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New limits on spin-dependent Lorentz- and CPT-violating interactions Michael Romalis Princeton University

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Experimentalist’s Motivation Is the space truly isotropic? Remove magnetic field, other known spin interactions Remove the Earth EE Spin Up Spin Down 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)

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Is the space really isotropic? –ask astrophysicists Cosmic Microwave Background Radiation Map The universe appears warmer on one side! v = 369 km/sec ~ 10 c 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)

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A theoretical framework for 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, 231602 (2002) CPT-violating interactions break Lorentz symmetry, give anisotropy signals Can search for CPT violation without the use of anti-particles L = – (m+a +b 5 ) + i 2 ( +c +d 5 ) a,b - CPT-odd c,d - CPT-even Fermions: Alan Kostelecky Although see arXiv:1103.0168v1

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Modified dispersion relations: E 2 = m 2 + p 2 + p 3 Jacobson Amelino-Cameli n - preferred direction, ~ 1/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 Effective Lagrangian:

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Summary of SERF Atomic Magnetometer Alkali metal vapor in a glass cell Magnetization Magnetic Field Linearly Polarized Probe light Circularly Polarized Pumping light Polarization angle rotation B y x z y Cell contents [K] ~ 10 14 cm -3 He buffer gas, N 2 quenching

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K- 3 He Co-magnetometer 1.Optically pump potassium atoms at high density (10 13 -10 14 /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, 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)

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Magnetic field self-compensation

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

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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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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 = 0.001 fT ± 0.019 fT stat ± 0.010 fT sys y He y e = 0.032 fT ± 0.019 fT stat ± 0.010 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 0.002 fT by torsion pendulum experiments (B.R. Heckel et al, PRD 78, 092006 (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, 105021 (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, 151604 (2010)

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Improvement in spin anisotropy limits

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Recent compilation of CPT limits V.A. Kostelecky and N. Russell arXiv:0801.0287 v3 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 quite excluded Natural size for CPT violation ? Need 10 GeV for 1/M pl 2 effects 10 GeV

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CPT-even Lorentz violation Maximum attainable particle velocity Implications for ultra-high energy cosmic rays, Cherenkov radiation, etc Best limit c 00 ~ 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 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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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 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

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First results with Ne-Rb-K co-magnetometer Replace 3 He with 21 Ne A factor of 10 smaller gyromagnetic ratio of 21 Ne makes the co-magnetometer have 10 times better energy resolution for anomalous interactions Use hybrid optical pumping K Rb 21 Ne Allows control of optical density for pump beam, operation with 10 15 /cm 3 Rb density, lower 21 Ne pressure. Eventually expect a factor of 100 gain in sensitivity Differences in physics: Larger electron spin magnetization (higher density and larger 0 ) Faster electric quadrupole spin relaxation of 21 Ne Quadrupole energy shifts due to coherent wall interactions Sensitivity already better than K- 3 He Fast damping of transients

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

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

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Uncertainty (1 ) = 18 pHz or 4.3·10 35 GeV 3 He energy after 1 month (smallest energy shift ever measured) 2 = 0.87 K- 3 He co- magnetometer Sensitivity: 0.7 fT/Hz 1/2 Search for nuclear spin-dependent forces Spin Source: 10 22 3 He spins at 20 atm. Spin direction reversed every 3 sec with Adiabatic Fast Passage

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

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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 21 Ne is underway, limits maximum achievable velocity for neutrons (c n -c)~10 -28 Can achieve frequency resolution as low as 20 pHz, path to sub-pHz sensitivity, search for 1/M Pl 2 effects

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