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Published on November 15, 2007

Author: Lassie

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Slide1:  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] Slide4:  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 ... Slide5:  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 ... Slide6:  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 ... Slide7:  Quick Review of Lense-Thirring Effect Slide19:  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: Slide24:  Quick Look at Atom-Interferometry Slide33:  Atomic Sagnac Interferometer Slide34:  Quick Look at Sagnac Effect Slide35:  General View of the Sagnac Effect WAVE SOURCES: ??? Slide36:  General View of the Sagnac Effect R DEFINE: CW(+) CCW(-) VP : Phase Velocity in Absence of Rotation : time for the Phase Fronts to travel from BS1 t BS2 Slide37:  General View of the Sagnac Effect Slide38:  General View of the Sagnac Effect Slide39:  General View of the Sagnac Effect 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 Slide40:  General View of the Sagnac Effect Slide41:  General View of the Sagnac Effect Result is independent of Axis of Rotation Slide42:  General View of the Sagnac Effect OPTICAL SAGNAC PHASE SHIFT: MATTER-WAVE SAGNAC PHASE SHIFT: Relevant Frequency is the Compton Frequency: Slide43:  Wrong View of the Sagnac Effect Slide44:  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. Slide45:  “Wrong” View of the Optical Sagnac Effect Slide46:  “Wrong” View of the Atomic Sagnac Effect Slide47:  “Wrong” View of the Atomic Sagnac Effect However, fundamentally wrong! VCOM does not influence the result Slide48:  Quick Look at Slow and Fast Light Concept of Phase Velocity of a Monochromatic Wave:  Concept of Phase Velocity of a Monochromatic Wave Monochromatic plane wave Constant phase front  moves a distance z in time t Phase velocity vp > c does not contradict special theory of relativity Group Velocity: Non-monochromatic Signal:  Superposition of two single frequency plane waves Group Velocity: Non-monochromatic Signal Group velocity Phase velocity Pulse in a Dispersive Medium:  Pulse in a Dispersive Medium 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 Slide52:  Dispersion and Slow Light using EIT in a -System |+> |-> |2> Dressed State Basis Dark State gp, probe field gs, strong field 1 |1> |3> |2> -type atomic system 2 Susceptibility to first order in probe field amplitude For large amplitude of strong field and 1=0 ng can be as large as O(107)  vg (< c)  O(102) m/s -- 31 is decoherence rate for ground states Slow Light in Pr:YSO:  Slow Light in Pr:YSO 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 Slide54:  Observation of Slow Light in Pr:YSO Measured group delay ~ 100 s = 33 m/sec 70 s Turukhin et. al. Phys. Rev. Lett. 88 (2002) 023601 Slide55:  Fast Light Using Anomalous Dispersion L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000). Slide56:  Fast Light Using Anomalous Dispersion L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000). Inside pulse delayed by: T=L/Vg-L/C=(ng-1)L/C Inside pulse advanced by: -T=(1-ng)L/C Slide57:  Role of Fresnel Drag in Sagnac Effect same Fresnel Drag Coefficient Slide58:  Role of Fresnel Drag in Sagnac Effect same Fresnel Drag Coefficient Fresnel Drag Effect is Included in the Proper Description of the Sagnac Effect Slide59:  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 Slide60:  Doppler Shift and Laub Drag in Sagnac Effect Laser and MZI frame are stationery, and the medium moves with a relative Velocity of VM. CW(+) and CCW(-) beams are Doppler shifted by equal and opposite amounts, given by: The relativistic velocities are then given by: Slide61:  Doppler Shift and Laub Drag in Sagnac Effect Laser and MZI frame are stationery, and the medium remains stationery (or vice versa) Here VM=(-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) Slide62:  Doppler Shift and Laub Drag in Sagnac Effect Laser and MZI frame are stationery, and the medium remains stationery (or vice versa) (For ng>>no) Enhancement Factor Slide63:  Optical Sagnac Effect in a Passive Ring Cavity S. R. Balsamo and S. Ezekiel, Applied Physics Letters, 30, 478 (1977) Slide64:  Optical Sagnac Effect in a Passive Ring Cavity No Rotation: With Rotation: Slide65:  Enhancement of Sagnac Effect in a PRC using Fast-Light In general: (here  is considered a parameter whose amplitude is to be determined) Slide66:  Enhancement of Sagnac Effect in a PRC using Fast Light Self-Consistent Solution: Slide67:  Enhancement of Sagnac Effect in a PRC using Fast Light Constraint: Critically Anomalous Dispersion (CAD): Slide68:  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 no=1.5: The enhancement factor can be as high as 1012 while still satisfying the constraints Slide69:  Enhancement of General Purpose Interferometric Sensing Using Fast Light Slide70:  Enhancement of General Purpose Interferometric Sensing Using Using Fast Light Model: With no dispersion: With anomalous dispersion: Slide71:  Slow-Light Enhanced Rotation Sensing: Experiment Slide72:  Slow-Light Enhanced Rotation Sensing: Experiment Slide73:  Anomalous Dispersion Enhanced Rotation Sensing: Experiment Slide74:  Anomalous Dispersion Enhanced Rotation Sensing: Experiment Experimental Set-Up: vapor-cells Slide75:  Anomalous Dispersion Enhanced Rotation Sensing: Experiment Experimental Set-Up: Trapped Atoms Slide76:  Artificial Black-Hole Using Slow Light Slide77:  Analogy Between Charged Particles in a Magnetic Field And Photons in a Rotating Medium (Gravimagentism) Slide78:  Artificial Blackhole with Slow-Light in a Rotating Medium (effective magnetic field) Slide79:  Artificial Blackhole with Slow-Light in a Rotating Medium U. Leonhardt and P. Piwnicki Physical Review A, December 1999 Volume 60, Number 6 Slide80:  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 Slide81:  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 ...

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