Precision Tests of Lorentz Invariance Using Slow Light Interferometer

1. Group Members The Micromaser G. Wilkes M. Jones B. Sanguinetti M. Everitt H. Omer Precision Tests M. Blackman J. Cotter M. Hill Project students K. Vijiakuma N. Fletcher R. Lin Postdoc Dr. P. Blythe Past Members C. Moscrip P. Batchelor M. Grabbe J. New Dr. Lijun Li Precision Tests of Fundamental Physics Using Slow Light Ben Varcoe Quantum Information Group University of Sussex (University of Leeds)

2. Overview • Why Test Lorentz Invariance • What might we see? • How are tests performed? • What could experiments show? • The “Slow Light” Interferometer • Slow Light • Tests of Lorentz Invariance • Future Directions

3. Electro-weak Standard Model G.U.T. Super-symmetry? T.O.E. Quantum Gravity? String Loop Theory? String Theory? Modern Physics Nuclear Physics (QCD) Light and Matter (QED) Gravity (Gen. Relativity) Particle Physics (Weak Force) Hints… Neutrino Mass, Dark Matter (WIMPS, Axions?), Inflation (Dark Energy?)

4. Lorentz Invariance and the Standard Model • Kostelecky and Mewes introduced a modification of QED (Phys. Rev .D, 66, 056005) to account for potential violations… QED CPT-even CPT-odd • The CPT–odd term leads to instabilities in the theory • Result: the coefficient, (kAF)k , must be zero • (i.e. any violation of Lorentz Invariance must be CPT even) • The CPT even term, (kF)klmn, is rather less well known • This coefficient contains 19 independent parameters in the photon sector of QED • 10 parameters can be tested astronomically – leaving 9 that are most applicable to “bench top” tests

5. Which leads naturally to a new Lagrangian for the electromagnetic field where Lorentz Invariance and the Standard Model • The coefficient (kF)klmn, is conveniently parameterized by the coupling between E and B fields (Maxwell’s equations in a dielectric)

6. Atomic Sample (n0) nb na Spectrum analysis Spectrum analysis Atomic Sample amplitude amplitude Velocity (Vatom) Beat Freq. Beat Freq. na nb / n02 = 1 + e (Vatom) Michelson Interferometer Kennedy-Thorndike test • Ives-Stillwell Measurement Testing Lorentz Invariance 1. Michelson Interferometer: Fringe Shift Detection Vframe 2. Cavity Based Experiments: Frequency Shift Detection k0+, ke- Vatom=0.064c k0+, ke-, ktr

7. Current Experimental Tests1 1. Table from Kostelecky and Mewes Phys. Rev .D, 66, 056005 (2002) Latest modifications 2. Muller et al. Phys. Rev .Lett, 91, 020401 (2003) 3. J.A. Lipp Phys. Rev .Lett, 90, 060403 (2003) 4. Tobar, M., Wolf, P., Fowler, A., Hartnett, J. G. gr-qc/0408006

8. Motion of The Earth 1 year The large velocities are needed to provide a suitable platform for tests 2 days The solar system has a velocity of nearly 400km/s relative to the CMB

9. Detecting Lorentz Invariance(An Ives-Stillwell Experiment) Leaves a refractive index term • Three ways to proceed • Measure the “absolute shift” • Propotional to vatom (Very Hard) • Measure the “Fresnel drag” caused by motion through the medium • Proportional to v2atom and vmedium • Measure the relativistic change in density of the medium (relative shift) • Proportional to vatom and vmedium Atomic Sample (n0) nb-dn na+dn batom=Vatom/c

10. Overview Experimental Tests of Lorentz Invariance • Why test it? • How are tests performed? • What can they show? • The “Slow Light” Interferometer • Slow Light • A Slow Light Ives Stilwell Experiment • Future Directions

11. Implementing Slow Light Experimental Region Strong Drive Laser Absorption Rubidium - 87 gas cell Refractive Index |3> W D |1> |2>

12. Implementing Slow Light Experimental Region Strong Drive Laser Rubidium - 87 gas cell Wave Plates Polarising Beam Splitter Weak Probe Laser |3> W W P D |1> |2> Drive Laser Probe Laser

13. Preliminary Measurements Frequency Scan by Zeeman shifting degenerate states Oscillating B-Field 300kHz G. Jundt, G. T. Purves, C. S. Adams and I.G. HughesEur. Phys. J. D 27, 273 (2003) |a> W W P D |b> |c>

14. Position measured with 5 Hz error Preliminary Measurements Long Coherence Times, More Atoms  Narrower Resonance Group Velocity = 1/(1-ng) g |a> W |b> gbc |c> N – atomic density l – wavelength g – decay rate DwD – Doppler width

15. Current Sensitivity • We look for a 12Hr period in the frequency separation of peaks in the data • Measuring the maximum possible frequency splitting in the resonance we find a splitting of 11±51 Hz

16. How do we increase the sensitivity of the apparatus? Increase V increases Doppler Shift Decrease Linewidth By increasing atomic density Higher temperature or Using a beam rather than a cell Increase Laser Stability and Narrow Linewidth increases resolution What can we achieve? Future Direction…

17. Gravitational Frame Dragging • The General Relativistic line element, in cylindrical coordinates for an infinitely long massive cylinder rotating with and angular frequency W is • The final term describes frame dragging induced by the motion which introduces a general rotation to the frame.

18. 5D5/2 776nm Ion Source 5P3/2 780nm 5S1/2 Acceleration Potential Neutralisation The motion generates a frequency difference between the two beams of Gravitational frame dragging Rotating heavy object Atom Beam Ives Stillwell Laser Excitation 770km/s

19. Gravitational Frame Dragging

20. Summary • We have made one of the first direct tests of the refractive index of space • Our current measurement shows an “in principle” accuracy of a part in 1011 • A 1000,000 fold improvement in sensitivity • Future directions include a laboratory scale measurement of gravitational frame dragging.