Abstract

Light-matter interaction in the strong coupling regime is of profound interest for fundamental quantum optics, information processing and the realization of ultrahigh-resolution sensors. Here, we report a new way to realize strong light-matter interaction, by coupling metamaterial plasmonic “quasi-particles” with photons in a photonic cavity, in the terahertz frequency range. The resultant cavity polaritons exhibit a splitting which can reach the ultra-strong coupling regime, even with the comparatively low density of quasi-particles, and inherit the high Q-factor of the cavity despite the relatively broad resonances of the Swiss-cross and split-ring-resonator metamaterials used. We also demonstrate nonlocal collective interaction of spatially separated metamaterial layers mediated by the cavity photons. By applying the quantum electrodynamic formalism to the density dependence of the polariton splitting, we can deduce the intrinsic transition dipole moment for single-quantum excitation of the metamaterial quasi-particles, which is orders of magnitude larger than those of natural atoms. These findings are of interest for the investigation of fundamental strong-coupling phenomena, but also for applications such as ultra-low-threshold terahertz polariton lasing, voltage-controlled modulators and frequency filters, and ultra-sensitive chemical and biological sensing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

H. Groß, J. M. Hamm, T. Tufarelli, O. Hess, and B. Hecht, “Near-field strong coupling of single quantum dots,” Sci. Adv. 4(3), r4906 (2018).
[PubMed]

G. Duan, J. Schalch, X. Zhao, J. Zhang, R. D. Averitt, and X. Zhang, “Identifying the perfect absorption of metamaterial absorbers,” Phys. Rev. B 97(3), 035128 (2018).
[Crossref]

T. Stav, A. Faerman, E. Maguid, D. Oren, V. Kleiner, E. Hasman, and M. Segev, “Quantum entanglement of the spin and orbital angular momentum of photons using metamaterials,” Science 361(6407), 1101–1104 (2018).
[Crossref] [PubMed]

2017 (5)

S. D. Jenkins, J. Ruostekoski, N. Papasimakis, S. Savo, and N. I. Zheludev, “Many-body subradiant excitations in metamaterial arrays: experiment and theory,” Phys. Rev. Lett. 119(5), 053901 (2017).
[Crossref] [PubMed]

B. Yao, Y. S. Gui, J. W. Rao, S. Kaur, X. S. Chen, W. Lu, Y. Xiao, H. Guo, K.-P. Marzlin, and C.-M. Hu, “Cooperative polariton dynamics in feedback-coupled cavities,” Nat. Commun. 8(1), 1437 (2017).
[Crossref] [PubMed]

M. Wei, Q. Yang, X. Zhang, Y. Li, J. Gu, J. Han, and W. Zhang, “Ultrathin metasurface-based carpet cloak for terahertz wave,” Opt. Express 25(14), 15635–15642 (2017).
[Crossref] [PubMed]

A. Bayer, M. Pozimski, S. Schambeck, D. Schuh, R. Huber, D. Bougeard, and C. Lange, “Terahertz light–matter interaction beyond unity coupling strength,” Nano Lett. 17(10), 6340–6344 (2017).
[Crossref] [PubMed]

S. Brodbeck, S. De Liberato, M. Amthor, M. Klaas, M. Kamp, L. Worschech, C. Schneider, and S. Höfling, “Experimental verification of the very strong coupling regime in a GaAs quantum well microcavity,” Phys. Rev. Lett. 119(2), 027401 (2017).
[Crossref] [PubMed]

2016 (4)

Q. Zhang, M. Lou, X. Li, J. L. Reno, W. Pan, J. D. Watson, M. J. Manfra, and J. Kono, “Collective non-perturbative coupling of 2D electrons with high-quality-factor terahertz cavity photons,” Nat. Phys. 12(11), 1005–1011 (2016).
[Crossref]

X. Zhang, C. L. Zou, L. Jiang, and H. X. Tang, “Cavity magnomechanics,” Sci. Adv. 2(3), e1501286 (2016).
[Crossref] [PubMed]

Z. Wang, F. Cheng, T. Winsor, and Y. Liu, “Optical chiral metamaterials: a review of the fundamentals, fabrication methods and applications,” Nanotechnology 27(41), 412001 (2016).
[Crossref] [PubMed]

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), 127–130 (2016).
[Crossref] [PubMed]

2015 (5)

J. J. Viennot, M. C. Dartiailh, A. Cottet, and T. Kontos, “QUANTUM INFORMATION. Coherent coupling of a single spin to microwave cavity photons,” Science 349(6246), 408–411 (2015).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, “QUANTUM INFORMATION. Coherent coupling between a ferromagnetic magnon and a superconducting qubit,” Science 349(6246), 405–408 (2015).
[Crossref] [PubMed]

B. M. Yao, Y. S. Gui, Y. Xiao, H. Guo, X. S. Chen, W. Lu, C. L. Chien, and C.-M. Hu, “Theory and experiment on cavity magnon-polariton in the one-dimensional configuration,” Phys. Rev. B Condens. Matter Mater. Phys. 92(18), 184407 (2015).
[Crossref]

T. Roger, S. Vezzoli, E. Bolduc, J. Valente, J. J. F. Heitz, J. Jeffers, C. Soci, J. Leach, C. Couteau, N. I. Zheludev, and D. Faccio, “Coherent perfect absorption in deeply subwavelength films in the single-photon regime,” Nat. Commun. 6(1), 7031 (2015).
[Crossref] [PubMed]

2014 (3)

G. R. Keiser, H. R. Seren, A. C. Strikwerda, X. Zhang, and R. D. Averitt, “Structural control of metamaterial oscillator strength and electric field enhancement at terahertz frequencies,” Appl. Phys. Lett. 105(8), 081112 (2014).
[Crossref]

X. Zhang, C. L. Zou, L. Jiang, and H. X. Tang, “Strongly coupled magnons and cavity microwave photons,” Phys. Rev. Lett. 113(15), 156401 (2014).
[Crossref] [PubMed]

Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, “Hybridizing ferromagnetic magnons and microwave photons in the quantum limit,” Phys. Rev. Lett. 113(8), 083603 (2014).
[Crossref] [PubMed]

2013 (5)

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

R. Ameling and H. Giessen, “Microcavity plasmonics: strong coupling of photonic cavities and plasmons,” Laser Photonics Rev. 7(2), 141–169 (2013).
[Crossref]

H. Huebl, C. W. Zollitsch, J. Lotze, F. Hocke, M. Greifenstein, A. Marx, R. Gross, and S. T. B. Goennenwein, “High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids,” Phys. Rev. Lett. 111(12), 127003 (2013).
[Crossref] [PubMed]

S. Haroche, “Nobel lecture: controlling photons in a box and exploring the quantum to classical boundary,” Rev. Mod. Phys. 85(3), 1083–1102 (2013).
[Crossref] [PubMed]

V. Blank, M. D. Thomson, and H. G. Roskos, “Spatio-spectral characteristics of ultra-broadband THz emission from two-colour photoexcited gas plasmas and their impact for nonlinear spectroscopy,” New J. Phys. 15(7), 075023 (2013).
[Crossref]

2012 (1)

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
[Crossref] [PubMed]

2011 (3)

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[Crossref] [PubMed]

H. Tao, L. R. Chieffo, M. A. Brenckle, S. M. Siebert, M. Liu, A. C. Strikwerda, K. Fan, D. L. Kaplan, X. Zhang, R. D. Averitt, and F. G. Omenetto, “Metamaterials on paper as a sensing platform,” Adv. Mater. 23(28), 3197–3201 (2011).
[Crossref] [PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).
[Crossref] [PubMed]

2010 (6)

L. Novotny, “Strong coupling, energy splitting, and level crossings: A classical perspective,” Am. J. Phys. 78(11), 1199–1202 (2010).
[Crossref]

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010).
[Crossref] [PubMed]

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep strong coupling regime of the Jaynes-Cummings model,” Phys. Rev. Lett. 105(26), 263603 (2010).
[Crossref] [PubMed]

I. Chiorescu, N. Groll, S. Bertaina, T. Mori, and S. Miyashita, “Magnetic strong coupling in a spin-photon system and transition to classical regime,” Phys. Rev. B Condens. Matter Mater. Phys. 82(2), 024413 (2010).
[Crossref]

M. D. Thomson, V. Blank, and H. G. Roskos, “Terahertz white-light pulses from an air plasma photo-induced by incommensurate two-color optical fields,” Opt. Express 18(22), 23173–23182 (2010).
[Crossref] [PubMed]

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[Crossref]

2008 (2)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

2006 (2)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys. 69(5), 1325–1382 (2006).
[Crossref]

2004 (3)

S. J. van Enk, H. J. Kimble, and H. Mabuchi, “Quantum information processing in cavity-QED,” Quantum Inform. Process. 3(1-5), 75–90 (2004).
[Crossref]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[Crossref] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[Crossref] [PubMed]

2003 (2)

D. Dini, R. Köhler, A. Tredicucci, G. Biasiol, and L. Sorba, “Microcavity polariton splitting of intersubband transitions,” Phys. Rev. Lett. 90(11), 116401 (2003).
[Crossref] [PubMed]

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[Crossref] [PubMed]

2002 (1)

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[Crossref] [PubMed]

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73(3), 565–582 (2001).
[Crossref]

1992 (1)

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Figures (7)

Fig. 1
Fig. 1 1D terahertz PC cavity. (a) Experimental transmittance spectrum of the bare cavity measured by terahertz TDS (solid curve) and corresponding theoretical spectrum calculated with the transfer matrix method (TMM) (dashed curve). The inset shows a typical 1D terahertz PC cavity. (b) Distribution of the electric field within the bare cavity calculated with the TMM. The field strengths are given relative to the field amplitudes E0 of the incoming radiation. The solid grey rectangles indicate the positions of the Si dielectric layers.
Fig. 2
Fig. 2 Strong coupling of Swiss-cross MMs with photons in the cavity. (a) Schematic of the unit cell of the Swiss-cross MM. (b) Transmittance spectrum of the Swiss-cross MM with reflection resonance at vm = 0.895 THz (black curve) and theoretical spectrum (red curve). (c) Measured (red connected circles) transmittance spectra of the MM-loaded 1D terahertz cavities for the set of six MMs with varying vm. Each spectrum is shifted vertically for visibility. (d) Dispersion of the MM cavity polaritons. Experimental peak frequencies of the upper/lower primary polaritons plotted vs. the theoretical absorption resonance frequency of each bare MM (see (b) and Appendix). Red and blue solid curves: coupled-harmonic-oscillator model.
Fig. 3
Fig. 3 Strong coupling of SRR MMs with photons in the cavity. (a) Scheme of the SRR unit cell. (b) Calculated transmittance spectra of each SRR MM on Si surface. (c) Measured transmittance spectra with the SRRs positioned in the cavity, with the cavity mode fixed at 0.86 THz. Note that the weak spurious peaks at 0.79-0.8 THz are due to a small polarization leakage along the Y direction. (d) Extracted polariton resonance frequencies (solid circles and squares) from the measured spectra in (c) and fitted curves using the coupled-harmonic-oscillator model (solid red and blue curves).
Fig. 4
Fig. 4 Nonlocal collective interaction of SRR MMs with cavity photons. (a) Experimental transmittance spectra of coupled plasmon-photon modes for three different unit cell densities. The inset shows an AFM photograph of a part of the processed sample. (b) Dependence of Rabi splitting on SRR unit cell density. The red squares show the Rabi splitting obtained with a single MM layer in the cavity, while the blue stars are for the case of two layers of MMs in the cavity; the dash-dotted line represents a square-root fit.
Fig. 5
Fig. 5 The simulated (black dashed curve) and measured (red solid curve) transmittance of the 1D terahertz PC cavity (structure as shown).
Fig. 6
Fig. 6 Simulated transmittance spectra of the free-standing Swiss-cross MM samples used in the experiments, with different MM reflection resonance frequencies ν m (indicated by the labels for each curve) achieved by varying the MM dimension parameters (see Table 1). The curves are shifted vertically for better visibility.
Fig. 7
Fig. 7 Experimental transmittance spectra for the bare cavity (black dash-dot line) and MM-loaded cavity (red line).

Tables (2)

Tables Icon

Table 1 Dimensions of the processed Swiss-cross MMs and the calculated resonance frequencies.

Tables Icon

Table 2 Dimensions of the designed SRR MM (see Fig. 3(a)) and their calculated resonance frequencies ν m .

Equations (3)

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2g= D MM S THz μ MM ω 0 ( ε r L eff S THz ) 1 = D MM ω 0 ( ε r L eff ) 1 μ MM
x ¨ 1 +κ x ˙ 1 + ω c 2 x 1 +V x ˙ 2 =0 x ¨ 2 +γ x ˙ 2 + ω m 2 x 2 V x ˙ 1 =0,
ω ± =( ω c + ω m 2 )i( κ+γ 4 ). ± 1 2 ( ω m ω c ) 2 ( κγ 2 ) 2 +i( κγ 2 )( ω m ω c )+ V 2