Arm Cavity as Squeezing Filter via Entanglement Swapping

Transcription

1 Arm Cavity as Squeezing Filter via Entanglement Swapping Intra-Cavity Squeezing for White-Light Cavities Yanbei Chen on behalf of Yiqiu Ma, Haixing Miao, Jan Harms, Matt Evans, Roman Schnabel 1

2 p Degenerate vs Non-Degenerate OPA p a1,2 c1,2 degenerate OPA a1,2 b1,2 non-degenerate OPA c1,2 d1,2 c 1 = e +r a 1 c 2 = e r a 2 phase-sensitive amplification S c1 c 1 = e +2r, S c2 c 2 = e 2r, S c1 c 2 = 0. c2 c1 c 1 = a 1 cosh r + b 1 sinh r c 2 = a 2 cosh r b 2 sinh r d 1 = b 1 cosh r + a 1 sinh r d 2 = b 2 cosh r a 2 sinh r phaseinsensitive amplification additional noise S c1 c 1 = S c2 c 2 = cosh 2r, S c1,c 2 = 0 S d1 d 1 = S d2 d 2 = cosh 2r, S d1,d 2 = 0 r 1: c 1 d 1, c 2 d 2 2

3 EPR Entanglement! c2 d2 θ c1 θ d1 can predict c θ = c1cosθ - c2sinθ after subtraction: conditionally squeezed! S c c = 1 cosh 2r, S c /2 c /2 = cosh 2r ~3dB less than single squeezer measuring dθ = d1cosθ + d2sinθ Measurement of entangled beam produces conditional squeezing 3

4 Using EPR c2 d2 θ c1 θ d1 sent to dark-port of main IFO sent to filter cavity then detect frequency-dependent measurement of d [rotate by Φ=-θ, and measure 1st quadrature] means frequency dependent squeezing for c 4

5 Generating EPR a1,2 c1,2 a1,2 degenerate c1,2 OPA b1,2 non-degenerate OPA d1,2 Carrier Carrier +Δ Sub-Carrier signal sidebands c1,2 idler sidebands d1,2 ωgreen = 2 correlations between upper/ lower sideband fields ωgreen = 2+Δ correlations between upper/ lower sideband fields 5

6 Fancy Interpretation A B C D +Δ ωgreen = 2+Δ From squeezer: B & C form EPR pair Detection of sub-carrier: Joint measurement of C & D Conditioning : Classical Operation on B D teleported to B, carrier now squeezed. 6

7 Fancy Interpretation A B C D +Δ ωgreen = 2+Δ From squeezer: B & C form EPR pair Detection of sub-carrier: Joint measurement of C & D Conditioning : Classical Operation on B D teleported to B, carrier now squeezed. 7

8 Fancy Interpretation A B C +Δ D ωgreen = 2+Δ From squeezer: B & C form EPR pair Detection of sub-carrier: Joint measurement of C & D Conditioning : Classical Operation on B D teleported to B, carrier now squeezed. 8

9 Arm as filter cavity ETM resonance any microscopic detuning ITM TITM Carrier: resonance detuning phase of Δ LSR/c Green 2+Δ +Δ SRM TSR RSE for carrier at filter cavity for +Δ +Δ OMC 9

10 Example: Advanced LIGO Pc=800 kw TITM=1.4% TSR=35% farm = 370 Hz any microscopic detuning Sh (f) (Hz -1/2 ) Needs filter cavity with ffilter=51.3hz also detuned by 51.3 Hz detuning phase of Δ LSR/c TITM=1.4% φ= nπ TSR=35% filter cavity for +Δ f (Hz) 10 for LSR=15 meter Δ = 891 khz+10 n MHz n=0,1,2,

11 Noise Spectrum db squeezer Sh (f) (Hz -1/2 ) ideal 1%, 5%,10% loss (each detector) f (Hz) 11 Advanced LIGO ideal 7dB suppression (3dB penalty)

12 Improvement Factor 10 db squeezer 15 db squeezer Amplitude Improvemet lossless 1% 5% 10% Amplitude Improvemet lossless 1% 5% 10% f(hz) f (Hz) loss is the same for both photodetectors 12

13 Details Advanced LIGO Green 2+Δ +Δ y = e i (d 1 cos + d 2 sin ) + p 2 n y +Δ OMC Gain z = e 2i (c 2 Kc 1 ) + p 1 n z + e i p 2K h h SQL Ideal: 3dB less than single squeezer Losses: Filter loss much suppressed; other losses remain Only sub-carrier loss low frequencies 13

14 GEO 600: Detuned SR without RadiationPressure z = e i (c 1 cos + c 2 sin ) + h detuned frequency-dependent quadrature rotation +Δ y = e i (d 1 cos d 2 sin ) detuned oppositely opposite frequency-dependent quadrature rotation Direct subtraction achieves desired squeezing!! 14

15 Intra-Cavity Squeezing Optomechancail Filter for White-Light Cavity can also be realized this way anomalous dispersion Green 2+Δ Question: how to deal with optical instabilities? 15

16 Summary ETM Squeezer pumped at an offset frequency produces entangled beams Carrier: ITM Arm cavity can be used as squeezing filter. Examples: - Advanced LIGO - GEO 600 Filter for White-Light Cavity SRM Green 2+Δ +Δ +Δ OMC 16