Optomechanics: Hybrid Systems and Quantum Effects

Transcription

1 Centre for Quantum Engineering and Space-Time Research Optomechanics: Hybrid Systems and Quantum Effects Klemens Hammerer Leibniz University Hannover Institute for Theoretical Physics Institute for Gravitational Physics (Albert Einstein Institute) Cavity Optomechanics from the micro- to the macro scale Innsbruck Nov

2 Quantum Optomechanics Quantum effects so far in optomechanics (incl. μw electromechanics)» ground state cooling Chan Nature 478, 89 (2011). Teufel, Nature 475, 359 (2011).» ponderomotive squeezing Safavi-Naeini, arxiv: (2013). Brooks, Nature 488, 476 (2012). Purdy» back action noise in position sensing Purdy, Science 339, 801 (2013).» quantum coherent state transfer» optomechanical entanglement O Connell et al., Nature 464, 697 (2010) Palomaki, Nature 495, 210 (2013) Lehnert group (2013) Roukes, Schwab (2005)

3 Optomechanical entanglement» first nonclassical state of (micro)mechanical oscillator» resource for quantum state control of oscillator» entanglement as resource in Q-networks Rabl, Lukin Stannigel, Zoller

4 Stationary Entanglement Steady state of continuously driven optomechanical system can be entangled: Vitali, PRL 98, (2007) Genes, Mari, Mancini, Tombesi Paternostro Meystre Aspelmeyer, Zeilinger Eisert Genes, PRA 77, (2008) optomechanical cooperativity

5 Stationary Entanglement entanglement between mechanical oscillator & intracavity field unstable regime 10 coupling strength cooperativity detuning

6 Entanglement of mechanics and external field stationary entanglement: hard to produce/hard to verify entanglement has to be verified by measurements on external field Genes, Rev. A 78, (2008) entanglement with external modes required for applications in quantum information

7 Entanglement of mechanics and external field mechanical state conditioned on homodyne detection of light Wiseman, Milburn Quantum Measurement and Control mean phonon number conditioned on photocurrent necessary condition for correlations between mechanical oscillator & light (entanglement):

8 Conditional Phonon Number measurement of phase quadrature unstable regime 10 coupling strength cooperativity detuning

9 Conditional Phonon Number measurement of amplitude quadrature unstable regime 10 coupling strength cooperativity detuning

10 Conditional Phonon Number measurement of amplitude quadrature /phase quadrature conditional phonon number detuning for drive on upper sideband conditional state is essentially pure!

11 Drive on first blue sideband Resonant interaction is entangling Compare to parametric down-conversion in nonlinear optics: pump optical mode Ou, Pereira, Kimble, Peng, PRL 68, 3663 (1992) optical mode

12 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

13 Pulsed entanglement Drive on upper sideband creates entanglemt Problem: System is dynamically unstable for blue detuned drive Parametric heating leads to self induced oscillations Braginsky, Physics Letters A, 287:331, 2001 Marquardt, Ludwig, Khurgin, Armour, Nation EXP: Favero, Weig, Kippenberg, Vahala. Painter, Karrai, Khurgin unstable regime use a pulsed drive: solve scattering problem Sebastian G. Hofer, Witlef Wieczorek, Markus Aspelmeyer, KH Phys. Rev. A 84, (2011)

14 Pulsed Generation of Entanglement integrate for pulse suration central frequency at upper sideband assuming weak thermal decoherence sideband resolved limit for suppression of Anti-Stokes scattering weak coupling: adiabatic elimination of cavity mode (avoid memory effects)

15 Pulsed Generation of Entanglement will generate photons at cavity frequency in precise temporal mode mode profile input-output relations for scattered pulse in RWA, neglecting thermal noise squeezing parameter two mode squeezed state!

16 Pulsed Generation of Entanglement EPR variance, taking into account initial thermal occupation of mirror for if large EPR squeezing requires large cooperativity: for pulse length squeezing parameter

17 Verification of entanglement drive system on first red sideband: mechanical state is swapped to light Palomaki, Nature 495, 210 (2013) entanglement preparation and verification: entanglement 1 st pulse Precooling on red sideband entangling pulse on blue sideband time readout pulse on red sideband mec 2 nd pulse measure EPR quadratures of 1 st and 2 nd pulse and correlate red out Sebastian G. Hofer, Witlef Wieczorek, Markus Aspelmeyer, KH Phys. Rev. A 84, (2011)

18 Experiment by Lehnert group mw optomechanical system: Teufel, Nature 475, (2011) entangling pulse read-out pulse (= mechanics)

19 Experiment by Lehnert group mw optomechanical system: variances Variances covariances e.g.

20 Experiment by Lehnert group mw optomechanical system: T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert Entangling mechanical motion with microwave fields Science (2013) (to be published)

21 Extension I: Quantum Teleportation feedback B entangled Bell measurement A V Bennett PRL 1993 continuous variables: Braunstein, Kimble PRL 2003 Vaidman PRL 2003 feedback teleportation in optomechanics: talk by Paolo Tombesi Romero-Isart, Pflanzer, Cirac Sebastian G. Hofer, Witlef Wieczorek, Markus Aspelmeyer, KH Phys. Rev. A 84, (2011)

22 Extension II: Time Continuous Quantum Teleportation cw drive on upper sideband, continuous Bell measurement & (stabilizing) feedback?

23 Time Continuous Bell Measurements & Teleportation is special case of: system coupled to 1D field & continuous Bell measurement with system operator s for optomechanical system (with adiabatically eliminated cavity)

24 Stochastic Master Equation for Continuous Bell Measurement master equation for general case Gaussian input Hofer, Vasilyev, Aspelmeyer, KH, PRL 111, (2013)

25 Feedback Master Equation for Continuous Bell Measurement unconditional master equation including feedback Gaussian input Wiseman, Milburn, Quantum Measurement

26 Time Continuous Teleportation in Optomechanics 6dB input squeezing Gaussian input cooperativity applied to optomechanics squeezing: parametric drive time continuous quantum remote control: Non-Gaussian states reservoir engineering QND probe feedback more on quantum feedback control Paternostro, Vitali, Clerk, Marquardt talk by Mauro Paternostro Braginsky, Aspelmeyer, Schwab, Nunnenlamp Hofer, Vasilyev, Aspelmeyer, KH, PRL 111, (2013)

27 Quantum Optomechanics Quantum effects so far in optomechanics (incl. μw electromechanics)» ground state cooling Chan Nature 478, 89 (2011). Teufel, Nature 475, 359 (2011).» ponderomotive squeezing Safavi-Naeini, arxiv: (2013). Brooks, Nature 488, 476 (2012). Purdy» back action noise in position sensing Purdy, Science 339, 801 (2013).» quantum coherent state transfer» optomechanical entanglement O Connell et al., Nature 464, 697 (2010) Palomaki, Nature 495, 210 (2013) Lehnert group (2013)

28 Hybrid Quantum Systems Atoms coherent control & two level defects talk by Eva Weig talk by Peter Rabl Patrick Maletisnky talk by Mika Sillanpää

29 Hybrid Quantum Systems How can we coherently couple atomic ensembles (or single atoms) to solid state quantum systems?? Atomic ensembles/ single atoms Solid state systems e.g. mechanical oscillators Hybrid Mechanical Systems (review) Philipp Treutlein, Claudiu Genes, KH, Martino Poggio, Peter Rabl arxiv:

30 Related work I: Hybrid systems of Atoms and Micromechanical Oscillator Micromembrane Atoms in optical lattice Experiment: S. Camerer, M. Korppi, A. Jöckel, D. Hunger, T.W. Hänsch, P. Treutlein Phys. Rev. Lett. 107, (2011) Theory: KH, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch PRA 82, (2010) Berit Vogell et al. PRA 87, (2013) see POSTER

31 Quantum Treatment Hamiltonian: including membrane, atoms and electro-magnetic field as dofs laser drive will give rise in quadratic order in linear order kinetic energy of atoms optical potential to lattice potential for atoms and mean force on membrane to coupling of position fluctuations to EM vacuum fluctuations emission and reabsorption of sideband photons will give rise to effective coupling & quantum noise

32 Markovian Master Equation Resulting Markovian Master Equation Hamiltonian term for coherent atom-membrane interaction at strength Lindblad terms describing radiation pressure induced momentum diffusion of membrane K. Karrai PRL 100, (2008) optical spring between membrane and atomic COM motion and momentum diffusion of atoms at rates (requires 3D treatment) Gordon, Ashkin, Cohen-Tannoudji

33 Markovian Master Equation Resulting Markovian Master Equation Non-Lindblad term due to non-zero membrane transmittivity t effect is to reduce action of atoms on membrane atom membrane: membrane atom: Asymmetric coupling characteristic for cascaded quantum systems C.W. Gardiner, PRL 70, 2269 (1993) H. Carmichael, PRL 70, 2273 (1993)

34 Extension: Cavity enhancement & coupling to internal state enhances effective coupling by Finesse: saves a Lamb-Dicke factor in coupling g g F g g/(kx ZPF ) Berit Vogell et al. PRA 87, (2013) see POSTER Berit Vogell et al in prep.

35 Related Work II hybrid coupling inside one cavity KH, M. Wallquist, C. Genes, P. Zoller, M. Ludwig, F. Marquardt, P. Treutlein, J. Ye, H.J. Kimble, PRL 103, (2009), PRA (2010) other work: Meiser, Meystre Genes, Vital, Tombesi Ritsch Paternostro Sun, Nori cf talk by Aurelien Dantan talk by Darrick Chang

36 Collaborators: M. Aspelmeyer, W. Wieczorek P. Treutlein, S. Camerer, M. Korppi, A. Jöckel, D. Hunger, T.W. Hänsch B. Vogell, C. Genes, K. Stannigel, P. Zoller Group: Sebastian Hofer Denis Vasilyev Niels Loerch Sergey Tarabrin Klemens Hammerer Thank you! Centre for Quantum Engineering and Space- Time Research Institute for Theoretical Physics Albert Einstein Institute Quantum entanglement and teleportation in pulsed cavity-optomechanics Hofer, Wieczorek, Aspelmeyer, KH Phys. Rev. A 84, (2011) Continuous Bell Measurements Hofer, Vasilyev, Aspelmeyer, KH, arxiv: Support through: DFG (QUEST), EC (MALICIA, iquoems) WWTF