Classical and quantum non-linear dynamics in optomechanical systems - PowerPoint PPT Presentation

Classical and quantum non-linear dynamics in optomechanical systems Yaroslav M. Blanter Kavli Institute of Nanoscience, Delft University of Technology  Cavity/circuit optomechanics  Non-linear mechanical resonators  Non-linear cavities and self-sustained oscillations  Unsolved problems Yaroslav M. Blanter UPON 2015

Cavity/circuit optomechanics Movable mirror Static mirror Radiation w cav x ( ) pressure coupling Kippenberg's Group website ˆ ˆ = w + w - + † † † † ˆ ˆ ˆ ˆ( H h a a h b b h g a a b b ) cav m 0 Mechanical Cavity resonator Yaroslav M. Blanter UPON 2015

Cavity/circuit optomechanics Chan et al, Nature 478 , 89 (2011) Singh et al, Nature Nanotech. 9 , 820 (2014) Yuan et al, arXiv:1507.08898 Verhagen et al, Nature 482 , 63 (2012) Yaroslav M. Blanter UPON 2015

Coupling ˆ ˆ = w + w - + † † † † ˆ ˆ ˆ ˆ( H h a a h b b h g a a b b ) cav m 0 Dissipation rate in the cavity k w w = = m cav g Where is ? 0 Strong coupling Weak coupling ( ) = g g n + † † ˆ ˆ h g a b ab Driving and linearization: 0 cav Yaroslav M. Blanter UPON 2015

Conversion between optical and microwave light Andrews et al, Nature Physics 10 , 321 (2014) Yaroslav M. Blanter UPON 2015

Quantum signatures of mechanical motion Chan et al, Nature 478 , 89 (2011) Also: O'Connell et al, Nature 464 , 697 (2010); Teufel et al, Nature 475 , 359 (2011); Verhagen et al, Nature 482 , 63 (2012) Yaroslav M. Blanter UPON 2015

Non-linear optomechanics Why is non-linearity important? – Because it is there – Modifies the behavior, especially at strong coupling – Preparation of non-classical states of mechanical resonator Yaroslav M. Blanter UPON 2015

Non-linear optomechanics What is non-linear? – Cavity: Microwave with a Josephson junction – Mechanical resonator – Radiation pressure interaction Yaroslav M. Blanter UPON 2015

Non-linear cavity S. Etaki, F. Konschelle, H. Yamaguchi, YMB, H. S. J. van der Zant, Nature Comm. 4 , 1803 (2013) Yaroslav M. Blanter UPON 2015

dc SQUID p h c = + I I I F º F = F j - j p ( ) /(2 ) 1 2 0 0 2 1 e j , I j F , I 1 1 Josephson junctions: 2 2 = j I I sin 1,2 0 1,2 æ ö p F = j Total current through the loop: I 2 I cos sin ç ÷ 0 F è ø 0 Very sensitive detector of magnetic field Coupling to mechanical motion: æ ö æ ö æ ö p F p F p F = - + a = + 2 E E cos x g x sin g x cos ç ÷ ç ÷ ç ÷ c J 1 2 F F F è ø è ø è ø 0 0 0 Yaroslav M. Blanter UPON 2015

Non-linear cavity S. Etaki, F. Konschelle, H. Yamaguchi, YMB, H. S. J. van der Zant, Nature Comm. 4 , 1803 (2013) Self-sustained oscillations! Yaroslav M. Blanter UPON 2015

Non-linear cavity  Josephson junctions: RSJ model  Coupling: Lorentz force depends on the phases  Generally: coupled non-linear (stochastic) differential equations  Inertia term essential  Physics: Lorentz force back-action renormalizes the quality factor of the mechanical resonator and makes it negative F V C & = j + 1,2 + = j & I I sin CV , V 0 1,2 0 1,2 1,2 1,2 1,2 p R 2 I w M + + w = w + && & 2 & Mx x M x F cos t aBlI x x [ , ] 1 Q R ( V ) S. Etaki, F. Konschelle, H. Yamaguchi, YMB, H. S. J. van der Zant, Nature Comm. 4 , 1803 (2013) Yaroslav M. Blanter UPON 2015

Non-linear mechanical resonator Graphene membrane Singh et al, Nature Nanotech. 9 , 820 (2014) Yaroslav M. Blanter UPON 2015

Optomechanically induced transparency From: Aspelmeyer, Kippenberg, and Marquardt Rev. Mod. Phys. 86 , 1391 (2014) w - w Cavity is strongly red-driven at (red-detuned) cav m Probe laser measures the transmission around the cavity resonance Yaroslav M. Blanter UPON 2015

Optomechanically induced transparency Singh et al, Nature Nanotech. 9 , 820 (2014) First observation: S. Weis et al, Science 330, 1520 (2010) Constructive interference between the two probes results in OMIT Yaroslav M. Blanter UPON 2015

Non-linear OMIT Duffing oscillator: Does the shape of the transmission maximum repeat the response of the driven Duffing ocsillator? Not always, the phase dynamics is important. V. Singh et al, arXiv:1508.04298 Yaroslav M. Blanter UPON 2015

Input-output relations Langevin equations for the creation/annihilation operators: k ˆ æ ö da = D - - + k + - h kd ˆ ˆˆ ˆ i a igxa s (1 ) s ( ) t ç ÷ ext in c vac dt è 2 ø ˆ ˆ dx p Detuning and dissipation Input signal Quantum noise = in the cavity dt m ˆ dp = - w - a + -G + d 2 3 † ˆ ˆ ˆ ˆ ˆ m x x h ga a p F t ( ) m m th dt Mechanical Thermal noise Coupling dissipation Yaroslav M. Blanter UPON 2015

Non-linear OMIA Red-detuned drive Overcoupled cavity k 1 h = > O. Shevchuk et al, arXiv:1507.06851 k + k 2 ext Yaroslav M. Blanter UPON 2015

Non-linear OMIA O. Shevchuk et al, arXiv:1507.06851 Yaroslav M. Blanter UPON 2015

Unsolved problems: Creation of non-classical mechanical states Schoelkopf group, Yale: created cat states in a cavity Vlastakis et al, Science 342 , 607 (2013) How can we make non-classical mechanical states in the cavity architecture?  Transfer from the cavity  Make the cavity or the resonator non-linear (Yurke, Stoler) Yaroslav M. Blanter UPON 2015

Unsolved problems: Strong coupling ( ) ˆ ˆ + = w + w - + † † † † † † ˆ ˆ ˆ ˆ( ˆ ˆ / g a b h ab H h a a h b b h g a a b b ) cav m 0 k g ?  Use non-linearized interaction pressure: need o single-photon strong coupling (Nunnenkamp, Borkje, Girvin) 2 g  For cooling the resonator to the ground state: Cooperativity = G C 0 k  Photon blockade: a non-linear resonator; entangles phonons and photons (Didier, Pugnetti, YMB, Fazio) What else? Yaroslav M. Blanter UPON 2015

Unsolved problems: Strong coupling w g ?  What happens at very strong coupling? o m † † ˆ ˆ ˆ ˆ Ka a aa  Role of non-linearity at strong coupling? Beyond Kerr  Role of quantum noise?  Novel physical phenomena? Yaroslav M. Blanter UPON 2015

Unsolved problems: Optomechanical arrays Next complexity level? Example: M. Schmidt, V. Peano, F. Marquardt, arXiv:1410.8483: optically tunable Dirac-type structire  What happens to dissipation?  Non-linear effects? Chaos?  Quantum effects? Yaroslav M. Blanter UPON 2015

Conclusions  Non-linear effects are important  The are even more important if coupling is strong  There are many things ahead of us Yaroslav M. Blanter UPON 2015

Classical and quantum non-linear dynamics in optomechanical systems Delft-Experiment Delft-Theory Vibhor Singh Olga Shevchuk Sal Bosman João Machado Ben Schneider François Konschelle Mingyun Yuan Gary Steele SNS Pisa Nicolas Didier Samir Etaki Stefano Pugnetti Menno Poot NTT Rosario Fazio Herre van der Zant Imran Mahboob Koji Onomitsu Hiroshi Yamaguchi  Support: FOM (Stichting voor Fundamenteel Onderzoek der Materie) Yaroslav M. Blanter UPON 2015