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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 DE 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 ~ 10-3 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 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, (2002) CPT-violating interactions break Lorentz symmetry, give anisotropy signals Can search for CPT violation without the use of anti-particles 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: v1

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**Phenomenology of Lorentz/CPT violation**

Modified dispersion relations: E2 = m2 + p2 + h p Jacobson Amelino-Cameli nm - preferred direction, h ~ 1/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 h g = m 2 5 ) ( n L Effective Lagrangian: Myers, Pospelov, Sudarsky Spin coupling to preferred direction ) )( ( ab mn q = F L

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**Summary of SERF Atomic Magnetometer**

Alkali metal vapor in a glass cell Linearly Polarized Probe light Magnetization Magnetization Magnetic Field Circularly Polarized Pumping light Cell contents [K] ~ cm-3 He buffer gas, N2 quenching With optically pumped alkali atom vapor, we can make a sensitive magnetic field sensor without cryogenic maintenance. Alkali atoms will be polarized by absorbing circularly polarized light due to the selection rule. And this makes total magnetization. The magnetization will be tipped around the magnetic field. In this case, the By field going through the screen. The tipping makes x component of magnetization, this gives the different refraction indexes for the right and the left circularly polarized lights, respectively. As a result, the cell rotates the polarization angle of the linearly polarized probe light. So we can measure the By field by detecting this angle rotation. z Polarization angle rotation By x y

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**Turn most-sensitive atomic magnetometer into a co-magnetometer!**

K-3He Co-magnetometer Optically pump potassium atoms at high density ( /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, (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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**Magnetic field sensitivity**

Best operating region 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

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**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?

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**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

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**Final results Previous limit |bnxy| = (6.4 ± 5.4) 10-32 GeV**

Anamolous magnetic field constrained: bxHe-bxe = fT ± fTstat ± fTsys byHe-bye = fT ± fTstat ± 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 fT by torsion pendulum experiments (B.R. Heckel et al, PRD 78, (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, (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, (2010) Previous limit |bnxy| = (6.4 ± 5.4) 10-32 GeV D. Bear et al, PRL 85, 5038 (2000)

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**Improvement in spin anisotropy limits**

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**Recent compilation of CPT 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 ~ 1/Mpl effects are quite excluded Natural size for CPT violation ? Need 10-37GeV for 1/Mpl2 effects V.A. Kostelecky and N. Russell arXiv: v3

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**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 Best limit c00 ~ 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 Coleman and Glashow Jacobson ) ˆ 1 ( 00 k j jk MAX v c - = 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 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

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**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 KRb21Ne 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 Fast damping of transients Sensitivity already better than K-3He

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**N-S E-W 21Ne Semi-sidereal Fits A< 1 fT**

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

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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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**Search for nuclear spin-dependent forces**

Spin Source: He 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 GeV 3He energy after 1 month (smallest energy shift ever measured)

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**New limits on neutron spin-dependent forces**

Constraints on pseudo-scalar coupling: Limit on proton nuclear-spin dependent forces (Ramsey) Recent limit from Walsworth et al PRL 101, (2008) 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, (2009) Anomalous spin forces between neutrons are: < 210-8 of their magnetic interactions < 210-3 of their gravitational interactions First constraints of sub-gravitational strength!

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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 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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