Introduction to Optomechanics – Part 2

Lo¨ıc 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

(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

Cavity Optomechanics setup m

k I Mirror motion impacting

E0(t) the light phase Ein I Light gives momentum to x(t) 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 the x(t) 1/Γ PSD

≈√T I Fluctuation-Dissipation Theorem eff

2kBT t Sxx(ω) = Im(χ) ω PSD(ω)

I Equipartition theorem Z 2 Sxx(ω)dω = hx i ∝ Teff ω

R -ωm ωm

(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 5 of 20 Cavity Opto-mechanics

Finally, coupled equations system

 ε0 2  mx¨ + mΓx˙ + mωmx = Ffluct(t) + |E0| nA(1 + R)  2   x(t)   E˙ 0 = i(ω − ω0 1 − − γ0 E0 + κEin  L

Rewrote :

mx¨ + m(Γ + δΓ)x˙ + m(ωm + δω)x = Ffluct(t)

 " # π2R 8n2ω γ γ P γ2 γ2  δΓ = 0 ex 0 in 0 + 0  2 2 2 2 2 2 2 2  (1 − R) mc ωm (ω − ω0) + γ0 (ω − ω0 + ωm) + γ0 (ω − ω0 − ωm) + γ0 " # π2R 4n2ω γ γ P (ω − ω + ω )γ (ω − ω − ω )γ  δω = 0 ex 0 in 0 m 0 + 0 m 0  2 2 2 2 2 2 2 2  (1 − R) mc ωm (ω − ω0 + γ0 (ω − ω0 + ωm) + γ0 (ω − ω0 − ωm) + γ0

(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

2 |E0|

ω ω-ωm ω ω+ωm

(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 8 of 20 Cavity cooling

2 |E0|

ω ω-ωm ω ω+ωm

(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 8 of 20 Cavity cooling

2 |E0|

ω ω-ωm ω ω+ωm

(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 8 of 20 Cavity cooling

2 |E0|

ω ω-ωm ω ω+ωm

Metzger & Karrai Nature 432, 1002 (2004).

(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 8 of 20 Cold damping

Active feedback Use radiation pressure to feedback a signal

FB Fopt = −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

Potential side-band resolved regime

I single emitters, single spins, . . .

I coupling through strain, magnetic or electric field.

Yeo, I. et al. Nat Nano (2013).

(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 1 1 E = mv2 + mω2 x2 E 2 2 m

I Quantum HO ħωm pˆ2 1 H = + mω2 xˆ2 2m 2 m 1 = h¯ω(b†b + ) 2 x I phonon creation and annhilation operators : b† and b

(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 13 of 20 Opto-mechanical systems

Kleckner & Bouwmeester Nature 444, 75 Groblacher¨ et al. Nat. Phys. 5, 485 (2009) Schliesser et al. Nat. Phys. 4, 415 (2008) (2006)

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 Groblacher¨ et al. Nat. Phys. 5, 485 (2009) Schliesser et al. Nat. Phys. 4, 415 (2008) (2006)

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 OH † I a,a : photon annihilation, creation operators I Hamiltonian † † † † I H = h¯ω0a a + h¯ωmb b + hg¯ 0xZPM(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

Signal processing Metrology

Macroscopic Quantum Physics

(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 18 of 20 Force sensing

(http://photonics.ethz.ch) Introduction to Optomechanics – Part 2 19 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

p Fmin = 4kBTeffΓeff

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

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

(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

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