1.
Controlling the motion of levitated particles
by coherent scattering
Ondřej Černotík, Iivari Pietikäinen, Anil Kumar, and Radim Filip
Department of Optics, Palacký University Olomouc, Czechia
APS March Meeting, March 3, 2020 @cernotik

2.
Ondrej Cernotík: Controlling the motion of levitated particles by coherent scatteringˇˇ @cernotik
Optical levitation allows for high-quality mechanical
motion without damping.
2
Nonspherical particles
S. Kuhn et al., Optica 4, 356 (2017)
Hybrid systems
L.P. Neukirch et al., Nat. Photon. 9, 653 (2015)
Cavity optomechanics
N. Kiesel, PNAS 110, 14180 (2013)
Thermodynamics
I.A. Martinez et al., Nat. Phys. 12, 67 (2016)

3.
Ondrej Cernotík: Controlling the motion of levitated particles by coherent scatteringˇˇ @cernotik
Coherent scattering is a new, powerful tool for
optomechanical interactions.
3
U. Delic et al., PRL 122, 123602 (2019)
D. Windey et al., PRL 122, 123601 (2019)
U. Delic et al., Science 367, 892 (2020)

4.
Ondrej Cernotík: Controlling the motion of levitated particles by coherent scatteringˇˇ @cernotik
The system is versatile, allowing one-, two-, and three-
dimensional coupling.
4
C. Gonzalez-Ballestero et al., PRA 100, 013805 (2019)
Intracavity intensity
Radial coupling
Axial coupling
Polarization
Etw<latexit sha1_base64="bRQQNOEkJg9znsC3zqgs56MYHpg=">AAACH3icbVDLSsNAFJ3UV42vqks3wSK4kJLEoi5LRXRZxT6gDWUynbRDJw9mbtQS8idu/BU3LhQRd/0bp2kX2nrgwuHcx5w5bsSZBNMca7ml5ZXVtfy6vrG5tb1T2N1ryDAWhNZJyEPRcrGknAW0Dgw4bUWCYt/ltOkOLyf95gMVkoXBPYwi6vi4HzCPEQxK6hbOOkCfILvTvruuOoltmye2basqp4ne8TEMXC+5SrsZFX4Cj6medgtFs2RmMBaJNSNFNEOtW/ju9EIS+zQAwrGUbcuMwEmwAEY4TfVOLGmEyRD3aVvRAPtUOknmKzWOlNIzvFCoCsDI1N8bCfalHPmumpyYlPO9ifhfrx2Dd+EkLIhioAGZPuTF3IDQmIRl9JigBPhIEUwEU14NMsACE1CR6ioEa/7Li6Rhl6zTkn1bLlaqszjy6AAdomNkoXNUQTeohuqIoGf0it7Rh/aivWmf2td0NKfNdvbRH2jjH0y5oe4=</latexit>
Ecav<latexit sha1_base64="nvRiBR5yCYIOD0X3nzXvyGTc6/c=">AAACIHicbVDLSsNAFJ3UV42vqks3wSK4kJLEQl2Wiuiyin1AG8pkOmmHTh7M3BRLyKe48VfcuFBEd/o1TtMutPXAhcO5jzlz3IgzCab5peVWVtfWN/Kb+tb2zu5eYf+gKcNYENogIQ9F28WSchbQBjDgtB0Jin2X05Y7upz2W2MqJAuDe5hE1PHxIGAeIxiU1CtUukAfILvTubuuOYltm2e2basqp4ne9TEMXS+5SnsZFX5C8DjV016haJbMDMYyseakiOao9wqf3X5IYp8GQDiWsmOZETgJFsAIp6nejSWNMBnhAe0oGmCfSifJjKXGiVL6hhcKVQEYmfp7I8G+lBPfVZNTl3KxNxX/63Vi8C6chAVRDDQgs4e8mBsQGtO0jD4TlACfKIKJYMqrQYZYYAIqU12FYC1+eZk07ZJ1XrJvy8VqbR5HHh2hY3SKLFRBVXSD6qiBCHpEz+gVvWlP2ov2rn3MRnPafOcQ/YH2/QP8tqJH</latexit>
Hint ∝ Ecav(r) ⋅ Etw(r)
≃ − (λxx + λyy)(c + c†
) − iλzz(c − c†
)

5.
Ondrej Cernotík: Controlling the motion of levitated particles by coherent scatteringˇˇ @cernotik
We are interested in generating one-mode mechanical
squeezing.
5
·c = − (κ + iΔ)c + iλx + 2κcin
·x = ωmp
·p = − ωmx − γp + λ(c + c†
) + ξ
H =
ωm
2
(x2
+ p2
) + Δc†
c − λ(c + c†
)x

6.
Ondrej Cernotík: Controlling the motion of levitated particles by coherent scatteringˇˇ @cernotik
Strong squeezing can be generated with a modulated
trapping beam.
6
OC, R. Filip, PRResearch 2, 013052 (2020)ˇ
tweezer amplitudeEtw(t) = E0[1 + α cos(2ωmt + ϕ)]
H = Δc†
c +
ωm
2
p2
+
ωm
2
[1 + α cos(2ωmt + ϕ)]2
x2
−λ[1 + α cos(2ωmt + ϕ)](c + c†
)x

7.
Ondrej Cernotík: Controlling the motion of levitated particles by coherent scatteringˇˇ @cernotik
Strong squeezing can be generated with a modulated
trapping beam.
7
OC, R. Filip, PRResearch 2, 013052 (2020)ˇ
transient regime, Δ ≫ λ, κ, ωm
parametric squeezing
steady state, Δ = ωm
dissipative and parametric squeezing

8.
Ondrej Cernotík: Controlling the motion of levitated particles by coherent scatteringˇˇ @cernotik
Extensions and applications of this scheme are possible.
8
• Towards full control of motion of a levitated particle
• Mechanical squeezing for force sensing
J. Gieseler et al., Nat. Phys. 9, 806 (2013)
• Parametric and dissipative two-mode squeezing
A. Pontin et al., PRL 116, 103601 (2016)
C.F. Ockeloen-Korppi et al., Nature 556, 478 (2018)
• Analysis beyond RWA
I. Pietikäinen, OC, R. Filip, arXiv:2002.xxxxx
Talk by Iivari: M02.00008, Wednesday, 12:39 PM, room 105

9.
Ondrej Cernotík: Controlling the motion of levitated particles by coherent scatteringˇˇ @cernotik
Coherent scattering allows versatile interactions with
multiple particles.
9
H = − (λ1b1 + λ2b†
2
)c†
− (λ1b†
1
+ λ2b2)c

10.
Ondrej Cernotík: Controlling the motion of levitated particles by coherent scatteringˇˇ @cernotik
Coherent scattering is a powerful tool for levitated
optomechanics.
10
• Multiparticle dynamics via coherent scattering
A. Kumar, OC, R. Filip, in preparationˇ
• Mechanical squeezing for force sensing
• Towards full control of motion of a levitated particle
OC, R. Filip, PRResearch 2, 013052 (2020)ˇ
• Mechanical squeezing for force sensing
• Analysis beyond RWA
I. Pietikäinen, OC, R. Filip, arXiv:2002.xxxxx
Talk by Iivari: M02.00008, Wednesday, 12:39 PM, room 105
ˇ