Skip to main content
Log in

Collective states of photons and phonons via inter-modal Brillouin scattering

  • Regular Article – Quantum Optics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

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

  1. R.W. Boyd, Nonlinear Optics, 3rd edn. (Elsevier, Amsterdam, 2008)

    Google Scholar 

  2. A. Kobyakov, M. Sauer, D. Chowdhury, Stimulated Brillouin scattering in optical fibers. Adv. Opt. Photon. 2, 1 (2010)

    Article  Google Scholar 

  3. G.P. Agrawal, Nonlinear Fiber Optics, 5th edn. (Elsevier, Amsterdam, 2013)

    MATH  Google Scholar 

  4. B.J. Eggleton, C.G. Poulton, R. Pant, Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits. Adv. Opt. Photon. 5, 536 (2013)

    Article  Google Scholar 

  5. 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)

    Article  ADS  Google Scholar 

  6. 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)

    Google Scholar 

  7. J.E. Sipe, M.J. Steel, A Hamiltonian treatment of stimulated Brillouin scattering in nanoscale integrated waveguides. New J. Phys. 18, 045004 (2016)

    Article  ADS  Google Scholar 

  8. H. Zoubi, K. Hammerer, Optomechanical multi-mode Hamiltonian for nanophotonic waveguides. Phys. Rev. A 94, 053827 (2016)

    Article  ADS  Google Scholar 

  9. 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)

    Article  ADS  Google Scholar 

  10. E.A. Kittlaus, H. Shin, P.T. Rakich, Large Brillouin amplification in silicon. Nat. Photonics 10, 463 (2015)

    Article  ADS  Google Scholar 

  11. 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)

    Article  ADS  Google Scholar 

  12. 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)

    Article  ADS  Google Scholar 

  13. 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)

    Article  ADS  Google Scholar 

  14. B.J. Eggleton, C.G. Poulton, P.T. Rakich, M.J. Steel, G. Ball, Brillouin integrated photonics. Nat. Photonics 13, 664 (2019)

    Article  ADS  Google Scholar 

  15. N.T. Otterstrom, R.O. Behunin, E.A. Kittlaus, Z. Wang, P.T. Rakich, A silicon Brillouin laser. Sience 360, 1113 (2018)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  16. M. Merklein, B. Stiller, K. Vu, S.J. Madden, B.J. Eggleton, A chip-integrated coherent photonic–phononic memory. Nat. Commun. 8, 574 (2017)

    Article  ADS  Google Scholar 

  17. L. Thevenaz, Slow and fast light in optical fibres. Nat. Photonics 2, 474 (2008)

    Article  ADS  Google Scholar 

  18. N.T. Otterstrom, R.O. Behunin, E.A. Kittlaus, P.T. Rakich, Optomechanical cooling in a continuum media. Phys. Rev. X 8, 041034 (2018)

    MATH  Google Scholar 

  19. H. Zoubi, K. Hammerer, Nonlinear quantum optics in optomechanical nanoscale waveguides. Phys. Rev. Lett. 119, 123602 (2017)

    Article  ADS  Google Scholar 

  20. H. Zoubi, Phonon-polaritons in nanoscale waveguides. J. Opt. 20, 095001 (2018)

    Article  ADS  Google Scholar 

  21. H. Zoubi, Squeezed states of coupled photons and phonons in nanoscale waveguides. J. Opt. 21, 065202 (2019)

    Article  ADS  Google Scholar 

  22. H. Zoubi, Photon and phonon spectral functions for continuum quantum optomechanics. Phys. Rev. A 101, 043803 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  23. H. Zoubi, The formation of photon-molecules in nanoscale waveguides. Phys. Rev. A 104, 063510 (2021)

    Article  MathSciNet  ADS  Google Scholar 

  24. P. Kharel, R.O. Behunin, W.H. Renninger, P.T. Rakich, Noise and dynamics in forward Brillouin interactions. Phys. Rev. A 93, 063806 (2016)

    Article  ADS  Google Scholar 

  25. 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)

    Article  MATH  ADS  Google Scholar 

  26. E.A. Kittlaus, N.T. Otterstorm, P.T. Rakich, On-chip inter-modal Brillouin scattering. Nat. Commun. 8, 15819 (2017)

  27. C.W. Gardiner, P. Zoller, Quantum Noise (Springer, Berlin, 2010)

    MATH  Google Scholar 

  28. D.F. Walls, G.J. Milburn, Quantum Optics (Springer, Berlin, 2008)

  29. 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)

    Article  ADS  Google Scholar 

  30. A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill Book Company, New York, 1971)

    Google Scholar 

  31. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford, UK, 2000)

  32. H. Zoubi, G.C. La-Rocca, Microscopic theory of anisotropic organic cavity exciton polaritons. Phys. Rev. B 71, 235316 (2005)

    Article  ADS  Google Scholar 

  33. H. Zoubi, H. Ritsch, Excitons and cavity polaritons for ultracold atoms in an optical lattice. Phys. Rev. A 76, 013817 (2007)

    Article  ADS  Google Scholar 

  34. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hashem Zoubi.

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-023-00753-y

Navigation