QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Entanglement between test masses Helge Müller-Ebhardt, Henning Rehbein, Kentaro Somiya, Stefan Danilishin, Roman Schnabel, Karsten Danzmann, Yanbei Chen and the AEI-Caltech-MIT MQM discussion group Max-Planck-Institut für Gravitationsphysik (AEI) Institut für Gravitationsphysik, Leibniz Universität Hannover TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Entanglement between end mirrors Logarithmic negativity [Vidal, Werner] a quantitative measure of entanglement: Total system: Input squeezing Entangled output Compare with optics:

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Conditioning on continuous measurement Time domain:Stochastic Master Equation Frequency domain:Wiener Filtering  Prepare state by collecting data and finding optimal filter function. Need verification stage? → Stefan’s talk. Each (common and differential) mode: Conditional second-order moments not changed by any linear feedback control! Radiation pressure & classical forces. Shot & classical sensing noise.

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Wiener Filtering Conditional moments of Gaussian state: unknownknown Steady state!

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Conditional test-mass state Equality for:  = 0,  x /  F > 2 → non-zero frequency band in which classical noise is completely below the SQL! Differently squeezed for different  . Homodyne detection angle

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt   c = 11.5  F,   d = 0.87  F  x /  F   c = 7.0  F,   d = 0.8  F   c = 10.6  F,   d = 0.3  F  x /  F Constrains on conditional mirror entanglement Laser noise level. 10 dB 5 dB Common mode detection at  » -  /2.  x /  F - threshold larger than 2 for entanglement. [arXiv:quant-ph/ ] Detection close to amplitude quadrature (  » -  /2) → modes more squeezed – but at same time even more anti-squeezed! Optimal: Detect both modes at  » -  / 2 → then independent from laser noise!

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Conditional mirror entanglement Log [   c /  F ] Log [   d /  F ]  x /  F = 10  x /  F = 8  x /  F = 6  x /  F = 4 No laser noise!

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Survival of conditional mirror entanglement In “rotating frame”. Second-order moments at t =  conditioned on measurement at t < 0: Erase, if laser turned off at t = 0.  x /  F = 5.6   c = 11.5  F,   d = 0.87  F   c = 7.0  F,   d = 0.8  F xx  x /  F  F Lifetime No laser noise!  x /  F = 10

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Controlled test-mass state With optimal controller in terms of conditional second-order moments: ProbeDetector Filtered output decreasing   BAC  x /  F = 10 Controlled state always more mixed than conditional state. Test masses fixed → can do simultaneous verification. Weak measurement optimal for low noise - but phase transition. Less mixed at quadrature close to amplitude → back-action- compensating (BAC).

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Constrains on controlled mirror entanglement  x /  F   c = 18.3  F,   d = 2.05  F   c = 22.3  F,   d = 2.07  F Much higher demand on classical noise SQL-beating, i.e. higher  x /  F. Optimal detection at  »  / 3. More power needed: here even   d >  F.

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Sub-SQL classical noise Noise budget advanced LIGO: Noise budget CLIO: [Report LIGO M] [Miyoki et al., Class. Quantum Grav. 21, S1173 (2004)] SQL  x /  F » 10 Here  x »  F » 30 Hz → ratio far too small!!! Careful with low frequency noise!

QND, LSC / Virgo Collaboration Meeting, 2007, HannoverH. Müller-Ebhardt Hannover prototype 10 m prototype with 100 g to 1 kg end mirrors. Low mechanical loss (silica) in end mirrors and thin coating/ or just gratings. Cool mirrors down to 20 K? Inject squeezed input! High power and frequency stabilized laser system… Implement double readout or entangle differential motion of a pair of coherently operated interferometers. → Need rigorous study of noise model.