L. A. P. T. Quick Look at Slow and Fast Light

Transcription

1 Quick Lk at Slw ad Fast Light Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

2 Ccept f Phase Velcity f a Mchrmatic Wave Mchrmatic plae wave z z 1 (c/) t 1 z Phase frt E ( ) i( k z ωt ) z, t E e Phase Dispersi relati Cstat phase frt mves a distace z i time t Phase velcity + φ k z ωt k c.c. ω c k z ω t z ω v p t k c t 1 t t v p > c des t ctradict special thery f relativity t

3 Grup Velcity: N-mchrmatic Sigal Superpsiti f tw sigle frequecy plae waves E E [ cs( k1z ω1 t) + cs( k z ωt) ] { E cs( k z ωt) } cs( k z ωt) 1 ω v evelpe Grup velcity ( ω ω ), k ( k k ) 1 g ω k Fr -dispersive medium 1 v g c Rapidly scillatig term Phase velcity ω k v ( ω + ω ), c ω c i ( k + k ), k, i 1, 1 1 p ω k i Wave grup v p V g

4 Pulse i a Dispersive Medium I a dispersive medium, (), fr pulse distrti, frequecy cmpets add i phase at pulse peak φ ( ω) k( ω) z ωt, k( ω) dφ 0 dω Grup Velcity Grup Idex d ωz + dω c g v g Phase Idex z c d + ω dω ( ω) c ω t 0, z c d + ω dω Dispersi v dω dk Slw & fast light effects make use f large d/d i the viciity f material resace g t d > 0 dω d < 0 dω ( rmal dispersi) t Pulse Slw Light ( amalus dispersi) Fast Light

5 Dispersi ad Slw Light usig EIT i a -System δ δ 0 1 > 1 > g p, prbe field 1> Susceptibility t first rder i prbe field amplitude g s, strg field 3> -type atmic system g + g p s Dark State +> -> Dressed State Basis χ i N µ h 1 [ i + γ31] ( iδ γ )[ i + γ ] g is decherece rate fr grud states idex rmal dispersi 31 s Fr large amplitude f strg field ad 1 0 χ i 4N µ h 1 [ i( ω ω ) γ ] g ca be as large as O(10 7 ) v g (< c) O(10 ) m/s g 0 s 31, g ω 0 N hg µ 1 s absrp. ceff. mag. f grup idex x 10-3 x Γ g s /Γ x 10-4 psitive grup idex x detuig (δ 1 ) x 10 7

6 Slw Light i Pr:YSO 5/ 3/ 1/ m (Site 1) Cuplig Repump 1/ 3/ 5/ Prbe Eergy Diagram Experimetal Setup -- Repump refills the spectral hles bured by pump ad prbe fields r prevets persistet SHB due t lg ppulati life time f grud state sublevels 5K) -- Apprpriate pulse sequeces fr the beams are geerated usig AOM switchig

7 Observati f Slw Light i Pr:YSO 0. msec Cuplig beam switched at 00 s 1 msec 10 msec C P 70 s Iput prbe beam 5/ 3/ 1/ R Pulse sequece Cuplig Repump Prbe trasmissi (%) Icmplete Prbe absrpti N cuplig beam (x0.5) Grup delay Slwed light 1/ 3/ 5/ Prbe Measured grup delay ~ 100 s 33 m/sec Eergy Diagram Turukhi et. al. Phys. Rev. Lett. 88 (00) 03601

8 Fast Light Usig Amalus Dispersi L.J. Wag, A. Kuzmich, ad A. Dgariu, Nature, 406, 77 (000).

9 Fast Light Usig Amalus Dispersi Iside pulse delayed by: TL/V g -L/C( g -1)L/C Iside pulse advaced by: -T(1- g )L/C L.J. Wag, A. Kuzmich, ad A. Dgariu, Nature, 406, 77 (000).

10 Rle f Fresel Drag i Sagac Effect CW(+) V P : Phase Velcity i Absece f Rtati BS1 R BS CCW(-) V R T : Relativistic Phase Velcities See i a Iertial Frame : time fr the Phase Frts t travel frm BS1 t BS A : Area rmal t V V v L π R vt P R 1 V P v / C T L / V R same V R C m 1 vα F ; α F (1 ) Fresel Drag Cefficiet Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

11 Rle f Fresel Drag i Sagac Effect V V v L π R vt P R 1 V P v / C T L / V R same V R C m 1 vα F ; α F (1 ) Fresel Drag Cefficiet ( (1 α ) F t t t ) ( (1 α ) F φ φ φ ) Fresel Drag Effect is Icluded i the Prper Descripti f the Sagac Effect Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

12 Dppler Shift ad Laub Drag i Sagac Effect W Det Det CW V M V M V M VM Frame & surce statiary; medium rtatig B. Flexible Fiber Clamp CCW statiary Det A. Frame & surce rtatig; medium statiary C. N Dppler Effect if the is statiery, but the stage rtates, with the relative mti betwee the mirrrs ad the medium Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

13 Dppler Shift ad Laub Drag i Sagac Effect ad MZI frame are statiery, ad the medium mves with a relative Velcity f V M. W Det Det CW V M V M V M VM Frame & surce statiary; medium rtatig B. Flexible Fiber Clamp CCW statiary Det A. Frame & surce rtatig; medium statiary C. V CW(+) ad CCW(-) beams are Dppler shifted by equal ad ppsite amuts, give by: ω ωv M / C The relativistic velcities are the give by: R C ( ) ω C ω C g ( 1 ) m vα F m VM m vα F m VM ω ω F m vα ; Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

14 Dppler Shift ad Laub Drag i Sagac Effect ad MZI frame are statiery, ad the medium remais statiery (r vice versa) W Det Det CW V M V M V M VM Frame & surce statiary; medium rtatig B. Flexible Fiber Clamp CCW statiary Det A. Frame & surce rtatig; medium statiary C. Here V M (-v)-r, s that the relativistic velcities are the give by: V R C m vα ; L α L 1 1 ( ) g The Laub Drag Cefficiet G.A. Saders ad S. Ezekiel J. Opt. Sc. Am. B, 5, 674 (1988) Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

15 Dppler Shift ad Laub Drag i Sagac Effect ad MZI frame are statiery, ad the medium remais statiery (r vice versa) Ω Det Ω Det CW V M V M V M VM Ω Frame & surce statiary; medium rtatig Ω B. Flexible Fiber Clamp CCW statiary Det V R C m vα ; L A. α L Frame & surce rtatig; medium statiary 1 1 ( ) g C. t ( (1 α )) ; φ ( (1 α L )) L t (Fr g >> ) φ Ehacemet Factr t g t ; φ g φ Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

16 Optical Sagac Effect i a Passive Rig Cavity V 1 beat det f VCO1 AOM1 AOM VCO V S. R. Balsam ad S. Ezekiel, Applied Physics Letters, 30, 478 (1977) Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

17 Optical Sagac Effect i a Passive Rig Cavity V 1 Σ beat det f VCO1 Ω AOM1 AOM VCO Σ V N Rtati: ω C πn P With Rtati: ω πn ω ΩRω ω VE ω ; VE VR v; ω P C C ΩA P Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

18 Ehacemet f Sagac Effect i a PRC usig Fast-Light V 1 Σ beat det f VCO1 Ω AOM1 AOM VCO Σ V I geeral: ω ω ω V E πn P V E C v VR v 1 ( ω ) C( ω ) (here is csidered a parameter whse amplitude is t be determied) Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

19 Ehacemet f Sagac Effect i a PRC usig Fast Light V E C v VR v 1 ( ω ) C( ω ) V 1 Σ VCO1 Ω beat det f AOM1 AOM VCO Σ V V E C v ~ ω ~ 1 m ; [ / ω]/ C ω ω ω V E πn P Self-Csistet Sluti: ω ω 1+ ω~ ω g Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

20 Ehacemet f Sagac Effect i a PRC usig Fast Light V 1 Σ VCO1 Ω beat det f ω ω 1+ ω ~ ω g ω ξ AOM1 AOM VCO Σ V ~ << Cstrait: ω 1 ω ω ξ; 1 << ξ << C / v; v ΩR; / ω 1 ( / ω )[1 ξ ] Critically Amalus Dispersi (CAD): ( ω ) / ω / Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

21 Ehacemet f Sagac Effect i a PRC usig Fast Light V 1 Σ VCO1 Ω beat det f ω ω 1+ ω ~ ω g ω ξ AOM1 AOM VCO Σ V Numerical Example fr the Cstrait: ω ω ξ; 1 << ξ << C / v; v ΩR; / ω 1 ( / ω )[1 ξ ] Csider a rig cavity with R1 meter, a rtati rate f ~73 micr-radia per secd (earth rate), ad 1.5: The ehacemet factr ca be as high as 10 1 while still satisfyig the cstraits Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

22 Ehacemet f Geeral Purpse Iterfermetric Sesig Usig Fast Light V 1 beat det f VCO1 Referece Chamber Test Chamber AOM1 AOM VCO V Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

23 Ehacemet f Geeral Purpse Iterfermetric Sesig Usig Usig Fast Light V 1 Σ beat det f VCO1 Referece Chamber Test Chamber AOM1 Mdel: AOM VCO Σ V 1 ref regi : ( ω) + ω ; { / ω ( / ω )[1 ξ ]; ξ >> 1} ω g test regi : ( ω) + ω + S ; { / S σ, idepedet f ω} ω S With dispersi: ω ω σ S ω With amalus dispersi: ω ω ξ; { ξ >> 1; the CAD cditi} g Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

24 Slw-Light Ehaced Rtati Sesig: Experimet Dye PBS S-plarized AOM HWP Pump Prbe PBS Pump Spiig Sdium Vapr Cell Det Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

25 Slw-Light Ehaced Rtati Sesig: Experimet 6 Saturated pump absrpti Prbe absrpti i EIT cell 5P 1/ 5 Magitude (a.u.) 4 3 Pump Prbe 1 0 ~ 1.77 GHz Frequecy (GHz) 5S 3/ F GHz F 0.4 phtdide utput lck-i-detecti Magitude (a.u.) Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

26 Amalus Dispersi Ehaced Rtati Sesig: Experimet Flexible Fiber Rtati Stage Ti-Saph Clamp hwp BFPG AOM1 BF-Pump Rb vapr Cell beat det f Ω PBS AOM1 AOM PBS AOM > (BPFG: Bi-frequecy pump geeratr) BF-Pump Bi-frequecy pump prbe 3> (PBS: plarizig beam splitter) 1> Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

27 Amalus Dispersi Ehaced Rtati Sesig: Experimet Experimetal Set-Up: vapr-cells Off-resat Rama pump Rama cell PBS Optical pump Prbe (r seed) Fabry-Pert filter PBS WP Absrpti cell Sigle pht detectr PBS Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

28 Amalus Dispersi Ehaced Rtati Sesig: Experimet L.T.P A.. Experimetal Set-Up: Trapped Atms Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

29 Artificial Black-Hle Usig Slw Light Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

30 Aalgy Betwee Charged Particles i a Magetic Field Ad Phts i a Rtatig Medium (Gravimagetism) B A (vectr ptetial) (magetic field) B eff (effective magetic field) A eff (effective vectr ptetial) Rtatig Medium (Vrtex) B B B B eff B eff B eff B Frce v charged particle B eff Frce v phts Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

31 Artificial Blackhle with Slw-Light i a Rtatig Medium B eff (effective magetic field) A eff (effective vectr ptetial) Rtatig Medium (Vrtex) B eff B eff B eff Frce v B eff Slw-phts (1 cm/sec) Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

32 Artificial Blackhle with Slw-Light i a Rtatig Medium U. Lehardt ad P. Piwicki Physical Review A, December 1999 Vlume 60, Number 6 Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

33 Artificial Blackhle with Slw-Light i a Rtatig Medium Optical Schwarzschild Radius U. Lehardt ad P. Piwicki Physical Review A, December 1999 Vlume 60, Number 6 Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy

34 GR-Relevat Terrestrial Experimets SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Usig Fast-Light Iterfermetry Usig Atmic Iterfermetry 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... Ceter fr Phtic Cmmuicati ad Cmputig Labratry fr Atmic ad Phtic Techlgy