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Introduction to Optomechanics – Part 2

Loıc Rondin

[email protected]

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

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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

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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

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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

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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

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Cavity cooling

|E0|2

ωω ω+ωmω-ωm

Metzger & Karrai Nature 432, 1002 (2004).

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Cold damping

Active feedbackUse radiation pressure to feedback a signal

FFBopt =−mδΓx

Arcizet, O. et al. Phys. Rev. Lett. 97, 133601 (2006).

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Parametric feedback cooling

Gieseler et al. Phys. Rev. Lett. 109, 103603 (2012)

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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

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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.

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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

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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)

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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)

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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)

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Physical limit to measurement : SQL

Aspelmayer et al. arXiv :1303.0733 (2013)

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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

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Challenges of optomechanics

Metrology

Macroscopic Quantum Physics

Signal processing

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Force sensing

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Force sensing

Rugar et al. Nature 430, 329–332 (2004).

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Force sensing

Fmin =√

4kBTeffΓeff

Moser, J. et al. Nat Nano 8, 493–496 (2013).

Rugar et al. Nature 430, 329–332 (2004).

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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

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