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Entanglement between test masses

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)

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Entanglement between test masses

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  1. 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

  2. Compare with optics: Entangled output Input squeezing Entanglement between end mirrors Total system: Logarithmic negativity [Vidal, Werner] a quantitative measure of entanglement:

  3. Radiation pressure & classical forces. Conditional second-order moments not changed by any linear feedback control! Shot & classical sensing noise. Conditioning on continuous measurement Each (common and differential) mode: Prepare state by collecting data and finding optimal filter function. Need verification stage? → Stefan’s talk.

  4. known unknown Wiener Filtering Conditional moments of Gaussian state: Steady state!

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

  6. c = 11.5 F, d = 0.87 F 5 dB c = 7.0 F, d = 0.8 F 10 dB c = 10.6 F, d = 0.3 F Optimal: Detect both modes at » -  / 2 → then independent from laser noise! x / F x / F- threshold larger than 2 for entanglement. x / F Constrains on conditional mirror entanglement [arXiv:quant-ph/0702258] Laser noise level. Common mode detection at » -  /2. Detection close to amplitude quadrature (» -  /2) → modes more squeezed – but at same time even more anti-squeezed!

  7. No laser noise! Conditional mirror entanglement x / F = 10 x / F = 8 Log [ d / F ] Log [ d / F ] Log [ c / F ] Log [ c / F ] x / F = 6 x / F = 4 Log [ d / F ] Log [ d / F ] Log [ c / F ] Log [ c / F ]

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

  9. Probe Detector Filtered output x / F = 10 decreasing  BAC Controlled test-mass state With optimal controller in terms of conditional second-order moments: • 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).

  10. c = 18.3 F, d = 2.05 F c = 22.3 F, d = 2.07 F x / F Constrains on controlled mirror entanglement • Much higher demand on classical noise SQL-beating, i.e. higher x/F. • Optimal detection at » / 3. • More power needed: here even d > F.

  11. SQL Careful with low frequency noise! x / F» 10 Sub-SQL classical noise Noise budget advanced LIGO: Noise budget CLIO: [Report LIGO-060056-07-M] Herex»F» 30 Hz → ratio far too small!!! [Miyoki et al., Class. Quantum Grav. 21, S1173 (2004)]

  12. 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.

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