Verification of conditional quantum state in GW detectors. LSC-VIRGO Meeting, QND workshop Hannover, October 26, PDF Free Download

LIGO-G070764-00-Z Verification of conditional quantum state in GW detectors Y. Chen 1, S. Danilishin 1,2, H. Miao 3, H. Müller-Ebhardt 1, H. Rehbein 1, R. Schnabel 1, K. Somiya 1 1 MPI für Gravitationsphysik (AEI), 2 Moscow State University, 3 University of Western Australia LSC-VIRGO Meeting, QND workshop Hannover, October 26, 2006 Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 1 / 12

Outline 1 MQM experiment and philosophy of verification 2 Time scales and precision of verification experiment White noise Non- white noise 3 Conclusion Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 2 / 12

What is MQM experiment? Why do we need verification? GOAL of MQM experiment Prepare, manipulate and observe quantum state of macroscopic test masses, thereby testing quantum mechanics in macroscopic world, using interferometric gravitational wave detectors Why one needs verification? To check by an INDEPENDENT EXPERIMENT whether the state preparation using conditioning or control was successfull and QUANTITATIVELY VERIFY how successfull it was What the success of verification depends on, and why do we believe in it? On classical noise budget being below the SQL in the frequency band of interest; Use of QND measurement techniques will allow to probe quantum state with sub-sql precision! Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 3 / 12

Simple conceptual scheme of the MQM experiment Linear Gaussian system coupled with light = Heisenberg equations: Heisenberg equations for our system m ˆX + 2γp ˆX + ω 2 p ˆX = α Â 1 + F th, ˆB 1 = Â 1, ˆB 2 = Â2 + α ( ˆX + X th ). α = p mω q: measurement strength, Ω q 1/τ q: measurement timescale. How big is the probability to observe the quantum behavior of the test mass? The answer depends on how strong is it coupled to the environment, i.e. how big are thermal and quantum noises. Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 4 / 12

White noise Sh SSQL 10.0 5.0 2.0 1.0 0.5 Ω q/ω SQL = 1 quantum noise 0.2 0.1 0.2 0.5 1.0 2.0 5.0 10.0 f f SQL SQL Quantum noise Shot and radiation pressure noises = white: S q x = mω 2 q = const S q F = mω 2 q = const S q GW (Ω) = Sq x + Sq F m 2 Ω» 4 Ω 2 = + Ω2 q mω 2 Ω 2 Ω 2 q Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 5 / 12

White noise 10.0 Ω F /Ω q Ω x/ω q Sh SSQL 5.0 2.0 1.0 0.5 0.2 force noise SQL displacement noise Classical noise Classical suspension and mirror internal = white: S th x = 2 mω 2 x = const, S th F = 2 mω 2 F = const, S th GW(Ω) = S th x + Sforce F m 2 Ω 4. 0.1 0.2 0.5 1.0 2.0 5.0 10.0 f f SQL Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 5 / 12

White noise Sh SSQL 10.0 5.0 2.0 1.0 0.5 0.2 ζ F 1 1/ζ x Total noise SQL 0.1 0.2 0.5 1.0 2.0 5.0 10.0 f f SQL Spectral density of the total noise will be then: SGW(Ω) tot = S q GW (Ω) + Sth GW(Ω) = = S q x(1 + 2ζ 2 x) + Sq F (1 + 2ζ2 F) m 2 Ω 4, where ζ x = Ωq Ω x and ζ F = ΩF Ω q. Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 5 / 12

What do we mean by saying quantum and classical state? Gaussian states covariance matrix» V(t) = δˆx 2 δˆxδˆp sym δˆpδˆx sym δˆp 2 If the test mass is in Pure quantum state = det V = 2 /4 Classical mixed state = det V 2 /4 Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 6 / 12

Scheme of state preparation How long does quantum state survive? State survival timescales noise budget. Survival time = τ F 1/Ω F Preparation time: τ P < τ F Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 7 / 12

Scheme of state preparation How long does quantum state survive? State survival timescales noise budget. Survival time = τ F 1/Ω F Evolution time: τ E < τ F Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 7 / 12

Timescales of verification and survival of test mass state Covariance matrix of the test mass during verification has two parts V tot = V cond + V add V cond corresponds to the test mass conditional state after preparation, V add reflects additional uncertainties due to verification process. Order of magnitude estimate of entries of V cond Let test mass be driven by "white" noises with constant spectral densities: S tot x = S q x + S th x = S q x(1 + 2ζ 2 x) S tot F = S q F + Sth F = S q x(1 + 2ζ 2 F) Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 8 / 12

Timescales of verification and survival of test mass state Covariance matrix of the test mass during verification has two parts V tot = V cond + V add V cond corresponds to the test mass conditional state after preparation, V add reflects additional uncertainties due to verification process. Order of magnitude estimate of entries of V cond Let test mass be driven by "white" noises with constant spectral densities: S tot x = S q x + S th x = S q x(1 + 2ζ 2 x) S tot F Variance of test mass displacement at measurement time τ: δx 2 = V cond xx = Stot x τ = S q F + Sth F = S q x(1 + 2ζ 2 F) + τ3 SF tot m 2 Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 8 / 12

Timescales of verification and survival of test mass state Covariance matrix of the test mass during verification has two parts V tot = V cond + V add V cond corresponds to the test mass conditional state after preparation, V add reflects additional uncertainties due to verification process. Order of magnitude estimate of entries of V cond Let test mass be driven by "white" noises with constant spectral densities: S tot x = S q x + S th x = S q x(1 + 2ζ 2 x) S tot F = S q F + Sth F = S q x(1 + 2ζ 2 F) Estimate using inequality between arithmetic and geometric mean: δx 2 = Vxx cond = 1 Sx tot + 1 Sx tot + 1 r Sx tot + τ3 SF tot 4 1 3 τ 3 τ 3 τ m 2 (Sx tot 3 3 ) 3 S tot F m 2 Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 8 / 12

Timescales of verification and survival of test mass state Covariance matrix of the test mass during verification has two parts V tot = V cond + V add V cond corresponds to the test mass conditional state after preparation, V add reflects additional uncertainties due to verification process. Order of magnitude estimate of entries of V cond Let test mass be driven by "white" noises with constant spectral densities: S tot x = S q x + S th x = S q x(1 + 2ζ 2 x) S tot F Minimal displacement variance takes place at τ = τ q: δx 2 = V cond xx = S q F + Sth F = S q x(1 + 2ζ 2 F) r = 4 1 (Sx tot ) 3 SF tot (1 + 2ζ x) 3/4 (1 + 2ζ F) 1/4 (δx q ) 2 3 3 m 2 Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 8 / 12

Timescales of verification and survival of test mass state Covariance matrix of the test mass during verification has two parts V tot = V cond + V add V cond corresponds to the test mass conditional state after preparation, V add reflects additional uncertainties due to verification process. Order of magnitude estimate of entries of V cond Similarly V cond pp = δp 2 m 2 Sx tot /τ 3 + τsf tot (δp q) 2 (1 + 2ζx) 2 1 4 (1 + 2ζF) 2 3 4 and V cond xp δxδp /2(1 + 2ζ 2 x) 1 2 (1 + 2ζ 2 F ) 1 2. Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 8 / 12

Timescales of verification and survival of test mass state Covariance matrix of the test mass during verification has two parts V tot = V cond + V add V cond corresponds to the test mass conditional state after preparation, V add reflects additional uncertainties due to verification process. P 1.5 1.0 0.5 0.0 0.5 ΖF Ζx 0.7 ΖF Ζx 0.2 gnd. state q Purity of conditional state det V cond = Vxx cond Vpp cond (Vxp cond ) 2 2 4 (1 + 2ζ2 x)(1 + 2ζF) 2 2 4 1.0 1.5 1.5 1.0 0.5 0.0 0.5 1.0 1.5 X Parameters for left panel: ζ x = 0.2, ζ F = 0.2 ζ x = 0.7, ζ F = 0.7 Ground state of oscillator with frequency Ω q Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 8 / 12

QND methods in verification ETM N Back action evasion for quantum state verification Laser Power Recycling Mirror AM PM Arm Cavity Beamsplitter ITM N ITM E Signal Recycling Mirror squeezer Arm Cavity ETM E Use AM and FM of local oscillator light in homodyne scheme in the optimal way to eliminate radiation pressure of light from the measured output quadrature All terms corresponding to S q F nullify: (1 + 2ζ 2 F) = 2ζ 2 F local oscillator Photodetection S.P. Vyatchanin, E.A. Zubova, Phys. Lett. A 201, 265 (1995) Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 9 / 12

QND methods in verification Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 9 / 12

QND methods in verification ETM N Optimal modulation functions for BAE Arm Cavity 6 4 2 TM displacement measurement Laser Power Recycling Mirror AM PM Beamsplitter ITM N ITM E Signal Recycling Mirror squeezer Arm Cavity ETM E g1,2 t Τq 0 2 4 6 TM momentum measurement 0.0 0.5 1.0 1.5 2.0 t Τq All terms corresponding to S q F nullify: local oscillator Photodetection (1 + 2ζ 2 F) = 2ζ 2 F ζ F = Ω F/Ω q Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 9 / 12

QND methods in verification Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 9 / 12

QND methods in verification Order of magnitude estimate of V add δx 2 V Sx tot /τ + τ 3 SF th /m 2 (1 + 2ζx) 2 3/4 ζ 1/2 δx2 q δp 2 V m 2 Sx tot /τ 3 + τsf th (1 + 2ζx) 2 1/4 ζ 3/2 F δp2 q, F P 1.0 0.5 0.0 0.5 10 db squeezing No squeezing gnd. state q 3 db squeezing Precision of verification Sub-Heisenberg sensitivity available with BAE Squeezing increase precision 1.0 1.0 0.5 0.0 0.5 1.0 X Noise: ζ x = Ω q/ω x = 0.2, ζ F = Ω F/Ω q = 0.2 Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 9 / 12

Verification with realistic noise budget Verification with non- white noise Realistic noises = still sub-heisenberg precision 10 17 Sx m Hz 10 18 10 19 10 20 10 21 P 1.0 0.5 0.0 0.5 No squeezing 10 db squeezing gnd. state q 3 db squeezing 10 22 1000 f Hz Realistic noise budget for GW detector 1.0 1.0 0.5 0.0 0.5 1.0 X Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 10 / 12

Conclusion 1 GW detectors can be used to study quantum mechanics of truly macroscopic test masses, by using a two-staged process of preparation and verification; 2 Quantum state can be verified with sub-heisenberg precision using plausible experimental technology; 3 Elaborated procedure can be also applied in small scale devices, with even more ease; Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 11 / 12

THANK YOU FOR YOUR ATTENTION!!! Y. Chen et al (AEI Golm) Verification of conditional quantum state in GW detectors LSC-VIRGO 2007 12 / 12

Verification of conditional quantum state in GW detectors. LSC-VIRGO Meeting, QND workshop Hannover, October 26, 2006