Probing intensity-field correlations of single-molecule surface-enhanced Raman-scattered light

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.

Keywords

Raman scattering / SERS / phase-dependent fluctuations / squeezing / plasmonics

References

[1] L. E. C. Ru and P. G. Etchegoin, Principles of Surface-Enhanced Raman Spectroscopy and Related Plasmonic Effects, Elsevier, 2009

[2] 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)

[3] 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 bondbreaking, Phys. Rev. X 8(1), 011016 (2018)

[4] 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)

[5] H. Nabika, M. Takase, F. Nagasawa, and K. Murakoshi, Toward plasmon-induced photo-exitation of molecules, J. Phys. Chem. Lett. 1(16), 2470 (2010)

[6] 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)

[7] 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 surfaceenhanced light scattering at single hot spots, Nat. Commun. 3(1), 684 (2012)

[8] 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)

[9] 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)

[10] 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)

[11] 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)

[12] 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)

[13] 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)

[14] 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)

[15] 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)

[16] H. Xu, E. J. Bjerneld, M. Köll, and L. Börjesson, Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering, Phys. Rev. Lett. 83(21), 4357 (1999)

[17] 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)

[18] 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)

[19] M. Takase, S. Yasuda, and K. Murakoshi, Single-site surface-enhanced Raman scattering beyond spectroscopy, Front. Phys. 11(2), 117803 (2016)

[20] R. Hanbury-Brown and R. Q. Twiss, Correlations between photons in two coherent beams of light, Nature 177(4497), 27 (1956)

[21] D. F. Walls and P. Zoller, Reduced quantum fluctuations in resonance fluorescence, Phys. Rev. Lett. 47(10), 709 (1981)

[22] R. Loudon and P. L. Knight, Squeezed light, J. Mod. Opt. 34(6–7), 709 (1987)

[23] 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)

[24] 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)

[25] 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)

[26] 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)

[27] 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 (), Elsevier, 2004, p. 46

[28] 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)

[29] T. J. Kippenberg and K. J. Vahala, Cavity optomechanics, Opt. Express 15(25), 17172 (2007)

[30] 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)

[31] 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)

[32] 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)

[33] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86(4), 1391 (2014)

[34] 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)

[35] H. J. Carmichael, An Open Systems Approach to Quantum Optics, Springer-Verlag, 1993

[36] 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)

[37] E. R. Marquina-Cruz and H. M. Castro-Beltrán, Nonclassicality of resonance fluorescence via amplitude-intensity field correlations, Laser Phys. 18(2), 157 (2008)

[38] H. M. Castro-Beltrán, Phase-dependent fluctuations of resonance fluorescence beyond the squeezing regime, Opt. Commun. 283(23), 4680 (2010)

[39] H. M. Castro-Beltrán, L. Gutiérrez, and L. Horvath, Squeezed versus non-Gaussian fluctuations in resonance fluorescence, Appl. Math. Inf. Sci. 9, 2849 (2015)

[40] H. M. Castro-Beltrán, R. Román-Ancheyta, and L. Gutiérrez, Phase-dependent fluctuations of intermittent resonance fluorescence, Phys. Rev. A 93(3), 033801 (2016)

[41] 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)

[42] 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)

[43] C. E. Strimbu, J. Leach, and P. R. Rice, Conditioned homodyne detection at the single-photon level: Intensityfield correlations for a two-level atom in an optical parametric oscillator, Phys. Rev. A 71(1), 013807 (2005)

[44] 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)

[45] 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)

[46] Q. Xu, E. Greplova, B. Julsgaard, and K. Mølmer, Correlation functions and conditioned quantum dynamics in photodetection theory, Phys. Scr. 90(12), 128004 (2015)

[47] 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)

[48] W. Vogel, Squeezing and anomalous moments in resonance fluorescence, Phys. Rev. Lett. 67(18), 2450 (1991)

[49] W. Vogel, Homodyne correlation measurements with weak local oscillators, Phys. Rev. A 51(5), 4160 (1995)

[50] M. J. Collett, D. F. Walls, and P. Zoller, Spectrum of squeezing in resonance fluorescence, Opt. Commun. 52(2), 145 (1984)

[51] P. R. Rice and H. J. Carmichael, Nonclassical effects in optical spectra, J. Opt. Soc. Am. B 5(8), 1661 (1988)

[52] 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)

[53] G. Nienhuis, Spectral correlations in resonance fluorescence, Phys. Rev. A 47(1), 510 (1993)

[54] 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)

[55] 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)

[56] 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)

[57] M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, S. Saha, A. Dutta, , Roadmap on plasmonics, J. Opt. 20, 043001 (2018)

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