Dynamics of Nano-Particles Inside an Optical Cavity in the Quantum Regime
Abstract
:1. Introduction
2. Optical Force Calculation in the Quantum Regime
2.1. Low Polarizability
2.2. High Polarizability
3. Dynamics of a Dielectric Particle in the Optical Cavity
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
References
- Ashkin, A. Acceleration and Trapping of Particles by Radiation Pressure. Phys. Rev. Lett. 1970, 24, 156. [Google Scholar] [CrossRef]
- Ashkin, A.; Dziedzic, J.M.; Bjorkholm, J.E.; Chu, S. Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 1986, 11, 288. [Google Scholar] [CrossRef] [PubMed]
- Ashkin, A. Optical trapping and manipulation of neutral particles using lasers. Proc. Natl. Acad. Sci. USA 1997, 94, 4853–4860. [Google Scholar] [CrossRef]
- Grier, D. A revolution in optical manipulation. Nature 2003, 424, 810–816. [Google Scholar] [CrossRef]
- Neuman, K.C.; Block, S.M. Optical trapping. Rev. Sci. Instrum. 2004, 75, 2787–2809. [Google Scholar] [CrossRef] [PubMed]
- Dholakia, K.; Reece, P. Optical micromanipulation takes hold. Nano Today 2006, 1, 18–27. [Google Scholar] [CrossRef]
- Chen, J.; Ng, J.; Lin, Z.; Chan, C.T. Optical pulling force. Nat. Photonics 2011, 5, 531–534. [Google Scholar] [CrossRef]
- Gao, D.; Ding, W.; Nieto-Vesperinas, M.; Ding, X.; Rahman, M.; Zhang, T.; Lim, C.; Qiu, C.-W. Optical manipulation from the microscale to the nanoscale: Fundamentals, advances and prospects. Light Sci. Appl. 2017, 6, e17039. [Google Scholar] [CrossRef] [PubMed]
- Bustamante, C.J.; Chemla, Y.R.; Liu, S.; Wang, M.D. Optical tweezers in single-molecule biophysics. Nat. Rev. Methods Primers 2021, 1, 25. [Google Scholar] [CrossRef]
- Hu, J.; Lin, S.; Kimerling, L.C.; Crozier, K. Optical trapping of dielectric nanoparticles in resonant cavities. Phys. Rev. A 2010, 82, 053819. [Google Scholar] [CrossRef]
- Mandal, S.; Serey, X.; Erickson, D. Nanomanipulation Using Silicon Photonic Crystal Resonators. Nano Lett. 2010, 10, 99–104. [Google Scholar] [CrossRef] [PubMed]
- Lin, S.; Schonbrun, E.; Crozier, K. Optical Manipulation with Planar Silicon Microring Resonators. Nano Lett. 2010, 10, 2408–2411. [Google Scholar] [CrossRef] [PubMed]
- Descharmes, N.; Dharanipathy, U.P.; Diao, Z.; Tonin, M.; Houdré, R. Observation of Backaction and Self-Induced Trapping in a Planar Hollow Photonic Crystal Cavity. Phys. Rev. Lett. 2013, 110, 123601. [Google Scholar] [CrossRef]
- Grigorenko, A.; Roberts, N.; Dickinson, M.; Zhang, Y. Nanometric optical tweezers based on nanostructured substrates. Nat. Photonics 2008, 2, 365–370. [Google Scholar] [CrossRef]
- Juan, M.; Righini, M.; Quidant, R. Plasmon nano-optical tweezers. Nat. Photonics 2011, 5, 349–356. [Google Scholar] [CrossRef]
- Juan, M.; Gordon, R.; Pang, Y.; Eftekhari, F.; Quidant, R. Self-induced back-action optical trapping of dielectric nanoparticles. Nat. Phys. 2009, 5, 915–919. [Google Scholar] [CrossRef]
- Jaquay, E.; Martínez, L.J.; Mejia, C.A.; Povinelli, M.L. Light-Assisted, Templated Self-Assembly Using a Photonic-Crystal Slab. Nano Lett. 2013, 13, 2290–2294. [Google Scholar] [CrossRef] [PubMed]
- Huang, N.; Martínez, L.J.; Jaquay, E.; Nakano, A.; Povinelli, M.L. Optical Epitaxial Growth of Gold Nanoparticle Arrays. Nano Lett. 2015, 15, 5841–5845. [Google Scholar] [CrossRef] [PubMed]
- Romero-Isart, O.; Juan, M.L.; Quidant, R.; Cirac, J.I. Toward quantum superposition of living organisms. New J. Phys 2010, 12, 033015. [Google Scholar] [CrossRef]
- Chang, D.E.; Regal, C.A.; Papp, S.B.; Wilson, D.J.; Painter, O.; Kimble, H.J.; Zoller, P. Cavity opto-mechanics using an optically levitated nanosphere. Proc. Natl. Acad. Sci. USA 2010, 107, 1005. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Gieseler, J.; Novotny, L.; Quidant, R. Thermal nonlinearities in a nanomechanical oscillator. Nat. Phys. 2013, 9, 806–810. [Google Scholar] [CrossRef]
- Millen, J.; Monteiro, T.S.; Pettit, R.; Vamivakas, N. Optomechanics with levitated particles. Rep. Prog. Phys. 2020, 83, 026401. [Google Scholar] [CrossRef]
- Hoang, T.M.; Ahn, J.; Bang, J.; Li, T. Electron spin control of optically levitated nanodiamonds in vacuum. Nat. Commun. 2016, 7, 12250. [Google Scholar] [CrossRef]
- Pettit, R.M.; Neukirch, L.P.; Zhang, Y.; Vamivakas, A.N. Coherent control of a single nitrogen-vacancy center spin in optically levitated nanodiamond. J. Opt. Soc. Am. B 2017, 34, C31–C35. [Google Scholar] [CrossRef]
- Rahman, A.; Barker, P.F. Laser refrigeration, alignment and rotation of levitated Yb3+:YLF nanocrystals. Nat. Photonics 2017, 11, 634–638. [Google Scholar] [CrossRef]
- Neukirch, L.P.; von Haartman, E.; Rosenhol, J.M.; Vamivakas, A.N. Multi-dimensional single-spin nano-optomechanics with a levitated nanodiamond. Nat. Photonics 2015, 9, 653–657. [Google Scholar] [CrossRef]
- Tebbenjohanns, F.; Mattana, M.L.; Rossi, M.; Frimmer, M.; Novotny, L. Quantum control of a nanoparticle optically levitated in cryogenic free space. Nature 2021, 595, 378–382. [Google Scholar] [CrossRef]
- Delić, U.; Reisenbauer, M.; Dare, K.; Grass, D.; Vuletić, V.; Kiesel, N.; Aspelmeyer, M. Cooling of a levitated nanoparticle to the motional quantum ground state. Science 2020, 367, 892–895. [Google Scholar] [CrossRef]
- Monteiro, T.S.; Millen, J.; Pender, G.A.T.; Marquardt, F.; Chang, D.; Barker, P.F. Dynamics of levitated nanospheres: Towards the strong coupling regime. New J. Phys 2013, 15, 015001. [Google Scholar] [CrossRef]
- Arita, Y.; Chen, M.; Wright, E.M.; Dholakia, K. Dynamics of a levitated microparticle in vacuum trapped by a perfect vortex beam: Three-dimensional motion around a complex optical potential. J. Opt. Soc. Am. B 2017, 34, C14–C19. [Google Scholar] [CrossRef] [Green Version]
- Arita, Y.; Simpson, S.H.; Zemánek, P.; Dholakia, K. Coherent oscillations of a levitated birefringent microsphere in vacuum driven by nonconservative rotation-translation coupling. Sci. Adv. 2020, 6, eaaz9858. [Google Scholar] [CrossRef]
- Ranfagni, A.; Bøkje, K.; Marino, F.; Marin, F. Two-dimensional quantum motion of a levitated nanosphere. Phys. Rev. Res. 2022, 4, 033051. [Google Scholar] [CrossRef]
- Yang, D.; Gao, F.; Cao, Q.-T.; Wang, C.; Ji, Y.; Xiao, Y.-F. Single nanoparticle trapping based on on-chip nanoslotted nanobeam cavities. Photon. Res. 2018, 6, 99–108. [Google Scholar] [CrossRef]
- Romero-Isart, O.; Pflanzer, A.C.; Juan, M.L.; Quidant, R.; Kiesel, N.; Aspelmeyer, M.; Cirac, J.I. Optically levitating dielectrics in the quantum regime: Theory and protocols. Phys. Rev. A 2011, 8, 01380. [Google Scholar] [CrossRef]
- Huang, S.; Agarwal, G.S. Reactive-coupling-induced normal mode splittings in microdisk resonators coupled to waveguides. Phys. Rev. A 2010, 81, 053810. [Google Scholar] [CrossRef]
- Giovannetti, V.; Vitali, D. Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion. Phys. Rev. A 2001, 63, 023812. [Google Scholar] [CrossRef]
- Chaumet, P.C.; Nieto-Vesperinas, M. Time-averaged total force on a dipolar sphere in an electromagnetic field. Opt. Lett. 2000, 25, 1065. [Google Scholar] [CrossRef]
- Mancini, S.; Tombesi, P. Quantum noise reduction by radiation pressure. Phys. Rev. A 1994, 49, 4055–4065. [Google Scholar] [CrossRef]
- Li, M.; Pernice, W.H.P.; Tang, H.X. Reactive Cavity Optical Force on Microdisk-Coupled Nanomechanical Beam Waveguides. Phys. Rev. Lett. 2009, 103, 223901. [Google Scholar] [CrossRef] [PubMed]
- Law, C.K. Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation. Phys. Rev. A 1995, 51, 2537–2541. [Google Scholar] [CrossRef]
- Cheung, H.K.; Law, C.K. Nonadiabatic optomechanical Hamiltonian of a moving dielectric membrane in a cavity. Phys. Rev. A 2011, 84, 023812. [Google Scholar] [CrossRef]
- Viviescas, C.; Hackenbroich, G. Field quantization for open optical cavities. Phys. Rev. A 2003, 67, 013805. [Google Scholar] [CrossRef]
- Suzuki, Y.; Lu, M.; Ben-Jacob, E.; Onuchic, J.N. Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays. Sci. Rep. 2015, 6, 21037. [Google Scholar] [CrossRef] [PubMed]
- Neumeier, L.; Quidant, R.; Chang, D.E. Self-induced back-action optical trapping in nanophotonic systems. New J. Phys. 2015, 17, 123008. [Google Scholar] [CrossRef]
- Zhang, D.; You, C.; Lv, X. Intermittent chaos in cavity optomechanics. Phys. Rev. A 2020, 101, 053851. [Google Scholar] [CrossRef]
- Zhang, D.; Zheng, L.; You, C.; Hu, C.; Wu, Y.; Lu, X. Nonreciprocal chaos in a spinning optomechanical resonator. Phys. Rev. A 2021, 104, 033522. [Google Scholar] [CrossRef]
- Navarro-Urrios, D.; Capuj, N.; Colombano, M.; García, P.; Sledzinska, M.; Alzina, F.; Griol, A.; Martínez, A.; Sotomayor-Torres, C.M. Nonlinear dynamics and chaos in an optomechanical beam. Nat. Commun. 2017, 8, 14965. [Google Scholar] [CrossRef]
- Zhang, D.; Bin, S.; You, C.; Hu, C. Enhancing the nonlinearity of optomechanical system via multiple mechanical modes. Opt. Express 2022, 30, 1314. [Google Scholar] [CrossRef] [PubMed]
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Prada, C.M.; Martínez, L.J. Dynamics of Nano-Particles Inside an Optical Cavity in the Quantum Regime. Photonics 2022, 9, 641. https://doi.org/10.3390/photonics9090641
Prada CM, Martínez LJ. Dynamics of Nano-Particles Inside an Optical Cavity in the Quantum Regime. Photonics. 2022; 9(9):641. https://doi.org/10.3390/photonics9090641
Chicago/Turabian StylePrada, Camilo M., and Luis J. Martínez. 2022. "Dynamics of Nano-Particles Inside an Optical Cavity in the Quantum Regime" Photonics 9, no. 9: 641. https://doi.org/10.3390/photonics9090641