Cavity optomechanics: Introduction to Dynamical Backaction

CollaboratorsEPFL-CMI K. ListerJ. P. KotthausW. ZwergerI. Wilson-RaeA. MarxJ. Raedler

Tobias J. Kippenberg

EPFL

Laboratory of Photonics and QuantumMeasurements, EPFL

Diavolezza 2013

CollaboratorsEPFL-CMI K. Lister (EPFL)J. P. Kotthaus (LMU)W. Zwerger (TUM)I. Wilson-Rae (TUM)A. Marx (WMI)J. Raedler (LMU)R. Holtzwarth

(MenloSystem)T. W. Haensch (MPQ)

Dynamical backaction in cavityoptomechanics

Radiation pressure Description of optomechanical coupling Dynamical backaction

Optical tweezers: Used to study the motion of molecular motors(cf. work by C. Bustamente and Steve Block (Stanford)

Arthur Ashkin (Bell Labs)

1970: Radiation pressure trapping of particles

Terminology Note: The transverse light forces are called gradient forces as opposed to the forces in the propation direction (scatteringforce)

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.

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

V.B. Braginsky

Measuring motion with optomechanical coupling

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

V.B. Braginsky

Central question of Braginsky: What is the influence of radiation pressure in a parametric transducer?

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

Dan Rugar (IBM)

Gravitational wave interferometricDetection (VIRGO)

www.ligo-wa.caltech.edu/

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

LIGO mirrorsQuantum backaction: Radiation Pressure quantum fluctuation limitPosition Sensitivity: Standard Quantum Limit

[Roman Schnabel]

Canonical model for an optomechanical system

[More: F. Marquardt]

Optical frequency shift

Radiation pressure force

Model for an optomechanical system

vacuum optomechanicalcoupling rate

Canonical Model for an Optomechanical System

Input drive termCavity decay rate Position dependentDetuning

Parametric mechanical transducers: Weber bars

Principle of capacitive mechanicalgravitational 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).

Optomechanical systems at the macro, micro and nanoscale

opticalwhispering-gallery-mode (WGM)„meter“

mechanicalradial-breathing-mode (RBM)

„oscillator“

Coupling strength

Zero point motion

Natural optomechanical coupling

*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

Kippenberg, Vahala Optics Express (2007)

Fundamental mode

Scattering versus gradient forces in dielectric microresonators

“Putting Light’s Light Touch to WorkAs Optics Meets Mechanics», Science 2010

Sensitive position measurements and[The Standard Quantum Limit (SQL) ‐> 

Schnabel]

Coupling both to-and-from a 80mmicrotoroid on a chip

taper-microcavity junction exhibits extremely high ideality (coupling losses <0.3%)

Pin

T

40 m

EcavityEt

critical coupling

T=|E-E|2=0

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).

Probing the optomechanical coupling experimentally

Thermal motion

Brownian motion

Thermal motion

Detecting motion using optomechanical coupling

amplitude

Phase response

Homodyne detection allows : - quantum limited detection of

mechanical motion, also for lowprobe powers.

- Classical amplitude noise cancellation

-

Thermal motion LO

Homodyne detection of mechanical motion

Homodyne detection of the mechanical motion

-

H. Haus „Quantum optical measurements“

Homodyne signal receiver sensitivity:

Signal to noise ratio at the detector

Thermal fluctuations of a Harmonic oscillator

Mechanical oscillator undergoes Brownian motion:

-

Schliesser et al. Nature Physics 2008

Using a spectrum analyzer for a measurement time T weobtain the gated Fourier transform:

Thermal fluctuations of a Harmonic oscillator\

- Autocorrelation function for time trace (duration T)

Wiener-Khinchin theorem states that

Review: Fluctuation and Dissipation theorem

H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951)

Fluctuation dissipation theorem relates damping to a fluctuating force spectrum

Damping of the mechanical oscillator

Area is proportional to kT

Integrated noise spectrum isproportional to temperature

Schliesser, Anetsberger, Rivière, Arcizet, Kippenberg, NJP (2008)

Example noise spectral density of a toroid microresonator

mechanical modes (model)

Example noise spectral density of a toroid microresonator

Schliesser, Anetsberger, Rivière, Arcizet, Kippenberg, NJP (2008)

mechanical modes (model)thermorefractive noise (model)

Thermorefractive noise

Landau, Lifshitz, Statistical Physics, Pergamon Press (1980)Gorodetsky, Grundinin, JOSA B, 21, 697 (2004)

Example noise spectral density of a toroid microresonator

Schliesser, Anetsberger, Rivière, Arcizet, Kippenberg, NJP (2008)

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

Example noise spectral density of a toroid microresonator

Schliesser, Anetsberger, Rivière, Arcizet, Kippenberg, NJP (2008)

measuredmechanicalspectrum

zoom onindividual peaks

mode patternsobtained fromfinite elementmodeling

Observing Brownian motion of toroid microresonators 

Displacement

Background

Disp

lace

men

tspe

ctru

mS X

(au)

A figure of merit is to compare to spectral density of Zero Point Motion

(Standard Quantum Limit)

Limits of the sensitivity

Peak displacement spectral density

More on the SQL: Roman Schnabel

Microwave cavityTeufel et al., Nature Nanotechnology, 4, 820 (2009)~1 x SQL

SQUIDEtaki et al., Nature Physics 4, 785 (2008)~40 x SQL

Sx ≈ 1000 · SZPMx

Sx > 20 · SZPMx

Single-electron transistorLaHaye et al., Science, 304, 74 (2004)~20 x SQL

Atomic point contactFlowers-Jacobs et al., PRL 98, 096804 (2007)~40 x SQL

Nanomechanical transducers 

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

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)

Dynamical backaction

Dynamical backaction

Part II

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

Pin Pcav()

(m

x

Q0)

,Qm)

(0,

Dynamical backaction: The influence of finite feedback

Optical field responds on the mechanical motion with delay

Radiation pressure

Pin Pcav()

(m

x

Q0)

,Qm)

(0,

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

LIGO

Amplification Blue detuning

Cooling Red detuning

Dynamical backaction: Amplification and Cooling

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

Eichenfeld et al. Vol 459|28 May 2009| doi:10.1038/nature08061

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

Pow

er

An oscillating mirror will cause Doppler up- and down-shifted fields.

A cavity can create an imbalance due to resonant buildup

Excess anti-Stokes photons: Cooling

Frequency

Frequency

Pow

erV. Vuletic, S. Chu, Phys. Rev. Lett. , Vol. 84, No. 17 (2000)P. Maunz, Puppe, Schuster, Syassen, Pinkse, Rempe, Nature (2004)

Similar mechanism to cavity cooling of atoms and molecules (coherent scattering)

Dynamical backaction: Cooling

Pow

er

An oscillating mirror will cause Doppler up- and down-shifted fields.

A cavity can create an imbalance due to resonant buildup

Excess Stokes photons: amplification

Frequency

Frequency

Pow

erV. Vuletic, S. Chu, Phys. Rev. Lett. , Vol. 84, No. 17 (2000)P. Maunz, Puppe, Schuster, Syassen, Pinkse, Rempe, Nature 428, 50 (2004).

Similar mechanism to cavity cooling of atoms and molecules (coherent scattering)

Dynamical backaction: Amplification

Radiation pressure interaction: A NLO Perspective

Scattering from pump to redshiftedsideband (anti-Stokes scattering)

Cooling

Scattering from pump to redshiftedsideband (Stokes scattering)

Amplification

- The laser detuning determines which process is dominant in the interaction.- The optomechanical interaction effectively behave as Raman scattering since:

Frequency

Dynamical backaction Amplification 

- Mechanical damping vanishes

- Coherent oscillations emerge

+m

0

- m

Frequency

Pow

er

Amplification: the parametric oscillation instability

Amplification: the parametric oscillation instability

The parametric instability shows a clearthreshold dependence

Linewidth narrowing above threshold(similar to Maser)

Dynamical backaction leads amplification not to heating.

Threshold condition

Rokhsari, Kippenberg, Carmon,Vahala Optics Express Vol. 13, No. 14

Generation of low phase noies coherent signals

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

Fundamental linewidth of an oscillator (Originalformulation by Townes):

A more insightful and general expression in thepresence of quantum noise (e.g. Laser) andthermal noise (e.g. Maser, Phonon Laser) is:

Historic first treatment of oscillator linewidth:

Eichenfeld et. al. Nature 2009 (doi:10.1038/nature08524)

+m

0

- m

FrequencyPo

wer

Dynamical backaction Cooling

Mechanical oscillator is being cooled! Laser is a cold damper since thermal force isthe same.

Key Parameters:

•Mechanical frequency of the cooled mode: 57.8 MHz

•Initial temperature 300 K

•Final effective temperature 11 K

Nov. 2006: Arcizet, Cohadon, Briant, Pinard, Heidmann, Nature 444, 71Nov. 2006: S. Gigan et al., Nature 444, 67 Dec. 2006: Schliesser, Del'Haye,. Nooshi, Vahala, Kippenberg, Phys. Rev. Lett. 97, 243905

Demonstration of Radiation Pressure Cooling (2006)

Observation of radiation pressure cooling

Radiation pressure effects:•Mechanical oscillation frequency does increase in the regime of cooling, in excellence agreement with the Radiation pressure model.

No optical spring effect:Radiation pressure force is viscous

+m

0

- m

Frequency

Strong retardation regime

Quantum theory of cooling

Quantum theory of cooling

OscillatorThermal

BathTbath

Dissipation Dissipation

Fluctuation

Laser field

„Cold damper“

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)

Total damping:

Cooling: the naive picture 

OscillatorThermal

BathTbath

Dissipation Dissipation

Fluctuation

Laser field

„Cold damper“

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

Quantum Noise approach

Spectrum of Photon Number Fluctuations inside cavity

F. Marquardt, Chen, Clerk, Girvin, PRL 99, 093902 (2007)

Quantum noise picture: Shot noise in the cavity

Photon number variance

Laser detuning

Cavity decay rate

Quantum BackactionReservoir heating

„Doppler“ limitground-state cooling impossible

resolved sideband coolingground-state cooling possible

Quantum noise picture: Shot noise in the cavity

OscillatorThermal

BathTbath

Dissipation Dissipation

Fluctuation

„Cold damper“

Laser field

Improving mechanical Q Cryogenics....

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

Fluctuations

Cooling considerations 

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

Frequency landscape

Resolved sideband dynamical backaction cooling

Quantum theory : Only for:

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

Further reading:

Kippenberg, Vahala: Optics Express 15, 17172 (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:0901.2726

Schliesser, Kippenberg: Advances in Atomic, Molecular, and Optical Physics 58 (2010) (Experiment) also at arXiv:1003.5922

Further reading