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Fundamental Symmetry Tests with Atoms Michael Romalis Princeton University

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1.Atomic Parity Violation 2.Limits on CP violation from Electric Dipole Moments 3.Tests of CPT and Lorentz symmetries

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

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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 6 S 1/2 7 S 1/2 transition in Cs Experimental accuracy on PV amplitude E PV : 0.35%

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Relation to Standard Model Parameters Exchange of virtual Z 0 boson: Weak charge Q w Nuclear (neutron) distribution Best Atomic Calculation in Cs: 0.27% error - Derevianko (Reno, 2009) Phys. Rev. Lett. 102, (2009)

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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, (2009)

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Impact on Electroweak Physics

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

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

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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 22, 10 –27 ecm =100 TeV

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Experimental Detection of an EDM H=– B–d E 1 = 2 +2dE h 2 = 2 B 2 h 1 – 2 = 4 h Single atom with coherence time N uncorrelated atoms measured for time T >> : Statistical Sensitivity: BE d 11 BE d 11 Measure spin-precession frequencies = 1 d= h 2E 1 2 TN

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

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ILL neutron EDM Experiment 40 mHz n, 199 Hg

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Complicated effects of motional magnetic field B m = E v/c Random motion results in persistent rotating magnetic field Dependance on field gradient dB z /dz dB r /dr r Recent nEDM result dB z /dz d n = 0.6 1.5(stat) 0.8(syst) ecm |d n | < 3.0 ecm (90% CL) Factor of 2 improvement C.A. Baker et al Phys. Rev. Lett. 97, (2006) Rotating field causes frequency shift E and B 0 into page V V

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Cryogenic nEDM experiments Superthermal production in superfluid 4 He N increased by 100 – He-4 good isolator, low temperature E increased by 5 Superconducting magnetic shields SQUID magnetometers 1m1m

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Electron EDM 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+ B = 0, E 0 Enhanced in heavy atoms: Strong spin-orbit magnetic interaction Large Nuclear Coulomb field Relativistic electrons near the nucleus Cs: 114, Fr: 1150 E =0 Sandars, 1965 Thallium:

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Berkeley Tl EDM Experiment Na atoms used as a co-magnetometer 70 Hz d e = (6.9 7.4) e cm |d e | < 1.6 e cm (90% C.L.) B. Regan, E. Commins, C. Schmidt, D. DeMille, Phys. Rev. Lett. 88, (2002)

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YbF Experiment Polarized polar molecules have very high internal electric field It is hard to generate paramagnetic molecules New Result !!! d e = (−2.4 ± 5.7 ± 1.5) × 10 −28 e 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)

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

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Recent improvements in 199 Hg Experiment Use four 199 Hg 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 11 22 33 44 inner cells outer cells Magnetic Gradient Noise Cancellation Leakage Current Diagnostic S = E E L =

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

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Continued work on 199 Hg Still a factor of 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

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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: R A - 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.

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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 Interpretation of nuclear EDMs g NN n p Engel, Flambaum NNN gRS ) ~~ ( )1( duQCDNN ddRg Pospelov et al. g qq Sen’kov Oshima Flambaum

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Jon Engel calculations for 199 Hg(2010) isovector

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Octupole Enhancement I I |+ || EE P, T S intr ~ eZA 2 3 S lab ~ e Z A 2/3 2 E 223 Rn 223 Ra 225 Ra 223 Fr 225 Ac 229 Pa 199 Hg 129 Xe t 1/ 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 1/21/2 e th (keV) E exp (keV) S (efm 3 ) d A (e cm) 2, Haxton & Henley; Auerbach, Flambaum & Spevak; Hayes, Friar & Engel; Dobaczewski & Engel

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

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199 Hg Atom EDM: Neutron EDM: Electron EDM: Limits on EDMs of fundamental particles d e <3 –26 m e m d ecm e(d d +0.5d u )+1.3d d –0.32d u <3 –26 ecm ed d –d u <6 – 27 ecm d ~ m New 199 Hg Limit CMSSM m 1/2 = 250 GeV m 0 = 75 GeV tan = 10 K.A. Olive, M. Pospelov, A. Ritz, and Y. Santoso, PRD 72, (2005) New limits on , A

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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

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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

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A theoretical framework for CPT and Lorentz violation Introduce an effective field theory with explicit Lorentz violation a ,b ,c ,d 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, (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 = – (m+a +b 5 ) + i 2 ( +c +d 5 ) a,b - CPT-odd c,d - CPT-even Fermions: Alan Kostelecky Although see arXiv:

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Modified dispersion relations: E 2 = m 2 + p 2 + p 3 Jacobson Amelino-Cameli n - preferred direction, ~ /M pl Applied to fermions: H = m 2 /M Pl S·n Non-commutativity of space-time: [x ,x ] = Witten, Schwartz - a tensor field in space, [ Interaction inside nucleus: N N ijk jk S i Pospelov,Carroll Phenomenology of Lorentz/CPT violation 2 5 )(n L ))(( FFF L Myers, Pospelov, Sudarsky Spin coupling to preferred direction Dimention-5 operator:

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Experimental Signatures Spin coupling: L =–b 5 =–2b · S c.f. Spin Lorentz violation 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 h 1 = 2 1 B + 2 1 (b·n S ) h 2 = 2 2 B + 2 2 (b·n S ) )( S h nb n S – direction of spin sensitivity in the lab b is a (four-)vector field permeating all space CPT-violating interaction Magnetic moment interaction bb SB m ge Ae 2 L

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K- 3 He Co-magnetometer 1.Optically pump potassium atoms at high density ( /cm 3 ) 2. 3 He nuclear spins are polarized by spin-exchange collisions with K vapor 3. Polarized 3 He creates a magnetic field felt by K atoms 4. Apply external magnetic field B z to cancel field B K 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 3 0 M He J. C. Allred, R. N. Lyman, T. W. Kornack, and MVR, PRL 89, (2002) I. K. Kominis, T. W. Kornack, J. C. Allred and MVR, Nature 422, 596 (2003) T.W. Kornack and MVR, PRL 89, (2002) T. W. Kornack, R. K. Ghosh and MVR, PRL 95, (2005)

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Magnetic field self-compensation

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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 -metal Cell and beams in mtorr vacuum Polarization modulation of probe beam for polarimetry at rad/Hz 1/2 Whole apparatus in vacuum at 1 Torr

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

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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

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Long-term operation of the experiment 20 days of non-stop running with minimal intervention 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

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Final results Anamolous magnetic field constrained: x He x e = fT ± fT stat ± fT sys y He y e = fT ± fT stat ± fT sys Systematic error determined from scatter under various fitting and data selection procedures Frequency resolution is 0.7 nHz Anamalous electron couplings b e are constrained at the level of fT by torsion pendulum experiments (B.R. Heckel et al, PRD 78, (2008).) 3 He 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, (2009). b x n = (0.1 ± 1.6) 10 GeV b y n = (2.5 ± 1.6) 10 GeV |b n xy | < 3.7 10 GeV at 68% CL Previous limit |b n xy | = (6.4 ± 5.4) 10 32 GeV D. Bear et al, PRL 85, 5038 (2000) J. M. Brown, S. J. Smullin, T. W. Kornack, and M. V. R., Phys. Rev. Lett. 105, (2010)

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Improvement in spin anisotropy limits 199

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

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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 M SUSY /M Planck 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 (M SUSY /M Plank ) 2 ~ , still not significantly constrained, could be the lowest order at which Lorentz violation appears 2 5 )(n L Pospelov, Mattingly

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CPT-even Lorentz violation 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 L = – (m+a +b 5 ) + i 2 ( +c +d 5 ) a,b - CPT-odd c,d - CPT-even ) ˆˆˆ 1( 000kjjkjjMAX vvcvcccv Coleman and Glashow Jacobson Something special needs to happen when particle momentum reaches Plank scale!

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

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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 201 Hg and 21 Ne with sensitivity of about 0.5 Hz Bounds on neutron c n <10 – already most stringent bound on c coefficient! Suppressed by v Earth I,L pnpn

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

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Search for CPT-even Lorentz violation with 21 Ne-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

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Results of Tensor Lorentz-Violation Search × East-WestNorth-SouthComb. c xx c yy c xx +c yy c yz +c zy c xz +c zx Constrain 4 out of 5 spatial tensor components of c at 10 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 21 Ne – need a better wavefunction Assume kinetic energy of valence nucleon ~ 5 MeV

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

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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!

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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.

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