Quantum Effects in Optomechanics

Transcription

1 Centre for Quantum Engineering and Space-Time Research Quantum Effects in Optomechanics Klemens Hammerer Leibniz University Hannover Institute for Theoretical Physics Institute for Gravitational Physics (Albert Einstein Institute) Quantum Phononics Workshop Heraklion May

2 Optomechanical systems D. Bowmeester, Santa Barbara/Leiden LIGO Laser Interferometer Gravitational Wave Observatory up to

3 Optomechanical systems Micromirrors Micromembranes Microtoroids Aspelmeyer (Vienna) Heidmann (Paris) Bouwmeester (St Barbara, Leiden) Harris (Yale) Kimble (Caltech) Vengalattore (Cornell) Treutlein (Basel) Polzik (Copenhagen) Kippenberg (MPQ) Weig (LMU) Vahala (Caltech) Bowen (UQ)

4 Optomechanical systems Optomechanical Crystals Painter (Caltech) Tang (Yale) Pernice (KIST) Groeblacher (Delft) Optomechanics with BEC Esslinger (Caltech) Stamper-Kurn (Berkeley) Levitated Nanoobjects Aspelmeyer/Arndt (Wien) Raizen (Austin) Novotny (ICFO, ETH)

5 Electromechanics Cleland Lehnert Teufel Schwab Hybrid system: O Connell et al Nature 464, 697 (2010).

6 Mechanical Systems Coupled to Light Quantum Optomechanics M. Aspelmeyer, F. Marquardt, T. Kippenberg, RMP, arxiv: A short walk through quantum optomechanics P. Meystre Annalen der Physik 525, 215 (2013). Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics Y. Chen J Phys. B (2013) Quantum Optomechanics - throwing a glance M. Aspelmeyer, S. Groeblacher, KH, N. Kiesel JOSA B 27, A189 (2010)

7 Mechanical oscillators Small vibrations described by: Eigenfrequencies Eigenmodes Displacement field J. Harris 1mm x 1mm x 50 nm amplitude slide: F. Marquardt

8 response amplitude Mechanical oscillators Small vibrations described by: Eigenfrequencies Eigenmodes Displacement field Each eigenmode is a harmonic oscillator effective mass damping external force slide: F. Marquardt frequency

9 Optomechanical systems radiation pressure interaction

10 M. Aspelmeyer, F. Marquardt, T. Kippenberg, RMP, arxiv: Optomechanical systems radiation pressure interaction example: for

11 Radiation pressure interaction phase of cavity is shifted according to position of mirror phase quadrature mirror receives momentum transfer from reflected photons amplitude quadrature

12 Linearized Radiation pressure interaction phase of cavity is shifted according to position of mirror for f luctuations around mean field phase quadrature in terms of quadratures mirror receives momentum transfer according to amplitude fluctuations amplitude quadrature

13 Linearized Radiation pressure interaction linearized equations of motion phase quadrature effective coupling strength amplitude quadrature number of circulating photons for 1mW and 1 MHz line width strong coupling & normal mode splitting Groeblacher, KH, Vanner, Aspelmeyer, Nature 460, 724 (2009)

14 Linearized Radiation pressure interaction linearized equations of motion phase quadrature effective Hamiltonian amplitude quadrature

15 Decay and Noise vacuum noise on cavity thermal noise on mirror mean number of phonons in thermal equilibrium thermal decoherence rate

16 Optomechanical Cooperativity condition for quantum coherent dynamics: large optomechanical cooperativity

17 Quantum Effects in Optomechanics Quantum effects so far in optomechanics (incl. μw electromechanics)» ground state cooling» Quantum coherent coupling» ponderomotive squeezing» back action noise in position sensing» quantum coherent state transfer» optomechanical entanglement Chan Nature 478, 89 (2011). Teufel, Nature 475, 359 (2011). Verhagen, Nature 482, 63 (2012). Safavi-Naeini, arxiv: (2013). Brooks, Nature 488, 476 (2012). Purdy, Science 339, 801 (2013). O Connell et al., Nature 464, 697 (2010) Palomaki, Nature 495, 210 (2013) Palomaki, Science 342, 710 (2013)» feedback control within decoherence time Wilson, arxiv: (2014) Roukes, Schwab (2005) KH, Science (2013)

18 Optomechanical Ground State Cooling drive on red sideband hot mirrror cavity cold effective equation of motion for (complex) mirror amplitude increased damping radiation pressure noise thermal force

19 I. Wilson-Rae, PRL 99, (2007) F. Marquardt, PRL 99, (2007) Optomechanical Ground State Cooling Steady State Phonon Number increased damping radiation pressure noise thermal force mirrror radiation pressure noise thermal force ground state cooling achieved for strong cooperativity sideband resolution

20 Optomechanical Ground State Cooling mw electromechanics Teufel et al. Nature 475, 359 (2011) optomechanics Chan et al. Nature 478, 89 (2011)

21 Optomechanical Ground State Cooling Optimal regime for sideband cooling: drive with detuning sideband resolved regime Enhanced Anti-Stokes scattering: Suppressed Stokes scattering: photon number phonon number

22 Optomechanical Phase Diagramm unstable coupling strength unstable cooperativity stable detuning C. Genes, D. Vitali et al. Phys. Rev. A 77, (2008)

23 Optomechanical Cooling unstable regime 10 coupling strength cooperativity detuning Teufel, Painter, Aspelmeyer, Regal, Purdy

24 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

25 Digression: Two Mode Squeezing Squeezed states of two modes each mode looks like it was in a thermal state overall state is pure with corresponding wave function

26 Digression: EPR Correlations for infinite squeezing this corresponds to the ideal EPR state Center of mass position and relative momentum take sharp values for two mode squeezed states with finite squeezing limit for uncorrelated states in ground state

27 Digression: Entanglement Two mode squeezed states are entangled: cannot be written as product state a mixed states is entangled if it can not be written as a mixture of product states general EPR entanglement criterion for two modes a state is entangled if limit for uncorrelated states in ground state for Gaussian states this is necessary & sufficient (after slight generalization) Duan PRL (2000) Simon PRL (2000)

28 Pulsed entanglement Drive on upper sideband creates entanglement Problem: System is dynamically unstable for blue detuned drive unstable regime noise use a pulsed drive: solve scattering problem Sebastian G. Hofer, Witlef Wieczorek, Markus Aspelmeyer, KH Phys. Rev. A 84, (2011) O. Romero-Isart et al., Physical Review A 83, (2011)

29 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)

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

31 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 Sebastian G. Hofer, Witlef Wieczorek, Markus Aspelmeyer, KH Phys. Rev. A 84, (2011)

32 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 red out measure EPR quadratures of 1 st and 2 nd pulse and correlate Sebastian G. Hofer, Witlef Wieczorek, Markus Aspelmeyer, KH Phys. Rev. A 84, (2011)

33 Experiment by Lehnert group mw optomechanical system: Entangling mechanical motion with microwave fields T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert Science (2013) news & views: KH, Science (2013)

34 Optomechanical Entanglement Two-mode squeezed (Gaussian), entangled state of a macroscopic (micron-sized) mechanical oscillator and a travelling pulse of (mw) light detection of single photon projects mechanical oscillator in single phonon Fock state Galland, Sangouard, Piro, Gisin, Kippenberg, PRL 112, (2014)

35 Binary Observable Add coherent amplitude before detection no click define the binary observable no click click!

36 Bell Inequality for Binary Observables source of entangled systems A & B CHSH Inequality (implied by realism & locality) For two (effective) spin ½ systems in singlet state: rules out (realism and locality)

37 Bell Inequality in Optomechanics 0) Initialization of mechanics in ground state by red sideband cooling 1) Optomechanical entanglement by blue sideband pulse 2) Displacement by amplitude α & photon counting 3) Swap of mechanical state to photons by red sideband pulse 4) Displacement by amplitude β & photon counting Repeat for various measurement setting α and β and infer

38 Realization in Electro-Mechanics Lecocq, arxiv: qubit cavity optomechanical master equation for cascaded cavity setup: collaboration with Konrad Lehnert (JILA)

39 Photon-Counting in Electro-Mechanics Lecocq, arxiv: qubit cavity qubit transition frequency photon number in cavity

40 Photon-Counting in Electro-Mechanics Lecocq, arxiv: qubit cavity qubit transition frequency photon number in cavity

41 Photon-Counting in Electro-Mechanics Lecocq, arxiv: qubit cavity qubit transition frequency photon number in cavity measurement of qubit in e

42 Bell Inequality in Optomechanics transmittivity Bell violation cooperativity For parameters of: T. A. Palomaki, Science (2013) with Includes thermal decoherence, finite detection efficiency, transmission losses

43 Quantum Optomechanics quantum effects so far demonstrate large cooperativity rely on linear dynamics use homodyne detections preserve Gaussian states therefore, have an equivalent classical interpreation (with some level of noise) Bell inequality violation excludes any classical interpretation! So far only achieved with photons, trapped ions and superconducting qubits.

44 Optomechanical Phase Diagram unstable regime 10 coupling strength cooperativity stable regime detuning cooling read-out position sensing heating entanglement BI violation

45 CW drive on blue side: Time Continuous Teleportation continuous wave drive on upper sideband, continuous Bell measurement & (stabilizing) feedback: feedback Bell measurement B entangled A V Hofer, Vasilyev, Aspelmeyer, KH, PRL 111, (2013) Hofer, KH arxiv:

46 CW drive on blue side: Limit Cycles nonlinear model for mechanical amplitude nonlinear optical damping classical: Marquardt, Ludwig RMP, arxiv: quantum: J. Qian, A. Clerk, KH, F. Marquardt, PRL 109, (2012) N. Lörch, J. Qian, A. Clerk, F. Marquardt, KH, arxiv: , PRX (2014)

47 diffusion damping CW drive on blue side: Limit Cycles nonlinear model for mechanical amplitude quantum mechanical treatment classical: Marquardt, Ludwig RMP, arxiv: quantum: J. Qian, A. Clerk, KH, F. Marquardt, PRL 109, (2012) N. Lörch, J. Qian, A. Clerk, F. Marquardt, KH, arxiv: , PRX (2014)

48 Group: Sebastian Hofer Niels Loerch Ondrej Cernotik Alexander Roth Jonas Lammers Marius Schulte Hashem Zoubi Klemens Hammerer Thank you! Centre for Quantum Engineering and Space- Time Research Collaborators on optomechanics Konrad Lehnert (JILA) Florian Marquardt (Erlangen) Ash Clerk (McGill) Roman Schnabel (Hannover/Hamburg) Farit Khalili (Moscow) Markus Aspelmeyer (Vienna) Eugene Polzik (Copenhagen) Philipp Treutlein (Basel) Peter Zoller (Innsbruck) Klaus Hornberger (Duisburg) Institute for Theoretical Physics Albert Einstein Institute Support through: DFG (QUEST, GRK 1991) EC (MALICIA, iquoems) Vienna (WWTF)