2. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Manifestation of General Relativity in Practical Experiments Selim M. Shahriar Laboratory for Atomic and Photonic Technology Northwestern University Evanston, IL [http://lapt.ece.northwestern.edu]

3. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology

4. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology

5. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology GR-Relevant Terrestrial Experiments SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light Interferometry Using Atomic Interferometry ARTIFICAL BLACKHOLE USING SLOW LIGHT GPS AND QUANTUM CLOCK-SYNCHRONIZATION EQUIVALENCE PRINCIPLE AND SLOW-LIGHT LIGO PROJECT FOR DETECTING GRAV. WAVES FAST-LIGHT AND ATOMIC INTER. FOR DET. GRAV. WAVES...

6. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology GR-Relevant Terrestrial Experiments SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light Interferometry Using Atomic Interferometry ARTIFICAL BLACKHOLE USING SLOW LIGHT GPS AND QUANTUM CLOCK-SYNCHRONIZATION EQUIVALENCE PRINCIPLE AND SLOW-LIGHT LIGO PROJECT FOR DETECTING GRAV. WAVES FAST-LIGHT AND ATOMIC INTER. FOR DET. GRAV. WAVES...

7. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology GR-Relevant Terrestrial Experiments SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light Interferometry Using Atomic Interferometry ARTIFICAL BLACKHOLE USING SLOW LIGHT GPS AND QUANTUM CLOCK-SYNCHRONIZATION EQUIVALENCE PRINCIPLE AND SLOW-LIGHT LIGO PROJECT FOR DETECTING GRAV. WAVES FAST-LIGHT AND ATOMIC INTER. FOR DET. GRAV. WAVES...

8. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Quick Review of Lense-Thirring Effect

9. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Rotation with respect to absolute space gives rise to centrifugal forces, as illustrated by the “bucket experiment“:

10. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Inertia is a phenomenon that relates the motion of bodies to the motion of all matter in the universe (“Mach‘s Principle“).

11. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology w will later be called Thirring-Lense frequency.  The rotation of the earth should “drag“ (local) inertial frames. very small effect very small frequency

12. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology More convenient than water buckets are torque-free gyroscopes... Dragging = precession of gyroscope axes

13. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology The interior of a rotating spherical matter shell is (approximately) an inertial frame that is dragged, i.e. rotates with respect to the exterior region: (valid in the weak field approximation = linearized theory) M = mass of the sphere R = radius of the sphere

14. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Dragging effects outside the shell: In the equatorial plane:

15. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Dragging effects near a massive rotating sphere:

16. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Dragging of the orbital plane: Newtonian gravityGeneral relativity

17. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Magnitude of the effect: d d = 0.13 cm ( = 0.886 cm) Circular orbit of radius r : Earth satellite with close orbits: 0.26 arc-seconds/year Angular frequency of the orbital plane:

18. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Useful analogy that applies for stationary (weak) gravitational fields: “Newtonian“ part of the gravitational field  “electric“ behaviour: “Machian“ part of the gravitational field  “magnetic“ behaviour (sometimes called “gravimagnetism“): 1/r² attractive force matter flow Lense-Thirring frequency Rotating body: Both behaviours apply!

19. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Rotating charge distribution rotating matter

20. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology George Pugh (1959), Leonard Schiff (1960) Suggestion of a precision experiment using a gyroscope in a satellite I. Ciufolini, E. Pavlis, F. Chieppa, E. Fernandes-Vieira and J. Perez- Mercader: Test of general relativity and measurement of the Lense- Thirring effect with two Earch satellites Science, 279, 2100 (27 March 1998) Measurement of the orbital effect to 30% accuracy, using satellite data (preliminary confirmation) I. Ciufolini and E. C. Pavlis: A confirmation of the general relativistic prediction of the Lense-Thirring effect Nature, 431, 958 (21 October 2004) Confirmation of the orbital effect to 6% accuracy, using satellite data Gravity Probe B, 2005 Expected confirmation of gyroscope dragging to 1% accuracy Sattelite-based Tests:

21. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology 2 satellites LAGEOS (NASA, launched 1976) and LAGEOS 2 (NASA + ASI, launched 1992) Original goal: precise determination of the Earth‘s gravitational field Major semi-axes: 12270 km, 12210 km Excentricities: 0.004 km, 0.014 Diameter: 60 cm, Mass: 406 kg Position measurement by reflection of laser pulses (accurate up to some mm !) Main difficulty: deviations from spherical symmetry of the Earth‘s gravity field LAGEOS LAGEOS 2 LAGEOS LAGEOS 2 LAGEOS Project:

22. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Improved model of the Earth‘s gravitational field: EIGEN-GRACE02S Evaluation of 11 years position data Improved choice of observables (combination of the nodes of both satellites)  Observed value = 99% 5% of the predicted value LAGEOS LAGEOS 2

23. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Satellite based experiment, NASA und Stanford University Goal: direct measurement of the dragging (precession) of gyroscopes‘ axes by the Lense-Thirring effect (Thirring-Schiff-effect) 4 gyroscopes with quartz rotors: the roundest objects ever made! Launch: 20 April 2004 Orbital plane: Earth‘s center + north pole + IM Pegasi (guide star)  Launch window: 1 Second! Expectation for 2005: Measurement of the Thirring-Lense frequency with an accuracy of 1% Gravity Probe B:

24. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Terrestrial Tests Using Precision Gyroscopes Ring Laser Gyroscope Atom-Interferometric Gyroscope

25. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Quick Look at Atom-Interferometry

26. ATOM INTERFEROMETRY: BASIC IDEA ATOM AS A dE Broglie WAVE v v  = (h / m v) Rb at 300 o C:  = 0.0153 nm 22  Sin  ATOMIC INTERFERENCE FRINGES

27. LASER-CONTROLLED SPIN EXCITATION NBNB Time OFF-RESONANT |B>|B> |E> |A>|A> METHOD FOR ACHIEVING LARGE ANGLE:

28. RF EXCITATION OF ATOMS NBNB Time |B, p+  k > |E> |A, p> TRAVELLING WAVES

29. LASER-CONTROLLED SPIN EXCITATION NBNB Time |E> EASY TO LOCALIZE MUCH STRONGER OFF-RESONANT DECOHERENCE FREE STRONG RECOIL |A, p> |B, p+2  k >

30. LASER-CONTROLLED SPIN EXCITATION RECOIL |E> |A>|A> |B>|B> |A>|A> |B>|B> kk |A>|A> |B>|B> kk |A>|A> |B>|B> 2k2k

31. PUSHING TO THE RIGHT |E> |A>|A> |B, 2  k> PUSHING TO THE LEFT |E> |A, p> |B, -2  k>

32. SPLITTING ATOMIC WAVES USING LCSE |A>|A> |B>|B> |A>|A> |B, 2  k> |B,- 2  k > |A, 4  k>

33. INTERFEROMETER IN ONE DIMENSION  100  k SPLITTING POSSIBLE SYSTEM: 87 RB FRINGE SPACING: ~ 4 NM

34. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Atomic Sagnac Interferometer

35. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Quick Look at Sagnac Effect

36. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology General View of the Sagnac Effect Det W CW CCW Det Wave -Source W CW CCW WAVE SOURCES: Optical Waves Matter Waves Acoustic Waves ???

37. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology General View of the Sagnac Effect BS1 BS2 R DEFINE: CW(+) CCW(-) V P : Phase Velocity in Absence of Rotation : Relativistic Phase Velocities Seen in an Inertial Frame : time for the Phase Fronts to travel from BS1 t BS2

38. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology General View of the Sagnac Effect BS1 BS2 R CW(+) CCW(-) V P : Phase Velocity in Absence of Rotation : Relativistic Phase Velocities Seen in an Inertial Frame : time for the Phase Fronts to travel from BS1 t BS2

39. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology BS1 BS2 R CW(+) CCW(-) General View of the Sagnac Effect V P : Phase Velocity in Absence of Rotation : Relativistic Phase Velocities Seen in an Inertial Frame : time for the Phase Fronts to travel from BS1 t BS2 A : Area normal to 

40. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology BS1 BS2 R CW(+) CCW(-) General View of the Sagnac Effect V P : Phase Velocity in Absence of Rotation : Relativistic Phase Velocities Seen in an Inertial Frame : time for the Phase Fronts to travel from BS1 t BS2 A : Area normal to  NOTE: This expression does not depend at all on the velocity of the wave It involves the free space velocity of light only, even if acoustic waves or matter waves are used For optical waves, this results is independent of the refractive index

41. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology BS1 BS2 R CW(+) CCW(-) General View of the Sagnac Effect V P : Phase Velocity in Absence of Rotation : Relativistic Phase Velocities Seen in an Inertial Frame : time for the Phase Fronts to travel from BS1 t BS2 A : Area normal to 

42. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology General View of the Sagnac Effect Result is independent of Axis of Rotation

43. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology General View of the Sagnac Effect OPTICAL SAGNAC PHASE SHIFT: MATTER-WAVE SAGNAC PHASE SHIFT: f=C o / o Relevant Frequency is the Compton Frequency:

44. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Wrong View of the Sagnac Effect

45. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Wrong View of the Sagnac Effect Now a team led by Wolfgang Schleich at the University of Ulm in Germany have suggested a way to adapt the ring-laser gyros currently used to track rotation in aircraft and satellites….. These devices fire laser beams in opposite directions around a fibre-optic ring. If a plane is turning, the laser beam travelling with the rotation has to travel further to catch up with its starting point, so it arrives later than the beam travelling against the rotation. When the beams meet, they create an interference pattern from which it is possible to work out the difference in the arrival times of the two beams, and hence the rate of rotation….. Shleich points out that the same principle also works with cold atom beams, and because atoms move more slowly than light, the shift is more obvious. This should allow far slower rates of rotation to be measured.

46. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology “Wrong” View of the Optical Sagnac Effect This happens to be correct only when the index is unity This line of reasoning gives the wrong result when n  1 BS1 BS2 R CW(+) CCW(-) V P : Phase Velocity in Absence of Rotation : Phase Velocities Seen in an Inertial Frame : time for the Phase Fronts to travel from BS1 t BS2 A : Area normal to 

47. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology “Wrong” View of the Atomic Sagnac Effect

48. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology “Wrong” View of the Atomic Sagnac Effect Off by a factor of 2, but pretty close! BS1 BS2 R CW(+) CCW(-) V P : Phase Velocity in Absence of Rotation : Phase Velocities Seen in an Inertial Frame : time for the Phase Fronts to travel from BS1 t BS2 A : Area normal to  However, fundamentally wrong! V COM does not influence the result

49. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Quick Look at Slow and Fast Light

50. Concept of Phase Velocity of a Monochromatic Wave Monochromatic plane wave Constant phase front  moves a distance  z in time  t Phase velocity v p > c does not contradict special theory of relativity Dispersion relation Phase

51. Superposition of two single frequency plane waves Group Velocity: Non-monochromatic Signal envelope Rapidly oscillating term Group velocity Phase velocity VgVg vpvp Wave group 11 22 For non-dispersive medium

52. Pulse in a Dispersive Medium Pulse t In a dispersive medium, n(  ), for no pulse distortion, frequency components add in phase at pulse peak Dispersion Phase Index Slow & fast light effects make use of large dn/d  in the vicinity of material resonance

53. Dispersion and Slow Light using EIT in a  -System |+> |-> |2> Dressed State Basis Dark State g p, probe field g s, strong field 11 |1> |3> |2>  -type atomic system 22 == Susceptibility to first order in probe field amplitude For large amplitude of strong field and  1 =0 n g can be as large as O(10 7 )  v g (< c)  O(10 2 ) m/s --  31 is decoherence rate for ground states

54. Slow Light in Pr:YSO Coupling Probe Repump 4.6 4.8 10.2 17.3  5/2  3/2  1/2  3/2  5/2 Energy Diagram Experimental Setup =605.977 nm (Site 1) -- Repump refills the spectral holes burned by pump and probe fields or prevents persistent SHB due to long population life time of ground state sublevels (100s @ 5K) -- Appropriate pulse sequences for the beams are generated using AOM switching

55. Observation of Slow Light in Pr:YSO Measured group delay ~ 100  s = 33 m/sec Coupling beam switched on at –200  s Input probe beam No coupling beam (x0.25) Slowed light Incomplete Probe absorption Probe transmission (%) Group delay 70  s 10 msec R C P 1 msec 0.2 msec Pulse sequence Turukhin et. al. Phys. Rev. Lett. 88 (2002) 023601 Coupling Probe Repump 4.6 4.8 10.2 17.3  5/2  3/2  1/2  3/2  5/2 Energy Diagram

56. Fast Light Using Anomalous Dispersion L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000).

57. Fast Light Using Anomalous Dispersion L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000). Inside pulse delayed by:  T=L/V g -L/C=(n g -1)L/C Inside pulse advanced by: -  T=(1-n g )L/C

58. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Role of Fresnel Drag in Sagnac Effect BS1 BS2 R CW(+) CCW(-) V P : Phase Velocity in Absence of Rotation : Relativistic Phase Velocities Seen in an Inertial Frame : time for the Phase Fronts to travel from BS1 t BS2 A : Area normal to  same Fresnel Drag Coefficient

59. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Role of Fresnel Drag in Sagnac Effect same Fresnel Drag Coefficient Fresnel Drag Effect is Included in the Proper Description of the Sagnac Effect

60. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Doppler Shift and Laub Drag in Sagnac Effect No Doppler Effect if the Laser is stationery, but the stage rotates, with the no relative motion between the mirrors and the medium Laser  Det W W CW CCW VMVM VMVM VMVM VMVM Clamp Flexible Fiber Laser  Det Laser  stationary C. B. A. Frame & source stationary; medium rotating Frame & source rotating; medium stationary

61. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Doppler Shift and Laub Drag in Sagnac Effect Laser and MZI frame are stationery, and the medium moves with a relative Velocity of V M. Laser  Det W W CW CCW VMVM VMVM VMVM VMVM Clamp Flexible Fiber Laser  Det Laser  stationary C. B. A. Frame & source stationary; medium rotating Frame & source rotating; medium stationary CW(+) and CCW(-) beams are Doppler shifted by equal and opposite amounts, given by: The relativistic velocities are then given by:

62. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Doppler Shift and Laub Drag in Sagnac Effect Laser and MZI frame are stationery, and the medium remains stationery (or vice versa) Laser  Det W W CW CCW VMVM VMVM VMVM VMVM Clamp Flexible Fiber Laser  Det Laser  stationary C. B. A. Frame & source stationary; medium rotating Frame & source rotating; medium stationary Here V M =(-v)=-  R, so that the relativistic velocities are then given by: The Laub Drag Coefficient G.A. Sanders and S. Ezekiel J. Opt. Soc. Am. B, 5, 674 (1988)

63. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Doppler Shift and Laub Drag in Sagnac Effect Laser and MZI frame are stationery, and the medium remains stationery (or vice versa) (For n g >>n o ) Enhancement Factor

64. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Optical Sagnac Effect in a Passive Ring Cavity VCO1 AOM1 AOM2 VCO2 diff. Laser  V1V1 beat det ff diff.  V2V2  S. R. Balsamo and S. Ezekiel, Applied Physics Letters, 30, 478 (1977)

65. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Optical Sagnac Effect in a Passive Ring Cavity No Rotation: With Rotation:

66. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Enhancement of Sagnac Effect in a PRC using Fast-Light In general: (here  is considered a parameter whose amplitude is to be determined)

67. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Enhancement of Sagnac Effect in a PRC using Fast Light Self-Consistent Solution:

68. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Enhancement of Sagnac Effect in a PRC using Fast Light Constraint: Critically Anomalous Dispersion (CAD):

69. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Enhancement of Sagnac Effect in a PRC using Fast Light Numerical Example for the Constraint: Consider a ring cavity with R=1 meter, a rotation rate of ~73 micro-radian per second (earth rate), and n o =1.5: The enhancement factor can be as high as 10 12 while still satisfying the constraints

70. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Enhancement of General Purpose Interferometric Sensing Using Fast Light VCO1 diff. Laser  V1V1 beat det ff  V2V2 diff. AOM1 AOM2 VCO2 Test Chamber Reference Chamber

71. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Enhancement of General Purpose Interferometric Sensing Using Using Fast Light Model: With no dispersion: With anomalous dispersion:

72. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Slow-Light Enhanced Rotation Sensing: Experiment  Det Dye Laser AOM PBS Pump Probe Spinning Sodium Vapor Cell HWP S-polarized PBS Pump

73. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Slow-Light Enhanced Rotation Sensing: Experiment F=2  F=1 5S 3/2 Probe 1.772 GHz Pump 5P 1/2

74. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Anomalous Dispersion Enhanced Rotation Sensing: Experiment

75. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Anomalous Dispersion Enhanced Rotation Sensing: Experiment Raman cell Absorption cell Off-resonant Raman pump Probe (or seed) Optical pump Single photon detector Fabry-Perot filter PBS   WP PBS Experimental Set-Up: vapor-cells

76. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Anomalous Dispersion Enhanced Rotation Sensing: Experiment Experimental Set-Up: Trapped Atoms

77. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Artificial Black-Hole Using Slow Light

78. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Analogy Between Charged Particles in a Magnetic Field And Photons in a Rotating Medium (Gravimagentism) A (vector potential) B B B B (magnetic field) charged particle v Force (effective magnetic field) B A eff (effective vector potential) B eff photons v Force Rotating Medium (Vortex) B eff

79. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Artificial Blackhole with Slow-Light in a Rotating Medium (effective magnetic field) A eff (effective vector potential) B eff Slow-photons (1 cm/sec) v Force Rotating Medium (Vortex) B eff

80. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Artificial Blackhole with Slow-Light in a Rotating Medium U. Leonhardt and P. Piwnicki Physical Review A, December 1999 Volume 60, Number 6

81. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology Artificial Blackhole with Slow-Light in a Rotating Medium Optical Schwarzschild Radius U. Leonhardt and P. Piwnicki Physical Review A, December 1999 Volume 60, Number 6

82. Center for Photonic Communication and ComputingLaboratory for Atomic and Photonic Technology GR-Relevant Terrestrial Experiments SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light Interferometry Using Atomic Interferometry ARTIFICAL BLACKHOLE USING SLOW LIGHT GPS AND QUANTUM CLOCK-SYNCHRONIZATION EQUIVALENCE PRINCIPLE AND SLOW-LIGHT LIGO PROJECT FOR DETECTING GRAV. WAVES FAST-LIGHT AND ATOMIC INTER. FOR DET. GRAV. WAVES...