Abstract
In the context of the quantum-mechanical description of single-molecule surface-enhanced Raman scattering, intensity-field correlation measurements of photons emitted from a plasmonic cavity are explored, theoretically, using the technique of conditional homodyne detection. The inelastic interplay between plasmons and vibrations of a diatomic molecule placed inside the cavity can be manifested in phase-dependent third-order fluctuations of the light recorded by the aforesaid technique, allowing us to reveal signatures of non-classicality (indicatives of squeezing) of the outgoing Raman photons.
Similar content being viewed by others
References
L. E. C. Ru and P. G. Etchegoin, Principles of Surface-Enhanced Raman Spectroscopy and Related Plasmonic Effects, Elsevier, 2009
F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, Single-molecule opto-mechanics in “picocavities”, Science 354(6313), 726 (2016)
A. Lombardi, M. K. Schmidt, L. Weller, W. M. Deacon, F. Benz, B. de Nijs, J. Aizpurua, and J. J. Baumberg, Pulsed molecular opto-mechanics in plasmonic nanocavities: From nonlinear vibrational instabilities to bond-breaking, Phys. Rev. X 8(1), 011016 (2018)
A. M. Kern, D. Zhang, M. Brecht, A. I. Chizhik, A. V. Failla, F. Wackenhut, and A. J. Meixner, Enhanced single-molecule spectroscopy in highly confined optical fields: From l/2-Fabry-Pérot resonators to plasmonic nano-antenas, Chem. Soc. Rev. 43(4), 1263 (2014)
H. Nabika, M. Takase, F. Nagasawa, and K. Murakoshi, Toward plasmon-induced photo-exitation of molecules, J. Phys. Chem. Lett. 1(16), 2470 (2010)
R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. L. Yang, and J. G. Hou, Chemical mapping of a single molecule by plasmon-enhanced Raman scattering, Nature 498(7452), 82 (2013)
P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. Hueso, J. Aizpurua, and R. Hillenbrand, Resolving the electromagnetic mechanism of surface-enhanced light scattering at single hot spots, Nat. Commun. 3(1), 684 (2012)
S. Yampolsky, D. A. Fishman, S. Dey, E. Hulkko, M. Banik, E. O. Potma, and V. A. Apkarian, Seeing a single molecule vibrate through rime-resolved coherent anti-Stokes Raman scattering, Nat. Photonics 8(8), 650 (2014)
R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, Single-molecule strong coupling at room temperature in plasmonic nanocavities, Nature 535(7610), 127 (2016)
Y. Huang, Y. Fang, Z. Zhang, L. Zhu, and M. Sun, Nanowire-supported plasmonic waveguide for remote excitation of surface-enhanced Raman scattering, Light Sci. Appl. 3(8), e199 (2014)
S. J. P. Kress, F. V. Antolinez, P. Richner, S. V. Jayanti, D. K. Kim, F. Prins, A. Riedinger, M. P. C. Fischer, S. Meyer, K. M. McPeak, D. Poulikakos, and D. J. Norris, Wedge waveguides and resonators for quantum plasmonics, Nano Lett. 15(9), 6267 (2015)
C. Lee, F. Dieleman, J. Lee, C. Rockstuhl, S. A. Maier, and M. Tame, Quantum plasmonic sensing: Beyond the shot noise and diffraction limit, ACS Photonics 3(6), 992 (2016)
F. Peyskens, A. Dhakal, P. van Dorpe, N. Le Thomas, and R. Baets, Surface enhanced Raman spectroscopy using a single mode nanophotonic-plasmonic platform, ACS Photonics 3(1), 102 (2016)
M. D. Baaske and F. Vollmer, Optical observation of single atomic ions interacting with plasmonic nanorods in aqueous solution, Nat. Photonics 10(11), 733 (2016)
M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling, Nano Lett. 10(3), 891 (2010)
H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering, Phys. Rev. Lett. 83(21), 4357 (1999)
C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, Surface-enhanced Raman scattering from individual Au nanoparticles and nanoparticle dimer substrates, Nano Lett. 5(8), 1569 (2005)
W. Zhu and K. B. Crozier, Quantum mechanical limit to plasmonic enhancement as observed by surface-enhanced Raman scattering, Nat. Commun. 5(1), 5228 (2014)
M. Takase, S. Yasuda, and K. Murakoshi, Single-site surface-enhanced Raman scattering beyond spectroscopy, Front. Phys. 11(2), 117803 (2016)
R. Hanbury-Brown and R. Q. Twiss, Correlations between photons in two coherent beams of light, Nature 177(4497), 27 (1956)
D. F. Walls and P. Zoller, Reduced quantum fluctuations in resonance fluorescence, Phys. Rev. Lett. 47(10), 709 (1981)
R. Loudon and P. L. Knight, Squeezed light, J. Mod. Opt. 34(6–7), 709 (1987)
H. J. Carmichael, H. M. Castro-Beltrán, G. T. Foster, and L. A. Orozco, Giant violations of classical inequalities through conditional homodyne detection of the quadrature amplitudes of light, Phys. Rev. Lett. 85(9), 1855 (2000)
G. T. Foster, L. A. Orozco, H. M. Castro-Beltrán, and H. J. Carmichael, Quantum state reduction and conditional time evolution of wave-particle correlations in cavity QED, Phys. Rev. Lett. 85(15), 3149 (2000)
G. T. Foster, W. P. Smith, J. E. Reiner, and L. A. Orozco, Third-order correlations in cavity quantum electrodynamics, J. Opt. B Quantum Semiclassical Opt. 4(4), 306 (2002)
A. Denisov, H. M. Castro-Beltrán, and H. J. Carmichael, Time-asymmetric fluctuations of light and the breakdown of detailed balance, Phys. Rev. Lett. 88(24), 243601 (2002)
H. J. Carmichael, G. T. Foster, L. A. Orozco, J. E. Reiner, and P. R. Rice, Intensity-field correlations of nonclassical light, Progress in Optics, E. Wolf (Ed.), Elsevier, 2004, p. 46
A. Shalabney, J. George, J. Hutchison, G. Pupillo, C. Genet, and T. W. Ebbesen, Coherent coupling of molecular resonators with a microcavity mode, Nat. Commun. 6(1), 5981 (2015)
T. J. Kippenberg and K. J. Vahala, Cavity optomechanics, Opt. Express 15(25), 17172 (2007)
M. K. Schmidt, R. Esteban, A. González-Tudela, G. Giedke, and J. Aizpurua, Quantum mechanical description of raman scattering from molecules in plasmonic cavities, ACS Nano 10(6), 6291 (2016)
M. K. Schmidt, R. Esteban, F. Benz, J. J. Baumberg, and J. Aizpurua, Linking classical and molecular optomechanics descriptions of SERS, Faraday Discuss. 205, 31 (2017)
P. Roelli, C. Galland, N. Piro, and T. J. Kippenberg, Molecular cavity opto-mechanics as a theory of plasmonenhanced Raman scattering, Nat. Nanotechnol. 11(2), 164 (2016)
M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86(4), 1391 (2014)
M. K. Dezfouli and S. Hughes, Quantum optics model of surface-enhanced Raman spectroscopy for arbitrarily shaped plasmonic resonators, ACS Photonics 4(5), 1245 (2017)
H. J. Carmichael, An Open Systems Approach to Quantum Optics, Springer-Verlag, 1993
C. A. Parra-Murillo, M. F. Santos, C. H. Monken, and A. Jorio, Stokes-anti-Stokes correlation in the inelastic scattering of light by matter and generalization of the Bose-Einstein population function, Phys. Rev. B 93(12), 125141 (2016)
E. R. Marquina-Cruz and H. M. Castro-Beltrán, Nonclassicality of resonance fluorescence via amplitude-intensity field correlations, Laser Phys. 18(2), 157 (2008)
H. M. Castro-Beltrán, Phase-dependent fluctuations of resonance fluorescence beyond the squeezing regime, Opt. Commun. 283(23), 4680 (2010)
H. M. Castro-Beltrán, L. Gutiérrez, and L. Horvath, Squeezed versus non-Gaussian fluctuations in resonance fluorescence, Appl. Math. Inf. Sci. 9, 2849 (2015)
H. M. Castro-Beltrán, R. Román-Ancheyta, and L. Gutiérrez, Phase-dependent fluctuations of intermittent resonance fluorescence, Phys. Rev. A 93(3), 033801 (2016)
L. Gutiérrez, H. M. Castro-Beltrán, R. Román-Ancheyta, and L. Horvath, Large time-asymmetric quantum fluctuations in amplitude-intensity correlation measurements of V-type three-level atom resonance fluorescence, J. Opt. Soc. Am. B 34(11), 2301 (2017)
J. E. Reiner, W. P. Smith, L. A. Orozco, H. J. Carmichael, and P. R. Rice, Time evolution and squeezing of the field amplitude in cavity QED, J. Opt. Soc. Am. B 18(12), 1911 (2001)
C. E. Strimbu, J. Leach, and P. R. Rice, Conditioned homodyne detection at the single-photon level: Intensity-field correlations for a two-level atom in an optical parametric oscillator, Phys. Rev. A 71(1), 013807 (2005)
F. Wang, X. Feng, and C. H. Oh, Intensity-intensity and intensity-amplitude correlation of microwave photons from a superconducting artificial atom, Laser Phys. Lett. 13(10), 105201 (2016)
Q. Xu and K. Mølmer, Intensity and amplitude correlations in the fluorescence from atoms with interacting Rydberg states, Phys. Rev. A 92(3), 033830 (2015)
Q. Xu, E. Greplova, B. Julsgaard, and K. Mølmer, Correlation functions and conditioned quantum dynamics in photodetection theory, Phys. Scr. 90(12), 128004 (2015)
S. Gerber, D. Rotter, L. Slodicka, J. Eschner, H. J. Carmichael, and R. Blatt, Intensity-field correlations of single-atom resonance fluorescence, Phys. Rev. Lett. 102(18), 183601 (2009)
W. Vogel, Squeezing and anomalous moments in resonance fluorescence, Phys. Rev. Lett. 67(18), 2450 (1991)
W. Vogel, Homodyne correlation measurements with weak local oscillators, Phys. Rev. A 51(5), 4160 (1995)
M. J. Collett, D. F. Walls, and P. Zoller, Spectrum of squeezing in resonance fluorescence, Opt. Commun. 52(2), 145 (1984)
P. R. Rice and H. J. Carmichael, Nonclassical effects in optical spectra, J. Opt. Soc. Am. B 5(8), 1661 (1988)
J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 184(4), 1234 (2013)
G. Nienhuis, Spectral correlations in resonance fluorescence, Phys. Rev. A 47(1), 510 (1993)
E. del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, and M. J. Hartmann, Theory of frequency-filtered and time-resolved N-photon correlations, Phys. Rev. Lett. 109(18), 183601 (2012)
A. Frank, R. Lemus, M. Carvajal, C. Jung, and E. Ziemniak, SU(2) approximation to the coupling of Morse oscillators, Chem. Phys. Lett. 308(1–2), 91 (1999)
M. Carvajal, R. Lemus, A. Frank, C. Jung, and E. Ziemniak, An extended SU(2) model for coupled Morse oscillators, Chem. Phys. 260(1–2), 105 (2000)
M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, et al., Roadmap on plasmonics, J. Opt. 20, 043001 (2018)
Acknowledgements
I want to thank Prof. H. M. Castro-Beltrán for helpful suggestions. Thanks also to I. Ramos-Prieto for introducing me to the use of QuTip library in Python and for his help with Figs. 1 and 3, and Prof. J. Récamier for his kind hospitality at ICF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
de los Santos-Sánchez, O. Probing intensity-field correlations of single-molecule surface-enhanced Raman-scattered light. Front. Phys. 14, 61601 (2019). https://doi.org/10.1007/s11467-019-0914-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11467-019-0914-3