Post on 01-Nov-2020
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