Abstract
We explore the possibility of the formation of photon–phonon collective states in nanoscale wires by exploiting stimulated inter-modal Brillouin scattering of co-propagating photons that belong to distinct spatial optical modes. Inside nanowires, the photon–phonon coupling is significantly enhanced owing to radiation pressure. The Stokes and anti-Stokes processes are decoupled as they involve different phonon modes that lead to symmetry breaking, which results from different phase-matching requirements. For the Stokes process photon–phonon pairs are annihilated and created, in the presence of a classical field, and for the anti-Stokes process we obtain coherent oscillations between photons and phonons. The appearance of collective states, at hundreds of milli-Kelvin temperatures, can extend the use of nanowires into quantum information processing involving photons and phonons in a setup that can be easily integrated into an on-chip network.
Graphic abstract
Similar content being viewed by others
Data Availibility Statement
This manuscript has no associated data or the data will not be deposited [Authors’ comment: No datasets were generated or analysed during the current study.]
References
R.W. Boyd, Nonlinear Optics, 3rd edn. (Elsevier, Amsterdam, 2008)
A. Kobyakov, M. Sauer, D. Chowdhury, Stimulated Brillouin scattering in optical fibers. Adv. Opt. Photon. 2, 1 (2010)
G.P. Agrawal, Nonlinear Fiber Optics, 5th edn. (Elsevier, Amsterdam, 2013)
B.J. Eggleton, C.G. Poulton, R. Pant, Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits. Adv. Opt. Photon. 5, 536 (2013)
A.H. Safavi-Naeini, D. Van-Thourhout, R. Baets, R. Van-Laer, Controlling phonons and photons at the wavelength scale: integrated photonics meets integrated phononics. Optica 6, 213 (2019)
P.T. Rakich, C. Reinke, R. Camacho, P. Davids, Z. Wang, Giant enhancement of stimulated Brillouin scattering in the subwavelength limit. Phys. Rev. X 2, 011008 (2012)
J.E. Sipe, M.J. Steel, A Hamiltonian treatment of stimulated Brillouin scattering in nanoscale integrated waveguides. New J. Phys. 18, 045004 (2016)
H. Zoubi, K. Hammerer, Optomechanical multi-mode Hamiltonian for nanophotonic waveguides. Phys. Rev. A 94, 053827 (2016)
H. Shin, W. Qiu, R. Jarecki, J.A. Cox, R.H. Olsson III., A. Starbuck, Z. Wang, P.T. Rakich, Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides. Nat. Commun. 4, 1944 (2013)
E.A. Kittlaus, H. Shin, P.T. Rakich, Large Brillouin amplification in silicon. Nat. Photonics 10, 463 (2015)
R. Van-Laer, B. Kuyken, D. Van-Thourhout, R. Baets, Interaction between light and highly confined hypersound in a silicon photonic nanowire. Nat. Photonics 9, 199 (2015)
R. Van-Laer, A. Bazin, B. Kuyken, R. Baets, D. Van-Thourhout, Net on-chip Brillouin gain based on suspended silicon nanowires. New J. Phys. 17, 115005 (2015)
K.P. Huy, J.-C. Beugnot, J.-C. Tchahame, T. Sylvestre, Strong coupling between phonons and optical beating in backward Brillouin scattering. Phys. Rev. A 94, 043847 (2016)
B.J. Eggleton, C.G. Poulton, P.T. Rakich, M.J. Steel, G. Ball, Brillouin integrated photonics. Nat. Photonics 13, 664 (2019)
N.T. Otterstrom, R.O. Behunin, E.A. Kittlaus, Z. Wang, P.T. Rakich, A silicon Brillouin laser. Sience 360, 1113 (2018)
M. Merklein, B. Stiller, K. Vu, S.J. Madden, B.J. Eggleton, A chip-integrated coherent photonic–phononic memory. Nat. Commun. 8, 574 (2017)
L. Thevenaz, Slow and fast light in optical fibres. Nat. Photonics 2, 474 (2008)
N.T. Otterstrom, R.O. Behunin, E.A. Kittlaus, P.T. Rakich, Optomechanical cooling in a continuum media. Phys. Rev. X 8, 041034 (2018)
H. Zoubi, K. Hammerer, Nonlinear quantum optics in optomechanical nanoscale waveguides. Phys. Rev. Lett. 119, 123602 (2017)
H. Zoubi, Phonon-polaritons in nanoscale waveguides. J. Opt. 20, 095001 (2018)
H. Zoubi, Squeezed states of coupled photons and phonons in nanoscale waveguides. J. Opt. 21, 065202 (2019)
H. Zoubi, Photon and phonon spectral functions for continuum quantum optomechanics. Phys. Rev. A 101, 043803 (2020)
H. Zoubi, The formation of photon-molecules in nanoscale waveguides. Phys. Rev. A 104, 063510 (2021)
P. Kharel, R.O. Behunin, W.H. Renninger, P.T. Rakich, Noise and dynamics in forward Brillouin interactions. Phys. Rev. A 93, 063806 (2016)
C. Wolff, B. Stiller, B.J. Eggleton, M.J. Steel, C.G. Poulton, Cascaded forward Brillouin scattering to all stokes orders. New J. Phys. 19, 023021 (2017)
E.A. Kittlaus, N.T. Otterstorm, P.T. Rakich, On-chip inter-modal Brillouin scattering. Nat. Commun. 8, 15819 (2017)
C.W. Gardiner, P. Zoller, Quantum Noise (Springer, Berlin, 2010)
D.F. Walls, G.J. Milburn, Quantum Optics (Springer, Berlin, 2008)
R. Van-Laer, C.J. Sarabalis, R. Baets, D. Van-Thourhout, A.H. Safavi-Naeini, Thermal Brillouin noise observed in silicon optomechanical waveguide. J. Opt. 19, 044002 (2017)
A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill Book Company, New York, 1971)
R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford, UK, 2000)
H. Zoubi, G.C. La-Rocca, Microscopic theory of anisotropic organic cavity exciton polaritons. Phys. Rev. B 71, 235316 (2005)
H. Zoubi, H. Ritsch, Excitons and cavity polaritons for ultracold atoms in an optical lattice. Phys. Rev. A 76, 013817 (2007)
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zoubi, H. Collective states of photons and phonons via inter-modal Brillouin scattering. Eur. Phys. J. D 77, 171 (2023). https://doi.org/10.1140/epjd/s10053-023-00753-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjd/s10053-023-00753-y