Optomechanics: Hybrid Systems and Quantum Effects Klemens Hammerer Cavity Optomechanics – from the micro- to the macro scale – Innsbruck – Nov 06 2013 Centre for Quantum Engineering and Space-Time Research Leibniz University Hannover Institute for Theoretical Physics Institute for Gravitational Physics (Albert Einstein Institute)
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Optomechanics: Hybrid Systems and Quantum Effects · Optomechanics: Hybrid Systems and Quantum Effects Klemens Hammerer Cavity Optomechanics – from the micro- to the macro scale
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Optomechanics: Hybrid Systems and Quantum Effects
Klemens Hammerer
Cavity Optomechanics – from the micro- to the macro scale – Innsbruck – Nov 06 2013
Centre for Quantum Engineering
and Space-Time Research
Leibniz University Hannover
Institute for Theoretical Physics
Institute for Gravitational Physics (Albert Einstein Institute)
Quantum effects so far in optomechanics (incl. μw electromechanics)
» ground state cooling
» ponderomotive squeezing
» back action noise in position sensing
» quantum coherent state transfer
» optomechanical entanglement
Quantum Optomechanics
Chan Nature 478, 89 (2011).
Teufel, Nature 475, 359 (2011).
Safavi-Naeini, arXiv:1302.6179 (2013).
Brooks, Nature 488, 476 (2012).
Purdy
Purdy, Science 339, 801 (2013).
O’Connell et al., Nature 464, 697 (2010)
Palomaki, Nature 495, 210 (2013)
Lehnert group (2013)
Roukes, Schwab (2005)
» first nonclassical state of (micro)mechanical oscillator
» resource for quantum state control of oscillator
» entanglement as resource in Q-networks
Optomechanical entanglement
Rabl, Lukin
Stannigel, Zoller
Steady state of continuously driven
optomechanical system can be entangled:
optomechanical cooperativity
Stationary Entanglement
Vitali, PRL 98, 030405 (2007)
Genes, Mari, Mancini, Tombesi
Paternostro
Meystre
Aspelmeyer, Zeilinger
Eisert
…
Genes, PRA 77, 033804 (2008)
entanglement between mechanical oscillator & intracavity field
Stationary Entanglement
- 2 - 1 0 1 2 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
coupling
strength
detuning
unstable regime
1
2
5
10
cooperativity
stationary entanglement: hard to produce/hard to verify
entanglement has to be verified by measurements on external field
entanglement with external modes required for applications in quantum information
Entanglement of mechanics and external field
Genes, Rev. A 78, 032316 (2008)
mechanical state conditioned on
homodyne detection of light
mean phonon number conditioned on photocurrent
necessary condition for correlations between mechanical oscillator & light (entanglement):
Entanglement of mechanics and external field
Wiseman, Milburn
Quantum Measurement and Control
Conditional Phonon Number
- 2 - 1 0 1 2 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4 unstable regime
measurement of phase quadrature
coupling
strength
cooperativity
detuning
1
2
5
10
Conditional Phonon Number
- 2 - 1 0 1 2 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4 unstable regime
measurement of amplitude quadrature
coupling
strength
detuning
1
2
5
10
cooperativity
measurement of amplitude quadrature
for drive on upper sideband conditional state is essentially pure!
- 2 - 1 0 1 2 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Conditional Phonon Number
conditional
phonon
number
detuning
/phase quadrature
Resonant interaction is entangling
Compare to parametric down-conversion in nonlinear optics:
Drive on first blue sideband
pump
Ou, Pereira, Kimble, Peng,
PRL 68, 3663 (1992)
optical
mode
optical
mode
optical
mode
Digression: EPR Correlations
for infinite squeezing this corresponds to the ideal EPR state
Center of mass position and relative momentum take sharp values
for states with finite entanglement (EPR squeezing) limit for
uncorrelated states
in ground state
Drive on upper sideband creates entanglemt
Problem: System is dynamically unstable for blue detuned drive
Parametric heating leads to self induced oscillations
use a pulsed drive: solve scattering problem
Pulsed entanglement
- 2 - 1 0 1 2
1 2
5
10
unstable regime Braginsky, Physics Letters A, 287:331, 2001