1. White light Cavities University of Florida LIGO-G030231-00-Z Stacy Wise, Guido Mueller, David Reitze, D.B. Tanner, California Institute of Technology April 22 nd 2003

2. Table of Content Motivation Long GW-wavelength limit –Michelson Interferometer –Cavity enhanced Michelson Interferometer –Signal Recycling –White Light Cavity (WLC) Realistic GW-detector –Michelson Interferometer –Cavity enhanced MI –Signal recycling –WLC Outlook

3. Gravitational Waves:  Generated by huge accelerated masses such as accelerated black holes in a binary system  Predicted by Einstein, never detected  Amplitude is a relative length change: h=dL/L h ~ 2G Q c 4 r.. Q: Quadrupole Tensor But what type of sources do we expect to see ? Interferometer is the ideal tool to measure gravitational waves: Quadrupole waves: Stretch one direction Squeeze orthogonal direction

4. measure masses and spins of binary system Frequency increases over time Maximum frequency: 2kHz History of a big fat wedding

5. observe the dynamics: spin flips and couplings… Waveform unknown

6. History of a big fat wedding detect normal modes of ringdown to identify final NS or BH. Ringdown frequencies in NS: 1kHz – 20kHz

7. Advanced Configuration 10 -24 10 -25 10 Hz100 Hz1 kHz 10 -22 10 - 23 Initial LIGO 1 Hz Possible Sources: NS/NS mergers out to 300 Mpc BH/BH mergers Normal modes of NS (10 Mpc) Supernovae … NS/NS mergers ? We see the inspiral ! Probably the low frequency components of the wedding night, not the entire show. And probably nothing from the ringdown. NEED MORE BANDWIDTH !!!

8. LIGO I  Simplified picture (low frequency limit GW << FSR): GW modulates phase of cavity internal field ! E 0 (t) = E C + E + e i  t – E - e -i  t E 1 (t+  ) = r 1 r 2 ( E C + E +  e i  t – E -  e -i  t )  (  E C + E + e i  t+  ) – E - e -i  t+  ) ) E 2 (t+2  ) = ( r 1 r 2 ) 2 ( E C + E +  e i  t – E - e -i  t )  r 1 r 2  ( E C e -i  + E +  e i  t+  – E - e -i  t+  ) )  + ( E C + E + e i  t+2  ) – E - e -i  t+2  ) ) … Carrier -  +   = L rt /c

9. LIGO I Gives LIGO I response: BW = Cavity Pol E tot = E C  ( r 1 r 2 ) n + E + e i  t  ( r 1 r 2 ) n E + e in  - E - e -i  t  ( r 1 r 2 ) n E - e -in  = + - (1 – r 1 r 2 ) (r 1 -r 2 ) t MI E c (1 – r 1 r 2 e i  ) t 1 r MI E + e +i  t (1 – r 1 r 2 e -i  ) t 1 r MI E - e -i  t Carrier -  +  -  low frequency limit GW << FSR

10. LIGO II r eff e i  = r 1 -r S e i  SR 1-r 1 r S e i  SR Carrier -  +  ++ -  PM-sidebands: Signal recycling changes effective reflectivity of ITM (similar to PR for carrier) (1 – r eff r 2 e i  ) E + e +i  t (1 – r eff r 2 e -i  ) E - e -i  t 1.Shifts resonance (peak-) frequency 2.r eff changes build up 3.r eff changes bandwidth low frequency limit GW << FSR

11. Carrier IDEA: WLC -  +  -  (1 – r 1 r 2 ) E - e -i  t 1.Resonant at all frequency 2.Build up does not change BW pp nn pp nn Change reflectivity of end mirror: r 2 r 2 e -i  (1 – r 1 r 2 ) E+eitE+eit low frequency limit GW << FSR

12. White light cavity L  L  =  Or Make Cavity longer for longer wavelength Unlimited Bandwidth Basic Idea:

13. How ? Several methods: 1.Atomic resonances (Wicht-paper) Index of refraction in resonantly pumped two level system (see lasing without inversion) 2.Angular Dispersion a) Prisms (not dispersive enough ?) b) Gratings c) misaligned triangular cavities (tricky) LL L 0 ( ) = -   L  L  =  or  Original Idea published in: A. Wicht, K. Danzmann, M. Fleischhauer, M.O. Scully, G. Mueller, R.-H. Rinkleff Opt. Comm. 134 (1997), pg 431-439

14. White light cavity L0L0 L0L0 D   L( ) = L 0 + D [1+sin  sin  ( )] cos  ( ) Cavity length: L  L  L  =   = ! WLC requires:   = m dcos   L  = D cos 2  d with: New end Mirror !

15. Does this work ? Needed dispersion Grating dispersion Is the dispersion in a grating large enough ? Working Point

16. Parameters Final Bandwidth Bandwidth increased from 60 Hz to 36 MHz

17. Final Bandwidth This is the optical line width, not the GW-response ! Not the Same !

18. White light cavity L  L  =  Or Make Cavity longer for longer wavelength Unlimited Bandwidth But assumption GW << c/L not longer valid ! Basic Idea:

19. Michelson Interferometer ds 2 = 0 = c 2 dt 2 + [1+h(t)] 2 dx 2 + [1-h(t)] 2 dy 2 Response based on: Propagation of GW: z-direction Polarization of GW: + (optimum) T x = 1+ L c sin(  t-kL)-sin(  t)  h0h0 2 Light travel time in X-arm seen by beam splitter: c dt = (1+0.5h 0 sin(  t+kx))dx Y-arm:T y = 1- L c sin(  t-kL)-sin(  t)  h0h0 2 Phase difference at BS:  =  (T x -T y )

20. Cavities E cav = it 1 r 2 E in e i  t  (r 1 r 2 ) n e -i  n Cavity field at ITM x :  n = (n+1) + L c sin(  t-(n+1)kL)-sin(  t)  h0h0 2 L: round trip length  L/c = N2  E cav = it 1 r 2 E in e i  t 1-r 1 r 2 1 ih0ih0 4FSR e -i  / 2FSR sinc(  /2FSR) (1-r 1 r 2 )(1-r 1 r 2 e i  /FSR ) e -i  t ih0ih0 4FSR e -i  / 2FSR sinc(  /2FSR) (1-r 1 r 2 )(1-r 1 r 2 e -i  /FSR ) eiteit Carrier: Sideband:

21. Cavities E cav = it 1 r 2 E in e i  t  (r 1 r 2 ) n e -i  n Cavity field at ITM x :  n = (n+1) + L c sin(  t-(n+1)kL)-sin(  t)  h0h0 2 ih0ih0 4FSR e -i  / 2FSR sinc(  /2FSR) (1-r 1 r 2 ) (1-r 1 r 2 e i  /FSR ) e -i  t 11 Interpretation: GWCarrier build up Signal build up Signal recycling changes r 1 r eff e i  (not r 1 )

22. White Light Cavity ? E cav = it 1 r 2 E in e i  t  (r 1 r 2 ) n e -i  n Cavity field at ITM x :  n = (n+1)L/c + ? Carrier: Sideband: E cav = it 1 r 2 E in e i  t 1-r 1 r 2 1 ih0ih0 4FSR e -i  / 2FSR sinc(  /2FSR) (1-r 1 r 2 )(1-r 1 r 2 ) e -i  t ih0ih0 4FSR e -i  / 2FSR sinc(  /2FSR) (1-r 1 r 2 )(1-r 1 r 2 ) eiteit Hope for: r 2 r 2 e -i  /FSR Work in progress …

23. White Light Cavity ? Comments: Low frequency limit should be OK. If Not, we should check SR, too. Higher frequencies: ? Transfer function for optimum angle of incidence and optimum polarization All sky average will average out the sharp peaks.

24. Compare with Adv. LIGO Assume: 1MW in each arm cavity (infinite mirror masses): 5x10 -23 T 1/2 Hz 1/2 S h ~ for a non recycled MI (T transmission of ITM) Log T -1/2 : (~ Gain) Log T[ppm] 10 100 1k 10k 300 100 30 10 Log T[ppm] 10 100 1k 10k 0.05 0.5 5 50 BW = T x FSR / 2  SR: shifts to other frequencies, Gain, BW: replace T by T eff at DC

25. Scaling 5x10 -23 T 1/2 Hz 1/2 S h ~ Log T -1/2 : (~ Gain) Log T[ppm] 10 100 1k 10k 300 100 30 10 Log T[ppm] 10 100 1k 10k 0.05 0.5 5 50 BW = T x FSR / 2  Choices: want S h ~ 5x10 -25 BW ~ 0.5 Hz want S h ~ 5x10 -24 BW ~ 50 Hz Example for Grating: L = 10k ppm S h ~ 5x10 -24, BW ~ MHz (P in = 10kW) (T = Losses = L) L = 1k ppm S h ~ 1.6x10 -24, BW ~ MHz (P in = 1kW) L = 100 ppm S h ~ 5x10 -25, BW ~ MHz (Pin = 100W)

26. Remarks WLC reduces shot noise limit above cavity pol. Quadrature components of the quantum noise are uncoupled (no optical spring…). Radiation pressure noise will push on mirrors and noise will depend on mass of mirrors. Losses in gratings need to be below ~200ppm for grating, otherwise build up to low. Should be set up in an all reflective design. Nontransmissive materials for test masses possible: Silicon

27. Outlook Gratings with 97% losses from Uni Jena arrived They produced already gratings with >99% efficiency Stacy started to model gratings (preliminary: 99.6%) Designed tabletop with expected optical linewidth of 10GHz in 23cm cavity. GW-bandwith ? (need to study experimental setup) RPN+thermal noise: assumes equal masses and same materials in both cases. All reflective optics enables us to use new materials (Silicon): Larger masses, better thermal properties will reduce both noise sources.