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

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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

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UPON 2015 Yaroslav M. Blanter

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
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Cavity/circuit optomechanics

† † † †

ˆ ˆ ˆ ˆ ˆ ˆ( )

cav m

H a a b b g a a b b w w = +

  • +

h h h

Cavity Mechanical resonator Radiation pressure coupling

( )

cav x

w

Kippenberg's Group website

Movable mirror Static mirror

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Cavity/circuit optomechanics

Verhagen et al, Nature 482, 63 (2012) Yuan et al, arXiv:1507.08898 Chan et al, Nature 478, 89 (2011) Singh et al, Nature Nanotech. 9, 820 (2014)

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Coupling

† † † †

ˆ ˆ ˆ ˆ ˆ ˆ( )

cav m

H a a b b g a a b b w w = +

  • +

h h h

m cav

k w w = =

Dissipation rate in the cavity Where is ?

g

Weak coupling Strong coupling Driving and linearization:

cav

g g n =

( )

† †

ˆ ˆ g a b ab + h

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Conversion between optical and microwave light

Andrews et al, Nature Physics 10, 321 (2014)

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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)

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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

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Non-linear optomechanics

What is non-linear?

– Cavity: Microwave with a Josephson junction – Mechanical resonator – Radiation pressure interaction

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Non-linear cavity

  • S. Etaki, F. Konschelle, H. Yamaguchi,

YMB, H. S. J. van der Zant, Nature Comm. 4, 1803 (2013)

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dc SQUID

F

1 1

, I j

2 2

, I j

1 2

I I I = +

2 1

( ) /(2 ) j j p F = F

  • Josephson junctions:

1,2 1,2

sin I I j = c e p F º h

Total current through the loop:

2 cos sin I I p j æ ö F = ç ÷ F è ø

Very sensitive detector of magnetic field

2 1 2

cos sin cos

c J

E E x g x g x p p p a æ ö æ ö æ ö F F F = - + = + ç ÷ ç ÷ ç ÷ F F F è ø è ø è ø

Coupling to mechanical motion:

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Non-linear cavity

  • S. Etaki, F. Konschelle, H. Yamaguchi,

YMB, H. S. J. van der Zant, Nature Comm. 4, 1803 (2013)

Self-sustained oscillations!

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Non-linear cavity

  • S. Etaki, F. Konschelle, H. Yamaguchi, YMB, H. S. J. van der Zant,

Nature Comm. 4, 1803 (2013)

  • 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

1,2 1,2 1,2 1,2 1,2 1,2

sin , 2 V I I CV V R j j p F = + + = & &

R(V) C

I

2 1

cos [ , ] M Mx x M x F t aBlI x x Q w w w + + = + && & &

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Non-linear mechanical resonator

Singh et al, Nature Nanotech. 9, 820 (2014)

Graphene membrane

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Optomechanically induced transparency

From: Aspelmeyer, Kippenberg, and Marquardt Rev. Mod. Phys. 86, 1391 (2014) Cavity is strongly red-driven at

cav m

w w

  • (red-detuned)

Probe laser measures the transmission around the cavity resonance

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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

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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
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Input-output relations

2 3 †

ˆ ˆ ˆˆ ˆ (1 ) ( ) 2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ( )

ext in c vac m m th

da i a igxa s s t dt dx p dt m dp m x x ga a p F t dt k k h kd w a d æ ö = D -

  • +

+

  • ç

÷ è ø = = -

  • +
  • G

+ h

Langevin equations for the creation/annihilation operators:

Detuning and dissipation in the cavity Input signal Quantum noise Coupling Mechanical dissipation Thermal noise

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Non-linear OMIA

  • O. Shevchuk et al, arXiv:1507.06851

Red-detuned drive Overcoupled cavity

1 2

ext

k h k k = > +

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Non-linear OMIA

  • O. Shevchuk et al, arXiv:1507.06851
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Unsolved problems: Creation of non-classical mechanical states

Vlastakis et al, Science 342, 607 (2013)

Schoelkopf group, Yale: created cat states in a cavity 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)
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Unsolved problems: Strong coupling

† † † †

ˆ ˆ ˆ ˆ ˆ ˆ( )

cav m

H a a b b g a a b b w w = +

  • +

h h h

( )

† †

ˆ ˆ / g a b ab + h

  • Use non-linearized interaction pressure: need

single-photon strong coupling (Nunnenkamp, Borkje, Girvin)

  • g

k ?

  • For cooling the resonator to the ground state: Cooperativity

2

g C k = G

  • Photon blockade: a non-linear resonator; entangles phonons and photons

(Didier, Pugnetti, YMB, Fazio)

What else?

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Unsolved problems: Strong coupling

  • What happens at very strong coupling?
  • m

g w ?

  • Role of non-linearity at strong coupling? Beyond Kerr

† †

ˆ ˆ ˆ ˆ Ka a aa

  • Role of quantum noise?
  • Novel physical phenomena?
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Unsolved problems: Optomechanical arrays

Next complexity level?

Example: M. Schmidt, V. Peano,

  • F. Marquardt, arXiv:1410.8483:
  • ptically tunable

Dirac-type structire

  • What happens to dissipation?
  • Non-linear effects? Chaos?
  • Quantum effects?
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Conclusions

  • Non-linear effects are important
  • The are even more important if coupling is strong
  • There are many things ahead of us
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Classical and quantum non-linear dynamics in optomechanical systems

Olga Shevchuk João Machado François Konschelle

Delft-Theory Delft-Experiment

Vibhor Singh Sal Bosman Ben Schneider Mingyun Yuan Gary Steele

Support: FOM (Stichting voor Fundamenteel Onderzoek der Materie)

Samir Etaki Menno Poot Herre van der Zant Nicolas Didier Stefano Pugnetti Rosario Fazio

SNS Pisa NTT

Imran Mahboob Koji Onomitsu Hiroshi Yamaguchi