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Optically levitated nanoparticles present an attractive optomechanical platform owing to their lack of clamping losses. The most promising approach to control the state of nanoparticle motion is coherent scattering of tweezer photons into a cavity mode. Originally proposed as a technique for cooling the motion of atoms and ions, this mechanism has recently been used to cool the motion of a nanoparticle to its quantum ground state for the first time. In my presentation, I will discuss how coherent scattering can be used to create and measure complex motional states of levitated nanoparticles. Coherent scattering gives us access to the same basic types of interaction as the more usual radiation-pressure interaction (of the beam-splitter and two-mode-squeezing type) allowing the same protocols to be realized. An important distinction—relevant particularly for quantum nondemolition readout of nanoparticle motion—is that coherent scattering can be accompanied by additional effects modifying the free nanoparticle evolution. I will discuss these differences and address the consequences they have for controlling and measuring nanoparticle motion in the quantum regime.

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- 1. Gaussian control and readout of levitated nanoparticles via coherent scattering Ondřej Černotík and Radim Filip Department of Optics, Palacký University Olomouc, Czechia APS March Meeting, March 16, 2021 @cernotik
- 2. Ondrej Cernotík: Gaussian control and readout of levitated nanoparticles via coherent scattering E27.10 ˇ ˇ @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: Gaussian control and readout of levitated nanoparticles via coherent scattering E27.10 ˇ ˇ @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: Gaussian control and readout of levitated nanoparticles via coherent scattering E27.10 ˇ ˇ @cernotik The system is versatile, allowing one-, two-, and three- dimensional coupling. 4 C. Gonzalez-Ballestero et al., PRA 100, 013805 (2019) M. Toroš et al., arXiv:2012.15822 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: Gaussian control and readout of levitated nanoparticles via coherent scattering E27.10 ˇ ˇ @cernotik Strong squeezing can be generated with a modulated trapping beam. 5 OC, R. Filip, PRResearch 2, 013052 (2020) ˇ tweezer amplitude Etw(t) = E0[1 + α cos(2ωmt + ϕ)] Hint = ωmα 4 (b2 + b†2 ) −g ( b + α 2 b† ) c† − g ( b† + α 2 b ) c
- 6. Ondrej Cernotík: Gaussian control and readout of levitated nanoparticles via coherent scattering E27.10 ˇ ˇ @cernotik Coherent scattering allows versatile interactions with multiple particles. 6 A. K. Chauhan, OC, R. Filip, NJP 22, 123021 (2020) ˇ H = − (λ1b1 + λ2b† 2 )c† 1 − (λ1b† 1 + λ2b2)c1 +g1(b† 1 c2 + c† 2 b1) + g2(b† 2 c2 + c† 2 b2)
- 7. Ondrej Cernotík: Gaussian control and readout of levitated nanoparticles via coherent scattering E27.10 ˇ ˇ @cernotik Quasi-QND readout of motion is possible with a modulated tweezer. 7 tweezer amplitude Etw(t) = E0[1 + α cos(ωmt + ϕ)] H = Ω(b2 e−2iϕ + b†2 e2iϕ ) − λ(c + c† )(be−iϕ + b† eiϕ ) Δ = 0 resonant driving
- 8. Ondrej Cernotík: Gaussian control and readout of levitated nanoparticles via coherent scattering E27.10 ˇ ˇ @cernotik Parametric squeezing plays negligible role for weak readout. 8 H = Ω(b2 e−2iϕ + b†2 e2iϕ ) + g(c† 1 b + b† c1) − λ(c2 + c† 2 )(be−iϕ + b† eiϕ )
- 9. Ondrej Cernotík: Gaussian control and readout of levitated nanoparticles via coherent scattering E27.10 ˇ ˇ @cernotik Coherent scattering allows ef fi cient control and readout of levitated nanoparticles. 9 OC, R. Filip, PRResearch 2, 013052 (2020) ˇ • Mechanical squeezing for force sensing • Entanglement between particles A. K. Chauhan, OC, and R. Filip, NJP 22, 123021 (2020) ˇ Parametric squeezing breaks QND nature Next steps: Measurement sensitivity, counterrotating terms, compensation of parametric squeezing? • Quasi-QND readout via tweezer modulation