Cavity optomechanics: Introduction to Dynamical Backaction

Transcription

1 Cavity optomechanics: Introduction to Dynamical Backaction Tobias J. Kippenberg Collaborators EPFL-CMI K. Lister J. (EPFL) P. Kotthaus J. P. Kotthaus (LMU) W. Zwerger W. Zwerger (TUM) I. Wilson-Rae (TUM) A. Marx (WMI) J. Raedler J. Raedler (LMU) R. Holtzwarth (MenloSystem) T. W. Haensch (MPQ) EPFL Laboratory of Photonics and Quantum Measurements, EPFL Diavolezza 2013

2 Dynamical backaction in cavity optomechanics Radiation pressure Description of optomechanical coupling Dynamical backaction

3 1970: Radiation pressure trapping of particles Arthur Ashkin (Bell Labs) Optical tweezers: Used to study the motion of molecular motors (cf. work by C. Bustamente and Steve Block (Stanford) Terminology Note: The transverse light forces are called gradient forces as opposed to the forces in the propation direction (scattering force)

4 1975: Laser cooling using radiation pressure [1] D. J. Wineland and H. Dehmelt, Bull. Am. Phys. Soc. 20, 637 (1975); [2] T. W. Hänsch and A. L. Schawlow, "Cooling of Gases by Laser Radiation," Opt. Commun. 13, 68 (1975).

5 Prediction of radiation pressure cooling of mechanical osc. V.B. Braginsky Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977)

6 Measuring motion with optomechanical coupling V.B. Braginsky Central question of Braginsky: What is the influence of radiation pressure in a parametric transducer? Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977)

7 Measuring motion with optomechanical coupling The parametric transducer couples motion to a change in phase Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977)

8 Experimental implementations of parametric transducers Macroscale: Gravitational wave detectors nitiatives/supa_teops_ini.html Gravitational wave interferometric Detection (VIRGO) Dan Rugar (IBM) LIGO mirrors Quantum backaction: Radiation Pressure quantum fluctuation limit Position Sensitivity: Standard Quantum Limit [Roman Schnabel]

9 Canonical model for an optomechanical system [More: F. Marquardt]

10 Model for an optomechanical system vacuum optomechanical coupling rate Optical frequency shift Radiation pressure force

11 Canonical Model for an Optomechanical System Cavity decay rate Position dependent Detuning Input drive term

12 Parametric mechanical transducers: Weber bars Principle of capacitive mechanical gravitational wave detectors Joseph Weber adjusts the instrumentation on one of his aluminum cylinders 1] J. Weber, "Gravitational-Wave-Detector Events," Phys. Rev. Lett. 20, 1307 (1968).

13 Optomechanical systems at the macro, micro and nanoscale

14 Natural optomechanical coupling optical whispering-gallery-mode (WGM) meter mechanical radial-breathing-mode (RBM) oscillator Coupling strength Zero point motion *T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer and K.J. Vahala Physical Review Letters 95, Art. No (2005)

15 Naturally occuring optomechanical coupling Fundamental mode Kippenberg, Vahala Optics Express (2007)

16 Scattering versus gradient forces in dielectric microresonators Putting Light s Light Touch to Work As Optics Meets Mechanics», Science 2010

17 Sensitive position measurements and [The Standard Quantum Limit (SQL) > Schnabel]

18 Probing the optomechanical coupling experimentally critical coupling E t E cavity T= E-E 2 =0 T taper-microcavity junction exhibits extremely high ideality (coupling losses <0.3%) 40 m Pin Coupling both to-and-from a 80 m microtoroid on a chip S. M. Spillane, T. J. Kippenberg, O.J. Painter, K. J. Vahala. Phys. Rev. Lett. (2003). T.J. Kippenberg, S.M. Spillane, K.J. Vahala, Optics Letters, (2002).

19 Brownian motion Thermal motion

20 Detecting motion using optomechanical coupling Thermal motion amplitude Phase response

21 Homodyne detection of mechanical motion Thermal motion LO - Homodyne detection allows : - quantum limited detection of mechanical motion, also for low probe powers. - Classical amplitude noise cancellation

22 Homodyne detection of the mechanical motion Homodyne signal receiver sensitivity: - Signal to noise ratio at the detector H. Haus Quantum optical measurements

23 Thermal fluctuations of a Harmonic oscillator Mechanical oscillator undergoes Brownian motion: - Using a spectrum analyzer for a measurement time T we obtain the gated Fourier transform: Schliesser et al. Nature Physics 2008

24 Thermal fluctuations of a Harmonic oscillator - Autocorrelation function for time trace (duration T) Wiener-Khinchin theorem states that

25 Review: Fluctuation and Dissipation theorem Area is proportional to kt Damping of the mechanical oscillator Fluctuation dissipation theorem relates damping to a fluctuating force spectrum Integrated noise spectrum is proportional to temperature H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951)

26 Example noise spectral density of a toroid microresonator Schliesser, Anetsberger, Rivière, Arcizet, Kippenberg, NJP (2008)

27 Example noise spectral density of a toroid microresonator mechanical modes (model) Schliesser, Anetsberger, Rivière, Arcizet, Kippenberg, NJP (2008)

28 Example noise spectral density of a toroid microresonator mechanical modes (model) thermorefractive noise (model) Thermorefractive noise Landau, Lifshitz, Statistical Physics, Pergamon Press (1980) Gorodetsky, Grundinin, JOSA B, 21, 697 (2004) Schliesser, Anetsberger, Rivière, Arcizet, Kippenberg, NJP (2008)

29 Example noise spectral density of a toroid microresonator mechanical modes (model) thermorefractive noise (model) full model Schliesser, Anetsberger, Rivière, Arcizet, Kippenberg, NJP (2008)

30 Observing Brownian motion of toroid microresonators measured mechanical spectrum zoom on individual peaks mode patterns obtained from finite element modeling

31 Limits of the sensitivity Displacement spectrum S X (au) Background Displacement Peak displacement spectral density A figure of merit is to compare to spectral density of Zero Point Motion (Standard Quantum Limit) More on the SQL: Roman Schnabel

32 Nanomechanical transducers Single-electron transistor LaHaye et al., Science, 304, 74 (2004) ~20 x SQL S x > 20 S ZPM x Atomic point contact Flowers-Jacobs et al., PRL 98, (2007) ~40 x SQL S x 1000 S ZPM x Microwave cavity Teufel et al., Nature Nanotechnology, 4, 820 (2009) ~1 x SQL SQUID Etaki et al., Nature Physics 4, 785 (2008) ~40 x SQL

33 Imprecision below that at the SQL Optomechanical systems have achieved an imprecision below that at the SQL. Microwave domain: Teufel et al. Nature Nanotech. (2010) Optical domain: Anetsberger et al. Nature Physics (2009) / Phys. Rev. A. (2011) From signal to background one can deduce that the imprecision is below that at the SQL

34 Dynamical backaction Dynamical backaction Part II

35 Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977) Dynamical backaction: The influence of finite feedback Optical field responds on the mechanical motion with delay ( m,q m ) ( 0, Q 0 ) P in P cav ( ) x

36 Dynamical backaction: Amplification and Cooling ( 0, Q 0 ) ( m,q m ) LIGO P in P cav ( ) Radiation pressure x Amplification Blue detuning Cooling Red detuning Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977)

37 Linearized equations of motion Linearize equations of motion

38 The optical spring effect Opical spring effect refers to an optically induced rigidity Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977)

39 Example of a giant optical spring Mechanical rigidity can be dominated by the optical dipole field; «all optical mechanical oscillator» Eichenfeld et al. Vol May 2009 doi: /nature08061

40 Dynamical backaction: Cooling An oscillating mirror will cause Doppler up- and down-shifted fields. Power Frequency A cavity can create an imbalance due to resonant buildup Excess anti-stokes photons: Cooling Power Frequency Similar mechanism to cavity cooling of atoms and molecules (coherent scattering) V. Vuletic, S. Chu, Phys. Rev. Lett., Vol. 84, No. 17 (2000) P. Maunz, Puppe, Schuster, Syassen, Pinkse, Rempe, Nature (2004)

41 Dynamical backaction: Amplification An oscillating mirror will cause Doppler up- and down-shifted fields. Power Frequency A cavity can create an imbalance due to resonant buildup Excess Stokes photons: amplification Power Frequency Similar mechanism to cavity cooling of atoms and molecules (coherent scattering) V. Vuletic, S. Chu, Phys. Rev. Lett., Vol. 84, No. 17 (2000) P. Maunz, Puppe, Schuster, Syassen, Pinkse, Rempe, Nature 428, 50 (2004).

42 Radiation pressure interaction: A NLO Perspective Scattering from pump to redshifted sideband (Stokes scattering) Amplification Scattering from pump to redshifted sideband (anti-stokes scattering) Cooling - The laser detuning determines which process is dominant in the interaction. - The optomechanical interaction effectively behave as Raman scattering since:

43 Dynamical backaction Amplification 0 - m + m Power Frequency - Mechanical damping vanishes - Coherent oscillations emerge

44 Amplification: the parametric oscillation instability

45 Amplification: the parametric oscillation instability The parametric instability shows a clear threshold dependence Linewidth narrowing above threshold (similar to Maser) Threshold condition Dynamical backaction leads amplification not to heating. Rokhsari, Kippenberg, Carmon,Vahala Optics Express Vol. 13, No. 14

46 Generation of low phase noies coherent signals Historic first treatment of oscillator linewidth: Fundamental linewidth of an oscillator (Original formulation by Townes): A more insightful and general expression in the presence of quantum noise (e.g. Laser) and thermal noise (e.g. Maser, Phonon Laser) is: Eichenfeld et. al. Nature 2009 (doi: /nat ure08524) Gordon, Zeiger, Townes Phys. Rev. 99, 1264 (1955)

47 Dynamical backaction Cooling 0 - m + m Power Frequency Mechanical oscillator is being cooled! Laser is a cold damper since thermal force is the same.

48 Observation of radiation pressure cooling Key Parameters: Mechanical frequency of the cooled mode: 57.8 MHz Initial temperature 300 K Final effective temperature 11 K Demonstration of Radiation Pressure Cooling (2006) Nov. 2006: Arcizet, Cohadon, Briant, Pinard, Heidmann, Nature 444, 71 Nov. 2006: S. Gigan et al., Nature 444, 67 Dec. 2006: Schliesser, Del'Haye,. Nooshi, Vahala, Kippenberg, Phys. Rev. Lett. 97,

49 Strong retardation regime Radiation pressure effects: Mechanical oscillation frequency does increase in the regime of cooling, in excellence agreement with the Radiation pressure model. 0 - m + m No optical spring effect: Radiation pressure force is viscous Frequency

50 Quantum theory of cooling Quantum theory of cooling

51 Cooling: the naive picture Thermal Bath T bath Dissipation Fluctuation Oscillator Dissipation Laser field Cold damper Total damping: I. Wilson-Rae, Nooshi, Zwerger, Kippenberg, PRL 99, (2007) J. Dobrindt, Wilson-Rae, Kippenberg, PRL, 101, (2008) F. Marquardt, Chen, Clerk, Girvin, PRL 99, (2007)

52 Limits of backaction cooling Thermal Bath T bath Dissipation Fluctuation Oscillator Dissipation Laser field Cold damper I. Wilson-Rae, Nooshi, Zwerger, Kippenberg, PRL 99, (2007) J. Dobrindt, Wilson-Rae, Kippenberg, PRL, 101, (2008) F. Marquardt, Chen, Clerk, Girvin, PRL 99, (2007)

53 Quantum noise picture: Shot noise in the cavity Quantum Noise approach Laser detuning Photon number variance Spectrum of Photon Number Fluctuations inside cavity Cavity decay rate F. Marquardt, Chen, Clerk, Girvin, PRL 99, (2007)

54 Quantum noise picture: Shot noise in the cavity Reservoir heating Quantum Backaction Doppler limit ground-state cooling impossible resolved sideband cooling ground-state cooling possible

55 Cooling considerations Thermal Bath T bath Dissipation Fluctuation Oscillator Dissipation Fluctuations Laser field Cold damper Wilson-Rae, Nooshi, Zwerger, Kippenberg, PRL 99, (2007) Marquardt, Chen, Clerk, Girvin, PRL 99, (2007) Improving mechanical Q Cryogenics...

56 Frequency landscape Resolved sideband dynamical backaction cooling Quantum theory : Wilson-Rae, Nooshi, Zwerger, Kippenberg, PRL 99, (2007) Marquardt, Chen, Clerk, Girvin, PRL 99, (2007) Only for:

57 Further reading Science 327, 516 (2010) Nature Materials 9, S20 (2010) Science 328, 802 (2010) Further reading: Kippenberg, Vahala: Optics Express 15, (2007) Kippenberg, Vahala: Science 321, 1172 (2008) Marquardt, Girvin: Physics 2, 40 (2009) Genes, Mari, Vitali, Tombesi: Advances in Atomic, Molecular, and Optical Physics 57 (2009) (Theory) also at arxiv: Schliesser, Kippenberg: Advances in Atomic, Molecular, and Optical Physics 58 (2010) (Experiment) also at arxiv: