Einstein-Podolsky-Rosen entanglement t of massive mirrors

Transcription

1 Einstein-Podolsky-Rosen entanglement t of massive mirrors Roman Schnabel Albert-Einstein-Institut t i tit t (AEI) Institut für Gravitationsphysik Leibniz Universität Hannover Outline Squeezed and two-mode squeezed light EPR entanglement of two light fields EPR entanglement of two massive quasi-free mirrors conditioned on interferometric measurements Testing modified d quantum theories The Quantum Car Race 2 1

2 Quantum Noise of Monochromatic Fields (â(t)) E ˆ ˆ ˆX1 X 1, X 2 i 2 Tomografic Measurement, since (â(t)) Quadrature angle Coherent state quadrature noise: ˆX1 ˆX Quantum Noise of Monochromatic Fields (aˆ) E (aˆ) Quadrature angle Amplitude-quadrature squeezed state quadrature noise 4 2

3 Quantum Noise of Monochromatic Fields (aˆ) E (aˆ) Quadrature angle Phase-quadrature squeezed state quadrature noise 5 Quantum Noise of Monochromatic Fields (aˆ) E (aˆ) Quadrature angle Squeezed vacuum state quadrature noise 6 3

4 Wigner Function of Vacuum Squeezing Phase-space quasi-probability distribution of a squeezed vacuum state Measured: db / +16 db@5mhz [Mehmet et al., PRA 81, (2010)] 7 Wigner-Functions: EPR-Entanglement ˆ X 2, ˆ p Amplitude squeezed state Phase squeezed state ˆ X 1, ˆ x + Measurement of Amplitude Measurement of Phase /50 beam splitter +0 o o o + + B A X A A 1, X 2 i 2 X A B 1 X 1, X A B 2 X 2 Precise inference at A is possible through measurement at B [M. Reid, PRA 40, 913 (1989)] [Ou, Kimble et al. PRL 68, 3663 (1992)] 0 8 4

5 Due to Bell-tests we know: QM is complete! Subsystems of entangled states yield their individual properties with respect to the environment through the measurement. 9 The GEO600 Squeezed Light Laser 10 5

6 Generation of Squeezed Light (PDC) Pump field input (cw, 532nm) 2 -nonlinear crystal: MgO:LiNbO 3 Squeezed field output (cw, 1064nm) by parametric down-conversion (PDC) Standing wave cavity 11 Quantum Noise of Monochromatic Fields (aˆ) E (aˆ) Quadrature angle Squeezed vacuum state quadrature noise 12 6

7 Generation of Squeezed Vacuum [J. Bauchrowitz, T. Westphal, R. Schnabel, submitted to Am.J.Phys.] 13 EPR-Entangled Light ˆ X 2, ˆ p Amplitude squeezed state Phase squeezed state ˆ X 1, ˆ x + Measurement of Amplitude Measurement of Phase /50 beam splitter +0 o o o + + B A X A A 1, X 2 i 2 X A B 1 X 1, X A B 2 X 2 Precise inference at A is possible through measurement at B [M. Reid, PRA 40, 913 (1989)] [Ou, Kimble et al. PRL 68, 3663 (1992)]

8 Demonstration of EPR Entanglement E 2 = 0,205 0,2 = 0,041 < 1 [S. Steinlechner et al., PRA (2013) accepted, arxiv: ] 15 Demonstration of EPR Entanglement [S. Steinlechner et al., PRA accepted, arxiv: (2012)] 16 8

9 EPR-Entanglement / Decoherence ˆ X 2, ˆ p Amplitude squeezed state Phase squeezed state ˆ X 1, ˆ x + Measurement of Amplitude Measurement of Phase /50 beam splitter +0 o o o + + B A Mixing the state with vacuum states (due to loss) or with thermal states reduces and even destroys the squeezing. The measurement result at A can only be inferred if the loss is < 50%. Precise inference at A is possible through measurement at B [M. Reid, PRA 40, 913 (1989)] [Ou, Kimble et al. PRL 68, 3663 (1992)] 17 From Optics to Optomechanics Almost no thermal photons in the laser mode. Many thermal phonons in the pendulum mode. 18 9

10 Thermal Occupation number Many thermal phonons in the pendulum mode. Pendulum with period 1s: = 2 Hz n<1! T < K! 19 EPR entangled Mirrors: Challenging! How can the temperature be reduced? Are there other ways to get pure states of mirror motion? Do we need a joint radiation pressure force on two mirrors? What should the interferometric arrangement be? Radiation pressure does entangle mechanics and light! [Bose, Jacobs, Knight, Phys. Rev. A 56, 4175 (1997)] [Mancini, Manko, Tombesi, Phys. Rev. A 55, 3042 (1997)] [Vitali, Aspelmeyer et al., Phys. Rev. Lett. 98, (2007)] Light/mirror entanglement needs to be swapped! [Pirandola et al., Phys. Rev. Lett. 97, ( 2006)] 20 10

11 BHD: X com 1 (t) Low finesse A BHD:X 2 diff (t) B Michelson Interferometer with 2x balanced homodyne detection (BHD): Entanglement swapping Information on which the mechanical state can be conditioned* *also: [M. Haixing, S. Danilishin, H. Muller-Ebhardt, Y. Chen, New J. Phys. 12, (2010)] 21 Common and differential mode of motion p A (t) + p B (t) p A (t) p B (t) conditional common mode x A (t) + x B (t) x A (t) x B (t) conditional differential mode The conditional states are rather pure, even at T = 300K 22 11

12 Entangled Mirror Motion Noise Light/mirror entanglement Noise Entanglement swapping diff X 0 A. Franzen, AEI : p A? p B 0 X 90 com : x? x 0 A B [RS, H. Müller-Ebhardt, and H. Rehbein, Phys. Unserer Zeit 39, 234 (2008)] 23 EPR Entanglement and the SQL q,diff F x q,com Y diff (t) SQL: Standard Quantum Limit of (external) force measurement Classical sensing noise [H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, and Y. Chen, Quantumstate preparation and macroscopic entanglement in gravitational-wave detectors, Phys. Rev. A 80, (2009)] 24 12

13 Feasibility of EPR Entangled Mirrors P 6 W 1550 nm PR 0.02 L 10 m m 100 g m m T r 0 2 Hz Hz 15 K 1 cm Laser noise 10 db above quantum level. 25 Verification of EPR Entangled Mirrors Measurement of x A or p A BHD: X com 1 (t) Low finesse A B Measurement of x B or p B BHD:X diff 2 (t) Result: 1) Values of x A, x B, p A and p B show large uncertainties. 2) A comparision reveals the correlations: x A +x B 0 und p A p B 0 < ZPF A,B

14 Verification of EPR Entangled Mirrors [H.Miao, S.Danilishin, H.Müller-Ebhardt, H.Rehbein, K.Somiya, Y.Chen, Probing macroscopic quantum states with a sub-heisenberg accuracy, Phys. Rev. A 81, (2010)] 27 From Mesoscopic to Massiv Oscillators a) b) e) c) d) Macroscopic mechanical oscillators: visible to the naked eye. Massive mechanical oscillators: a weight one can feel, a frequency one can hear

15 Adding Self-Gravity to Quantum Mechanics Adding nonrelativistic Newtonian theory of gravity (NG) to quantum mechanics (QM), [Courtesy D. Giulini] [L. Diósi, Phys. Lett. A120, 377 (1987); Phys. Rev. A 40, 1165; J. Phys. A 40, 2989 (2007)] [R. Penrose, Gen. Rel. Grav. 28, 581 (1996)] 29 Adding Self-Gravity to Quantum Mechanics Diosi/Penrose model of modified quantum mechanics: Quantum superpositions vanish within a time scale of 1/ times (a) self-energy of the mass-distribution difference (Schrödinger cats) (b) mutual gravitational energy among components Example: L = 0.2 m, q = 1 khz, m = 1 kg = s = 10-6 s [L. Diósi, Phys. Lett. A120, 377 (1987); Phys. Rev. A 40, 1165; J. Phys. A 40, 2989 (2007)] [R. Penrose, Gen. Rel. Grav. 28, 581 (1996)] 30 15

16 Entangled Mirror Motion A. Franzen, AEI [RS, H. Müller-Ebhardt, and H. Rehbein, Phys. Unserer Zeit 39, 234 (2008)] 31 Quantum Car Race 32 16

17 Quantum Car Race x A p A x B p p B 33 Quantum Car Race p A p B 0 x A x B 0 [R. Wengenmayr, MaxPlanckForschung 4, 26 (2008)] 34 17

18 Summary The centre of mass motion of two heavy quasi-free mirrors can be prepared in an EPR-entangled state The ideal device is a Michelson interferometer, with balanced homodyne detection at both ports An independent verification of the EPR entanglement is possible The EPR-paradox contradicts classical mechanics Centre of Excellence: Quantum engineering and space time research 35 18