Cavity Optomechanics: Introduction to Dynamical Backaction

Cavity optomechanics: Introduction to Dynamical Backaction

Tobias J. Kippenberg

EPFL Collaborators EPFL-CMI K.K. Lister Lister Laboratory of Photonics and Quantum J.(EPFL) P. Kotthaus Measurements, EPFL J. P. Kotthaus (LMU) W. ZwergerZwerger (TUM) I. Wilson-Rae (TUM) Diavolezza 2013 A. Marx (WMI) J. Raedler (LMU) R. Holtzwarth (MenloSystem) T. W. Haensch (MPQ) Dynamical backaction in cavity optomechanics

. Radiation pressure . Description of optomechanical coupling . Dynamical backaction 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) 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). Prediction of radiation pressure cooling of mechanical osc.

V.B. Braginsky

Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977) 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) 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) Experimental implementations of parametric transducers

Macroscale: Gravitational wave detectors

http://www.supa.ac.uk/Research/astro/i nitiatives/SUPA_TEOPS_Ini.html

Dan Rugar (IBM)

Gravitational wave interferometric Detection (VIRGO) LIGO mirrors Quantum backaction: Radiation Pressure quantum fluctuation limit Position Sensitivity: Standard Quantum Limit

[Roman Schnabel]

www.ligo-wa.caltech.edu/ Canonical model for an optomechanical system

[More: F. Marquardt] Model for an optomechanical system

vacuum optomechanical coupling rate

Optical frequency shift

Radiation pressure force Canonical Model for an Optomechanical System

Cavity decay rate Position dependent Input drive term Detuning Parametric mechanical transducers: Weber bars

Principle of capacitive mechanical Joseph Weber adjusts the gravitational wave detectors instrumentation on one of his aluminum cylinders

1] J. Weber, "Gravitational-Wave-Detector Events," Phys. Rev. Lett. 20, 1307 (1968). Optomechanical systems at the macro, micro and nanoscale Natural optomechanical coupling optical mechanical whispering-gallery-mode (WGM) radial-breathing-mode (RBM) „meter“ „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. 033901 (2005) Naturally occuring optomechanical coupling

Fundamental mode

Kippenberg, Vahala Optics Express (2007) Scattering versus gradient forces in dielectric microresonators

“Putting Light’s Light Touch to Work As Optics Meets Mechanics», Science 2010 Sensitive position measurements and [The Standard Quantum Limit (SQL) ‐> Schnabel] Probing the optomechanical coupling experimentally

critical coupling E Et cavity

T=|E-E|2=0

40 m Pin taper-microcavity junction exhibits extremely high ideality (coupling losses Coupling both to-and-from a 80m <0.3%) 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). Brownian motion

Thermal motion Detecting motion using optomechanical coupling

Thermal motion

amplitude

Phase response 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 Homodyne detection of the mechanical motion

Homodyne signal receiver sensitivity:

Signal to noise ratio at the detector

H. Haus „Quantum optical measurements“ 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 \ Thermal fluctuations of a Harmonic oscillator

- Autocorrelation function for time trace (duration T)

Wiener-Khinchin theorem states that 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) Example noise spectral density of a toroid microresonator

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

mechanical modes (model)

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

mechanical modes (model) thermorefractive noise (model) full model

Schliesser, Anetsberger, Rivière, Arcizet, Kippenberg, NJP (2008) Observing Brownian motion of toroid microresonators

measured mechanical spectrum

zoom on individual peaks

mode patterns obtained from finite element modeling Limits of the sensitivity

Peak displacement spectral

(au) density X

Background A figure of merit is to compare to spectral density of Zero Displacement Point Motion Displacement spectrum S

(Standard Quantum Limit)

More on the SQL: Roman Schnabel Nanomechanical transducers

Single-electron transistor LaHaye et al., Science, 304, 74 (2004) ZPM ~20 x SQL Sx > 20 Sx Atomic point contact · Flowers-Jacobs et al., PRL 98, 096804 (2007) ~40 x SQL

S 1000 SZPM x ≈ · x

Microwave cavity Te u f e l et al., Nature Nanotechnology, 4, 820 (2009) ~1 x SQL

SQUID Etaki et al., Nature Physics 4, 785 (2008) ~40 x SQL Imprecision below that at the SQL Optomechanical systems have achieved an imprecision below that at the SQL.

From signal to background one can deduce that the imprecision is 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) Dynamical backaction

Dynamical backaction

Part II Dynamical backaction: The influence of finite feedback

Optical field responds on the mechanical motion with delay

(m ,Qm)

(0, Q0)

Pin Pcav()

Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977) Dynamical backaction: Amplification and Cooling

(m ,Qm) LIGO (0, Q0)

Pin Pcav()

Radiation pressure x

Amplification Blue detuning

Cooling Red detuning

Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977) Linearized equations of motion

Linearize equations of motion The optical spring effect

Opical spring effect refers to an optically induced rigidity

Braginsky, Manukin: Measurement of Weak Forces in Physics Experiments (1977) Example of a giant optical spring

Mechanical rigidity can be dominated by the optical dipole field; «all optical mechanical oscillator»

Eichenfeld et al. Vol 459|28 May 2009| doi:10.1038/nature08061 Dynamical Similar mechanism to cavity coolingof V. P.

Maunz, Vuletic, xesat-tkspoos Cooling Excess anti-Stokes photons: resonant buildup A cavitycancreate an imbalance due to p and down-shiftedfields. up- cause Doppler will oscillating mirror An

Puppe, S.

Chu,

Schuster, Phys. backaction:

Rev.

Syassen,

Lett.

Vol.

Pinkse, atoms and molecules(coherent scattering)

84,

Cooling

No.

Rempe,

(2000)

Nature (2004)

Power Power Frequency Frequency Dynamical Similar mechanism to cavity coolingof V. P.

Maunz, Vuletic, xesSoe htn:amplification Excess Stokesphotons: resonant buildup A cavitycancreate an imbalance due to p and down-shiftedfields. up- cause Doppler will oscillating mirror An

Puppe, S.

Chu,

Schuster, Phys. backaction:

Rev.

Syassen,

Lett.

Vol.

Pinkse, atoms and molecules(coherent scattering)

84,

Amplification

No.

Rempe,

(2000)

Nature

428,

(2004).

Power Power Frequency Frequency 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: Dynamical backaction Amplification

0

 - m +m Power

Frequency

- Mechanical damping vanishes - Coherent oscillations emerge Amplification: the parametric oscillation instability Amplification: the parametric oscillation instability

The parametric instability shows a clear Linewidth narrowing above threshold threshold dependence (similar to Maser)

Threshold condition Dynamical backaction leads amplification not to heating.

Rokhsari, Kippenberg, Carmon,Vahala Optics Express Vol. 13, No. 14 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 Eichenfeld et. thermal noise (e.g. Maser, Phonon Laser) is: al. Nature 2009 (doi:10.1038/nat ure08524)

Gordon, Zeiger, Townes Phys. Rev. 99, 1264 (1955) Dynamical backaction Cooling

0

 - m +m Power

Frequency

Mechanical oscillator is being cooled! Laser is a cold damper since thermal force is the same. 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, 243905 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: Frequency Radiation pressure force is viscous Quantum theory of cooling

Quantum theory of cooling Cooling: the naive picture

Dissipation Dissipation Thermal Laser field Bath Oscillator T „Cold damper“ bath Fluctuation

Total damping:

I. Wilson-Rae, Nooshi, Zwerger, Kippenberg, PRL 99, 093901 (2007) J. Dobrindt, Wilson-Rae, Kippenberg, PRL, 101, 263602 (2008) F. Marquardt, Chen, Clerk, Girvin, PRL 99, 093902 (2007) Limits of backaction cooling

Dissipation Dissipation Thermal Laser field Bath Oscillator T „Cold damper“ bath Fluctuation

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, 093902 (2007) Quantum noise picture: Shot noise in the cavity

Reservoir heating Quantum Backaction

resolved sideband cooling „Doppler“ limit ground-state cooling possible ground-state cooling impossible Cooling considerations

Laser field Dissipation Dissipation Thermal Bath Oscillator „Cold damper“ Tbath Fluctuation Fluctuations

Wilson-Rae, Nooshi, Zwerger, Kippenberg, PRL 99, 093901 (2007) Marquardt, Chen, Clerk, Girvin, PRL 99, 093902 (2007)

Improving mechanical Q Cryogenics.... Frequency landscape

Resolved sideband dynamical backaction cooling

Quantum theory : Only for: Wilson-Rae, Nooshi, Zwerger, Kippenberg, PRL 99, 093901 (2007) Marquardt, Chen, Clerk, Girvin, PRL 99, 093902 (2007) Further reading

Science 327, 516 (2010) Nature Materials 9, S20 (2010) Science 328, 802 (2010)