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Introduction to Optomechanics – Part 2
Loıc Rondin
Photonics Group – ETH Zurich
December 2014
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 1 of 20
Content
Reminders
Cooling of the centre of mass motion
Cavity cooling
Feedback cooling
Alternative cooling
Ground State of the mechanical resonator
Standard Quantum limit
Applications of OM
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 2 of 20
Content
Reminders
Cooling of the centre of mass motion
Cavity cooling
Feedback cooling
Alternative cooling
Ground State of the mechanical resonator
Standard Quantum limit
Applications of OM
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 3 of 20
Cavity Optomechanics
x(t)
k
m
EinE0(t)
Cavity Optomechanics setup
I Mirror motion impacting
the light phase
I Light gives momentum to
the mirror through
radiation pressure
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 4 of 20
Power spectral density PSD
Interesting results related to thePSD
I Fluctuation-Dissipation Theorem
Sxx(ω) =2kBT
ωIm(χ)
I Equipartition theorem∫R
Sxx(ω)dω = 〈x2〉 ∝ Teff
x(t)
t
≈1/Γ
≈√Teff
PSD(ω)
ωωm-ωm
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 5 of 20
Cavity Opto-mechanics
Finally, coupled equations systemmx+mΓx+mωmx = Ffluct(t)+
ε0
2|E0|2nA(1+R)
E0 =
[i(ω−ω0
(1− x(t)
L
)− γ0
]E0 +κEin
Rewrote :
mx+m(Γ+δΓ)x+m(ωm +δω)x = Ffluct(t)
δΓ =
π2R(1−R)2
8n2ω0
m2cωm
γexγ0Pin
(ω−ω0)2 + γ20
[γ2
0
(ω−ω0 +ωm)2 + γ20+
γ20
(ω−ω0−ωm)2 + γ20
]
δω =π2R
(1−R)24n2ω0
m2cωm
γexγ0Pin
(ω−ω20 + γ2
0
[(ω−ω0 +ωm)γ0
(ω−ω0 +ωm)2 + γ20+
(ω−ω0−ωm)γ0
(ω−ω0−ωm)2 + γ20
]
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 6 of 20
Content
Reminders
Cooling of the centre of mass motion
Cavity cooling
Feedback cooling
Alternative cooling
Ground State of the mechanical resonator
Standard Quantum limit
Applications of OM
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 7 of 20
Cavity cooling
|E0|2
ωω ω+ωmω-ωm
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 8 of 20
Cavity cooling
|E0|2
ωω ω+ωmω-ωm
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 8 of 20
Cavity cooling
|E0|2
ωω ω+ωmω-ωm
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 8 of 20
Cavity cooling
|E0|2
ωω ω+ωmω-ωm
Metzger & Karrai Nature 432, 1002 (2004).
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 8 of 20
Cold damping
Active feedbackUse radiation pressure to feedback a signal
FFBopt =−mδΓx
Arcizet, O. et al. Phys. Rev. Lett. 97, 133601 (2006).
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 9 of 20
Parametric feedback cooling
Gieseler et al. Phys. Rev. Lett. 109, 103603 (2012)
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 10 of 20
Sympathetic cooling
Joekel et al. Nat. Nano (2014)
Cool by coupling to a colder object
Here atoms can be optically cooled, and sympathetically cool down the
mechanical oscillator
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 11 of 20
Hybrid systems
Yeo, I. et al. Nat Nano (2013).
Potential side-band resolved
regime
I single emitters, single
spins, . . .
I coupling through strain,
magnetic or electric field.
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 12 of 20
Ground state of the mechanical resonator
How cold can we cool a mechanical resonator ?
I Classical HO
E =12
mv2 +12
mω2mx2
I Quantum HO
H =p2
2m+
12
mω2mx2
= hω(b†b+12)
I phonon creation and annhilation
operators : b† and b
E
x
ħωm
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 13 of 20
Opto-mechanical systems
Kleckner & Bouwmeester Nature 444, 75(2006)
Groblacher et al. Nat. Phys. 5, 485 (2009) Schliesser et al. Nat. Phys. 4, 415 (2008)
Chan et al. Nature (2011)
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 14 of 20
Opto-mechanical systems
Kleckner & Bouwmeester Nature 444, 75(2006)
Groblacher et al. Nat. Phys. 5, 485 (2009) Schliesser et al. Nat. Phys. 4, 415 (2008)
Chan et al. Nature (2011)
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 14 of 20
Ground state of the mechanical resonator
Going to the ground state : Quantum analysis
I The field is also described as an OHI a,a† : photon annihilation, creation operators
I HamiltonianI H = hω0a†a+ hωmb†b+ hg0xZPM(b† +b)a†a
Observing quantum effects ?
I Sideband asymmetry
Safavi-Naeini et al. Phys. Rev. Lett. 108, 033602. (2012)
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 15 of 20
Physical limit to measurement : SQL
Aspelmayer et al. arXiv :1303.0733 (2013)
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 16 of 20
Physical limit to measurement : SQL
Aspelmayer et al. arXiv :1303.0733 (2013)
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 16 of 20
Content
Reminders
Cooling of the centre of mass motion
Cavity cooling
Feedback cooling
Alternative cooling
Ground State of the mechanical resonator
Standard Quantum limit
Applications of OM
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 17 of 20
Challenges of optomechanics
Metrology
Macroscopic Quantum Physics
Signal processing
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 18 of 20
Force sensing
Rugar et al. Nature 430, 329–332 (2004).
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 19 of 20
Force sensing
Fmin =√
4kBTeffΓeff
Moser, J. et al. Nat Nano 8, 493–496 (2013).
Rugar et al. Nature 430, 329–332 (2004).
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 19 of 20
short bibliography
I Novotny, L. and Hecht, B. Principles of Nano-Optics. (Cambridge
University Press, 2012), Chapter 11
I Aspelmeyer, M., Kippenberg, T. J. and Marquardt, F. Cavity
Optomechanics. arXiv :1303.0733 (2013). at
http://arxiv.org/abs/1303.0733
I Meystre, P. A short walk through quantum optomechanics.
arXiv :1210.3619 (2012). at
http://arxiv.org/abs/1210.3619
(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 20 of 20