Quantum Properties of Idealized GW Detector

Transcription

1 Qm Prors of Idlzd GW Dor Sg Pyo Km Ks N l Uvrsy Osk Uvrsy J 3 Th 4 h Kor-J Worksho o KAGRA

2 Ol Idlzd Dor for Grvol Wvs Qm Thory for Dsso Wgr Fo of Tm-Dd Osllor Dmd Osllor Drv by Erl Fors Colso

3 Idlzd Dor for GW

4 Shm of GW Dors Advd LIGO KAGRA [Hrry l CQG 7 ] [Skkbr l CQG 9 ]

5 Idlzd Dor A dor mss s mh smllr h wvlgh of GW rvlg log h z-dro [MTW Grvo 73] d d d y d d o GW d o GW R R j y j ω A dl dor of wo msss od by srg d srd by ξ log h -dro s dmd osllor drv by GW ξ ξ ω ξ j j ω ω ω ω ω L y s θ os φ roo gl

6 Esmd Noss of KAGRA Brod-bd Rso Sd bd Ero Dd Rso Sdb d Ero [Aso Mhmr Somy Irfromr dsg of KAGRA 3]

7 Why Qm Thory for Dor? Th sy of GW rhs h sdrd q m lm SQL. C o b h sdrd qm lm? Qm odmolo QND oos m srms mr Wh qm ss d how h msrms?

8 Qm Thory for Dsso

9 CK Osllor Cldrol 4 d K 48 rodd os llor wh m-dd mss H m m ω CK Clssl moo s dmd osllor ω Qm hory s h Shrodgr qo [S hrodgr r hs lk] Ψ H CK Ψ

10 Cosro of Qm Ss Th m-dd hlo d ro orors q m vr orors [Mlk l 7; SPK L PRD ; SPK Pg PRA ] d my b of s for QND for hoo mbr or mld Th grl m-dd qm ss [ ] [ ] m H d d m CK H.C. ω! Ψ Ψ Ψ

11 Psdo-Sory Ss Th sdo-sory ss from / Ω / ħmω [Srvsv l 9; SPK J PA 3] Th dsrso rlos of h grod s SQL 4! / 4 / ω π Ω Ω Ω Ω Ω Ψ Ω m m H m m m ω Ω Ω

12 Dsy Mr Qm D ohr d Corrlo Th dsy mr [SPK l 3] ρ CK ' Ψ Ψ ' / [ ] / mω π Γ Γ Γ ' / ' / δ Th msr of qm dohr [Morkw 9] d lssl orrlo [Gl l 96] δ QD / Γ / Γ δ / δ δ µ δ δ CC m / Γ Γ / Γ Γ Ω / δ µ µ

13 Dsy Mr Qm D ohr d Corrlo Qm ohr o dohr δ / Γ / Γ << Clsslly NOT orrld δ QD CC δ / Γ Γ / Γ Γ >> δ µ µ CK osllor shows o qm dohr d s lsslly orrld wh b lsslly NOT orrld wh m l m Ω

14 Sqzd Psdo-Sory Ss Th grl m-dd ss [SPK L PR D ; SPK Pg PRA ] Th sqzd ss d dsrso rlos /! m H π Ψ sh osh / Ψ Ψ Ψ Ψ Ω Ω m m r r r r r r r φ φ φ φ φ φ

15 BFT Osllor Bm 3 d Fshbh-Tkohsky 77 lso rodd losd sysm for dmd osllor Th lssl moos Ω Ω 4 ω y m y m H y y BFT mlfd osllor dmd osllor y y y ω ω

16 Rdd Dsy Mr Th rdd dsy mr for h dmd osll or [SPK l JKPS 3] Ω ' ' ' D D A A A A N D D D m A A A D D A A N π ρ θ θ π

17 Qm Dohr d Cls sl Corrlo Th msr qm dohr d lssl orrlo mω / δqd mω / os θ D δ CC oθ [ ] mω / os θ D I h s of lrg dsso θ π/ d D mω/ħ sgf dgr of qm doh r δ QD / d lssl orrlo δ CC d hs loss of ry.

18 Wgr Fo of Tm-Dd Osllor

19 Tm-Dd Grlzd Osll or Tm-dd grlzd osllor Clssl moo s dmd osllor Tm-dd hlo/ ro orors vr orors [SPK Pg PRA ] Z Y X H X X XY XY Y XZ X d d { } C. H. Y X

20 Dsy Oror Th mos grl dsy oror [SPK Pg P LB 3] [ ] ρ β ω δ δ Z Th dsy oror hs fv rmrs: rl os βω for l hrml dsrbo oml os δ for h lssl oso d mo mm o sqz rmr d o sqz gl for

21 Dsrso Rlos Th dsrso rlo w.r.. h dsy oror Th oso d momm o vls Th dsrso rlos [ ] Tr O O ρ Y Y X ω β

22 Dsy Mr d Wgr Fo Th dsy mr ρ ρ Th Wgr fo Th hrml Wgr fo T y P y y dy P / ρ π 4 l / h / h X d d H H P E E T ω ω ω ω β π ω β

23 Wgr Fo Th grl solo o hrmo osllor [ ] ω φ ω r φ osh r sh r mω Th oor of h Wgr fo

24 Dmd Osllor Drv by E rl Fors

25 Drv Dmd Osllor CK dmd osllor drv by rl fors H HCK F Th lssl moo s dmd osllor ω F Th rl fors ld grvol wvs d hrml oss. Th qm hory s sll h m-dd Shrodgr qo Ψ H Ψ

26 Cosro of Qm Ss Two lr vr orors [SPK CMP 3] Th grod s s ohr s of CK osllor d hs h sm dsrsos mml ry d F f m b f b ' ' ' H.C. ω f b Ψ Ψ Ψ

27 Dsld Nmbr Ss Th dslm oror [SPK JKPS 4] Th dsld mbr ss MUS [ ] D D f b D!

28 Crod d Dsrsos Th rod Th dsrso rlos r h sm s dor [ ] [ ] m m

29 Colso Sdy h qm ss of dmd osllor s dl dor for grvol wvs Mml ry ss MUS Sqzd ss: SQ MUS b my b SQL Qm vr orors for QND msrms Dsss wo qm dsso modls for dm d osllor: CK osllor vs BFT osllor Qm dohr Clssl orrlo Provd h Wgr fo for h hs-s for