kinetic energy of valence nucleon ~ 5 MeV

Recent compilation of Lorentz limits 10-33 GeV pl M m c 2 ~ h m - SUSY breaking scale? h >1 allowed for m =1 TeV Natural size for CPT-even Lorentz violation ? Need to get to c ~ 10-31-10-32 10-29 GeV V.A. Kostelecky and N. Russell arXiv:0801.0287v4

Systematic errors Most systematic errors are due to two preferred directions in the lab: gravity vector and Earth rotation vector If the two vectors are aligned, rotation about that axis will eliminate most systematic errors Amundsen-Scott South Pole Station Within 100 meters of geographic South Pole No need for sidereal fitting, direct measurement of Lorentz violation on 20 second time scale!

Conclusions Precision atomic physics experiments have been playing an important role in searches for New Physics Currently severely constrain CP violation beyond the Standard Model Place stringent constraints on CPT and Lorentz violation at the Planck scale Important constraints on spin-dependent forces, variation of fundamental constants, other ideas.