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Experimentalist’s Motivation

New limits on spin-dependent Lorentz- and CPT-violating interactions Michael Romalis Princeton University. D E. Spin Up. Spin Down. Experimentalist’s Motivation. Is the space truly isotropic? Remove magnetic field, other known spin interactions Remove the Earth.

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Experimentalist’s Motivation

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  1. New limits on spin-dependent Lorentz- and CPT-violating interactionsMichael RomalisPrinceton University

  2. DE Spin Up Spin Down Experimentalist’s Motivation • Is the space truly isotropic? • Remove magnetic field, other known spin interactions • Remove the Earth Is there still an “Up” and a “Down” ? First experimentally addressed by Hughes, Drever (1960) V.W. Hughes et al, PRL 4, 342 (1960) R. W. P. Drever, Phil. Mag 5, 409 (1960); 6, 683(1961)

  3. Well, we are actually moving relative to CMB rest frame • Space and time vector components mix by Lorentz transformation • A test of spatial isotropy becomes a true test of Lorentz invariance (i.e. equivalence of space and time) v = 369 km/sec ~ 10-3 c Is the space really isotropic? –ask astrophysicists • Cosmic Microwave Background Radiation Map • The universe appears warmer on one side!

  4. – m m y g g g y = ( m + a + b ) + L m m 5 i n m m y g g g g ¶ y ( + c + d ) n mn mn 5 2 A theoretical framework for Lorentz violation • Introduce an effective field theory with explicit Lorentz violation • am,bm,cmn,dmn arevector 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 a,b- CPT-odd c,d - CPT-even Fermions: Alan Kostelecky Although see arXiv:1103.0168v1

  5. m 2 Spin coupling to preferred direction = y g h ¶ y L ( n ) m 5 mn ab = q L ( F )( F F ) mn ab Phenomenology of Lorentz/CPT violation • Modified dispersion relations: E2 = m2 + p2 + h p3Jacobson Amelino-Cameli • nm - preferred direction, h ~ 1/Mpl • Applied to fermions: H = h m2/MPlS·n • Non-commutativity of space-time: [xm,xn] = qmnWitten, Schwartz • qmn - a tensor field in space, [q] = 1/E2 • Interaction inside nucleus: NqmnsmnNeijkqjkSiPospelov,Carroll Effective Lagrangian: Myers, Pospelov, Sudarsky

  6. Magnetic Field Linearly Polarized Probe light Circularly Polarized Pumping light Magnetization Magnetization Summary of SERF Atomic Magnetometer Alkali metal vapor in a glass cell • Cell contents • [K] ~ 1014 cm-3 • He buffer gas, N2 quenching z Polarization angle rotation  By x y

  7. p 8 k B = M 3 0 He K 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! 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)

  8. Magnetic field self-compensation

  9. Magnetic field sensitivity • Sensitivity of ~1 fT/Hz1/2 for both electron and nuclear interactions • Frequency uncertainty of 20 pHz/month1/2 for 3He 20 nHz/month1/2 for electrons • Reverse co-magnetometer orientation every 20 sec to operate in the region of best sensitivity Best operating region

  10. 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?

  11. 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

  12. Final results • 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)

  13. Improvement in spin anisotropy limits

  14. Natural size for CPT violation ? m - fermion mass or SUSY breaking scale 2 m h b ~ Existing limits: h ~ 10-9- 10-12 M pl 1/Mpl effects are quite excluded Need 10-37GeV for 1/Mpl2 effects Recent compilation of CPT limits Many new limits in last 10 years 10-33 GeV V.A. Kostelecky and N. Russell arXiv:0801.0287v3

  15. – m m y g g g y = ( m + a + b ) + L m m 5 i n m m y g g g g ¶ y ( + c + d ) n mn mn 5 2 = - - - ˆ ˆ ˆ v c ( 1 c c v c v v ) MAX 00 0 j j jk j k CPT-even Lorentz violation • Maximum attainable particle velocity • Implications for ultra-high energy cosmic rays, Cherenkov radiation, etc • Best limit c00 ~ 10-23 from Auger ultra-high energy cosmic rays • Many laboratory limits (optical cavities, cold atoms, etc) • Motivation for Lorentz violation (without breaking CPT) • Doubly-special relativity • Horava-Lifshitz gravity a,b- CPT-odd c,d - CPT-even Coleman and Glashow Jacobson Something special needs to happen when particle momentum reaches Plank scale!

  16. Search for CPT-even Lorentz violation with nuclear spin • Need nuclei with orbital angular momentum and total spin >1/2 • Quadrupole energy shift proportional to the kinetic energy of the valence nucleon • Previosly 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! Suppressed by vEarth

  17. First results with Ne-Rb-K co-magnetometer • Replace 3He with 21Ne • A factor of 10 smaller gyromagnetic ratio of 21Ne makes the co-magnetometer have 10 times better energy resolution for anomalous interactions • Use hybrid optical pumping KRb21Ne • Allows control of optical density for pump beam, operation with 1015/cm3 Rb density, lower 21Ne pressure. • Eventually expect a factor of 100 gain in sensitivity • Differences in physics: • Larger electron spin magnetization (higher density and larger k0) • Faster electric quadrupole spin relaxation of 21Ne • Quadrupole energy shifts due to coherent wall interactions Sensitivity already better than K-3He Fast damping of transients

  18. 21Ne Semi-sidereal Fits • Data not perfect, but already an order of magnitude more sensitive than previous experiments N-S A< 1 fT E-W

  19. 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!

  20. Classic axion-mediated forces • Monopole-Monopole: • Monopole-Dipole: • Dipole-Dipole: J. E. Moody and F. Wilczek, Phys. Rev. D 30, 130 (1984)

  21. Search for nuclear spin-dependent forces Spin Source: 1022 3He spins at 20 atm. Spin direction reversed every 3 sec with Adiabatic Fast Passage 2= 0.87 K-3He co-magnetometer Sensitivity: 0.7 fT/Hz1/2 Uncertainty (1) = 18 pHz or 4.3·10-35 GeV3He energy after 1 month (smallest energy shift ever measured)

  22. Recent limit from Walsworth et al PRL 101, 261801 (2008) New limits on neutron spin-dependent forces • Constraints on pseudo-scalar coupling: Limit on proton nuclear-spin dependent forces (Ramsey) Limit from gravitational experiments for Yukawa coupling only (Adelberger et al) Present work G. Vasilakis, J. M. Brown, T. W. Kornack, MVR, Phys. Rev. Lett. 103, 261801 (2009) Anomalous spin forces between neutrons are: < 210-8 of their magnetic interactions < 210-3 of their gravitational interactions First constraints of sub-gravitational strength!

  23. Conclusions • Set new limit on Lorentz and CPT violation for neutrons at 3×10-33 GeV, improved by a factor of 30 • Highest energy resolution among Lorentz-violating experiments • Search for anomalous spin-dependent forces between neutrons with energy resolution of 4×10-35 GeV, first constrain on spin forces of sub-gravitational strength • Search for CPT-even Lorentz violation with 21Ne is underway, limits maximum achievable velocity for neutrons (cn-c)~10-28 • Can achieve frequency resolution as low as 20 pHz, path to sub-pHz sensitivity, search for 1/MPl2 effects

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