Multiple Rabi Splittings under Ultrastrong Vibrational Coupling

Jino George, Thibault Chervy, Atef Shalabney, Eloïse Devaux, Hidefumi Hiura, Cyriaque Genet, and Thomas W. Ebbesen

Phys. Rev. Lett. 117, 153601 – Published 6 October 2016

Abstract

From the high vibrational dipolar strength offered by molecular liquids, we demonstrate that a molecular vibration can be ultrastrongly coupled to multiple IR cavity modes, with Rabi splittings reaching 24% of the vibration frequencies. As a proof of the ultrastrong coupling regime, our experimental data unambiguously reveal the contributions to the polaritonic dynamics coming from the antiresonant terms in the interaction energy and from the dipolar self-energy of the molecular vibrations themselves. In particular, we measure the opening of a genuine vibrational polaritonic band gap of ca. 60 meV. We also demonstrate that the multimode splitting effect defines a whole vibrational ladder of heavy polaritonic states perfectly resolved. These findings reveal the broad possibilities in the vibrational ultrastrong coupling regime which impact both the optical and the molecular properties of such coupled systems, in particular, in the context of mode-selective chemistry.

Received 17 December 2015

DOI:https://doi.org/10.1103/PhysRevLett.117.153601

Physics Subject Headings (PhySH)

Optical materials & elements Optomechanics Polaritons

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Jino George¹, Thibault Chervy¹, Atef Shalabney^1,2, Eloïse Devaux¹, Hidefumi Hiura³, Cyriaque Genet^1,*, and Thomas W. Ebbesen^1,†

¹ISIS and icFRC, Université de Strasbourg and CNRS, 67000 Strasbourg, France
²Braude College, Snunit Street 51, Karmiel 2161002, Israel
³IoT Device Research Laboratories, NEC Corporation, 34 Miyukigaoka, Tsukuba 305-8501, Japan

^*Corresponding author. genet@unistra.fr
^†Corresponding author. ebbesen@unistra.fr

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Issue

Vol. 117, Iss. 15 — 7 October 2016

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Images

Figure 1
$Fe (CO)_{5}$ data are shown in columns for clarity, starting with the IR spectrum of 10 wt. % $Fe (CO)_{5}$ in toluene, the transmission spectrum of the FP cavity filled with the same solution (blue curve) with a Rabi splitting $Ω_{10 %} \sim 135 {cm}^{- 1}$ , followed by the mode diagram of the system under the corresponding coupling. The middle column shows the empty cavity modes with, on the right-hand side, the coupled diagram of the multiple polaritonic states when the cavity is filled with 100 wt. % $Fe (CO)_{5}$ . The last column to the right shows the corresponding experimental IR spectrum of the filled cavity with a resonant Rabi splitting $Ω_{100 %} \sim 480 {cm}^{- 1}$ .
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Figure 2
(a) Experimental (red line) and transfer matrix simulated (black line) IR transmission spectra of pure $Fe (CO)_{5}$ coupled to the fourth-order mode of a flow cell FP cavity; black dashed line is the simulated absorbance of CO stretching mode of pure $Fe (CO)_{5}$ . (b) $T$ -matrix simulation of the electric field distribution inside the FP cavity. Asymmetric field distribution on either side of the vibrational band is an indication of higher and lower mode folding effects due to a strongly dispersive refractive index. (c) Round-trip phase accumulation of the electromagnetic field in the cavity with (red line) and without (red dashed line) an absorber. Optical resonances occur for phase accumulation equal to integer multiples of $2 π$ (horizontal black lines). The dispersion of the refractive index of the intracavity medium allows multiple solutions for various mode indices (vertical dashed lines, the same color code as in Fig. 1). The fitted absorption line shape of $Fe (CO)_{5}$ is also shown in a black dashed line. The resonances lying in the strong absorption region are overdamped solutions and do not appear in the transmission spectra.
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Figure 3
Polaritonic dispersion diagram as a function of the cavity thickness. Experimental transmission peak positions are reported as blue dots. The exact cavity thickness is determined from the free spectral range of the cavity—see Supplemental Material (Sec. A [26]). The solid lines are the best fit to the data using the full Hamiltonian model that accounts for the dipolar self-energy and the contributions beyond the rotating wave approximation (RWA), while the dashed lines are solutions of the simple RWA model—see Supplemental Material (Sec. D [26]) for the fitting procedure. The color code is the same as in Fig. 1. The vibrational polaritonic band gap $Δ E_{g}$ appears only in the full Hamiltonian model.
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Figure 4
(a) Polaritonic dispersion diagram measured by angle-dependent IR transmission spectroscopy (unpolarized, 0°–28°). The solid lines are the solutions of the full Hamiltonian model, using the same parameters and color code as in Fig. 3. The vibrational polaritonic band gap is again clearly observed (blue horizontal band). (b) Photonic and vibrational fractions of the $P_{4}^{-}$ polaritonic branch (blue and red curves, respectively) and of the $P_{6}^{-}$ polaritonic branch (green and yellow curves, respectively). The photon-vibration energy detuning for the fourth cavity mode is shown in black dashes (right axis).
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