Dual-colour pump-probe spectroscopy to observe the transition between polariton branches in an ultrastrongly coupled microcavity containing organic dye molecules

A microcavity is a device that discretizes the optical mode and confines the photon in a wavelength-sized space. The matter inserted into the microcavity interacts with the light field differently than in free space. This unique interaction has conventionally been categorized as either a weak or a strong coupling regime. In a strong coupling regime, the polarization of the matter interacts coherently with the cavity photon and then new mixture quantum states are formed. These mixture quantum states in the microcavity can be treated as a quasiparticle which is called cavity polariton. The formation of the polaritons is observed in the spectra as the splitting of the cavity mode. This splitting is called vacuum Rabi splitting. Unique phenomena, for example, Bose–Einstein condensation at comparatively high temperature,^1,2) ultra-low threshold polariton lasing,^3,4) and ultrafast optical parametric amplification,⁵⁾ have been reported in such systems.

However, in recent years, a new regime has been added to the categories of weak and strong coupling: ultrastrong coupling. In this regime, the vacuum Rabi splitting energy ΔE becomes larger than that in the strong coupling regime and comparable with the excitonic transition energy of the matter E₀.⁶⁾ For example, some literature defines ultrastrong coupling as the regime with ΔE/E₀ ≥ 0.2.^7–10) In this, the rotating wave approximation breaks down, and the A² term, which is the square of the vector potential A, becomes significant.^6,9,11) Some researchers have predicted that, theoretically, these differences enable the observation of unique phenomena, for instance, the generation of an entangled photon pair from the polariton vacuum¹²⁾ and superradiant phase transition.^13,14)

Even in the early studies on the strong coupling regime, it was reported that the Rabi splitting energy in organic materials^15,16) is larger than those in atomic systems^17,18) and quantum nanostructure^19–21) because the numbers and strength of their oscillators are large. A vacuum Rabi splitting energy more than 100 meV was reported and a strong coupling regime was observed at the end of the 1990s using organic materials.^15,16) In addition, a huge vacuum Rabi splitting energy reaching 1 eV was realized in the 2010s.^7,9,22) These systems can be categorized as the ultrastrong coupling regime. These enormous vacuum Rabi splitting energies have only been reported in organic systems, although the ultrastrong coupling regime has been observed elsewhere.^11,23–25) Our own previous literature includes the observation of an ultrastrong coupling regime using organic dye, generally known as Lemke dye.²⁶⁾ Lemke dye is often used to fabricate poled polymers to emit terahertz waves via a second-order nonlinearity.^27,28)

The ultrafast nonlinear dynamics of cavity polaritons have been investigated in various ways.^29–35) However, there are few reports on Rabi splitting, that is, the transition between the upper polariton (UP) and lower polariton (LP) branches. In the strong coupling regime in semiconductor quantum nanostructures, the vacuum Rabi splitting energy is often located in the terahertz region. In this case, there is an example in which the polarization of UP and LP branches was simultaneously excited and the terahertz wave was generated by beating.^36,37) However, this does not mean to observe the direct transition from UP to LP. The direct transition between LP and UP is intriguing, from a viewpoint of not only basic science but also applied research. This transition can be applied to various photonic devices such as wavelength-tunable light sources, modulators, and so on.

However, the transitions between polariton branches are forbidden in inversion symmetric systems because they have the same parity.³⁶⁾ Therefore, the transition between polariton branches is difficult to be observed; indeed, its properties had never been investigated before. Moreover, as described above, in the case of a strongly coupled system in semiconductor quantum nanostructures, the transition energy is in the terahertz region, so it is not so easy to perform experimentally. In contrast, the huge vacuum Rabi splitting energy in the ultrastrongly coupled systems using organic materials corresponds to the near-infrared region^7,9,22,26) in which spectroscopic experiments are easier. Indeed, the microcavity containing the Lemke dye has a substantial vacuum Rabi splitting energy exceeding 1 eV.²⁶⁾ In addition, many organic dye molecules do not have inversion symmetry, and so the selection rule might be broken. The Lemke dye has a push-pull structure, in which the diethylamino functional group donates an electron and the dinitrile functional group withdraws an electron. In other words, it does not possess the inversion symmetry. In this paper, we investigated an ultrafast transient transmission properties of the ultrastrongly coupled microcavity containing Lemke dyes in order to observe a transition between polariton branches.

We fabricated a Fabry-Pérot microcavity made of aluminum mirrors containing (3-(2-(4-(N, N'-diethylamino)-phenyl)ethenyl)-5,5-dimethyl-1,2-cyclohexenylidene)-propanedinitrile, known as the Lemke dye.^38,39) The chemical constitution of the Lemke dye and the structure of the sample are shown in Fig. 1. The method of sample fabrication is described below. A 20-nm-thick aluminum mirror was deposited on a BK7 glass substrate by vacuum evaporation. The cavity layer consisted of a poly(methyl methacrylate) (PMMA) thin film, in which the Lemke dyes were dispersed homogeneously. They were dissolved in the toluene and spin-coated on the top of the aluminum mirror. The thickness of the Lemke/PMMA thin film was about 170 nm, and the weight ratio of Lemke to PMMA was 0.72. The absorption spectrum of the Lemke dye dispersed in the PMMA is shown in Fig. 2 by the dashed line. A remarkable absorption peak at 2.42 eV was observed. Finally, we redeposited the 20-nm-thick aluminum mirror on the cavity layer and formed the metal planar microcavity containing the Lemke dye. This structure performs as a λ/2 cavity, having the resonant energy at 2.42 eV, which is the transition energy of the dye, when the light-incident angle is oblique. This sample is the same microcavity used in our previous study.²⁶⁾

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To investigate the dispersion relation of the sample, we measured the dependence of the linear transmission spectra on the light-incident angle. The spectra of the sample were measured at the incident angles every 2^◦ from 0^◦ to 60^◦. The light source was a halogen lamp, and the polarization of the light was TE.

We performed the transient transmission spectroscopy in the two excitation configurations shown in Fig. 3—these will be referred to as schemes (a) and (b)—for the microcavity sample. In scheme (a), the sample was first pumped with light that had a photon energy corresponding to the LP branch and then probed with the light that corresponded to the vacuum Rabi splitting energy. In this experiment, the sample was probed with the differential energy between the UP and LP branches after the LP state was populated; thus, it was expected that the photoinduced absorption would occur by the transition from the LP state to the UP state. In scheme (b), both pump and probe pulses had the same photon energy corresponding to the LP state. In this case, it was thought that absorption saturation would be observed.

Zoom In Zoom Out Reset image size

To perform the transient transmission spectroscopy, we used two optical parametric amplifiers (OPA, TOPAS: Coherent Inc.) to generate the pump and probe pulses. The second harmonic of the signal light of one OPA was used as the pump pulse with a photon energy of 1.96 eV. The other OPA generated the signal light as a probe pulse with a photon energy of 1.03 eV in scheme (a). In scheme (b), we used the latter OPA to generate the second harmonic of the signal light, with a photon energy of 1.96 eV. The two pulses used were TE-polarized, and the time resolution of these systems estimated by the cross-correlation was less than 300 fs. For the spectrometer and photodetector, we used the multi-channel spectrometer [NIR-I (λ:1.7)]: Hamamatsu Photonics K. K.) in scheme (a) and the CCD camera (NTE2/CCD-1024/256-OP/1: Princeton Instruments, Inc.) connected to the polychromator (M25-TP: Bunkoukeiki Co., Ltd) in scheme (b). The incident angle of the probe light was 45^◦, being the resonant angle of the microcavity, as described below.

In this paper, we used the full Hopfield Hamiltonian which is often used to analyze ultrastrongly coupled systems.^6,7,9) The full Hopfield Hamiltonian contains anti-rotating and A² terms; thus, it can describe the non-approximated interaction in the ultrastrong coupling regime.

In fact, to calculate the theoretical dispersion relation, we used the diagonalized full Hopfield Hamiltonian:^6,40)

$$\begin{eqnarray}\,\left[\begin{array}{cccc}{E}_{\mathrm{ph}}(\theta )+2D & -{iV} & -2D & -{iV}\\ {iV} & {E}_{0} & -{iV} & 0\\ 2D & -{iV} & -{E}_{\mathrm{ph}}(\theta )-2D & -{iV}\\ -{iV} & 0 & {iV} & -{E}_{0}\end{array}\right]\left[\begin{array}{r}w\\ x\\ y\\ z\end{array}\right]=E\left[\begin{array}{r}w\\ x\\ y\\ z\end{array}\right],\end{eqnarray} \tag{ 1 }$$

where,

$$\begin{eqnarray}&&V={\hslash }g=\displaystyle \frac{{\rm{\Delta }}E}{2},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&D={\hslash }\displaystyle \frac{{g}^{2}}{{\omega }_{0}}=\displaystyle \frac{{\rm{\Delta }}{E}^{2}}{4{E}_{0}}.\end{eqnarray} \tag{ 3 }$$

Here, E_ph(θ), g and ω₀ are the resonant energy of the naked cavity mode, the coupling constant between the cavity field and the excitonic transition of the matter, and the frequency of the excitonic transition, respectively.

The incident angle θ is related to the wavenumber and energy of the naked cavity mode as follows:⁷⁾

$$\begin{eqnarray}&&{E}_{\mathrm{ph}}(\theta )={\hslash }{ck}(\theta )={E}_{\mathrm{ph}}(0){\left(1-\displaystyle \frac{{\sin }^{2}\theta }{{n}_{\mathrm{eff}}^{2}}\right)}^{-\tfrac{1}{2}}.\end{eqnarray} \tag{ 4 }$$

Here, E_ph(0), k (θ) , and n_eff are the resonant energy of the cavity when θ = 0, the wavenumber of the cavity mode, and the effective refractive index of the cavity layer, respectively. Thus, the dispersion relation can be obtained from the dependence of the linear transmission spectra on the light-incident angle.

4.1. Linear spectroscopy

The typical transmission spectrum of the microcavity is indicated by the solid line in Fig. 2. The transmission peak was split into two around the absorption-peak-energy of the Lemke/PMMA film. We extracted the transmission-peak-energies of the cavity from the measured spectra at each angle.

The obtained dispersion relation of the metal planar microcavity containing Lemke dye is shown in Fig. 4. The transmission peak split into two around the excitonic transition energy and obvious anti-cross-type dispersion curves were observed. We fit the experimentally obtained dispersion relation with the expression derived from the full Hopfield Hamiltonian, in order to extract the resonant incident angle and vacuum Rabi splitting energy. The theoretically calculated dispersion curves are shown in Fig. 4 by the solid lines. They closely agree with the experimental results. The vacuum Rabi splitting energy, which was extracted from the fitting parameter, was 1.03 eV, and the ratio of the vacuum Rabi splitting energy to the excitonic transition energy reached 0.42. Thus, we observed the ultrastrong coupling regime using the metal planar microcavity containing Lemke dye. The incident angle at the resonance of the cavity mode to the excitonic transition was estimated at about 45^◦ from the fitting results. At this angle, the energies of the LP and UP were 1.96 and 2.99 eV, respectively. Thus, the energy diagram at the resonance can be described as shown in Fig. 3. When the incident angle is 45^◦, the photon energies of 1.96 and 1.03 eV correspond to the energies of the LP state and magnitude of the vacuum Rabi splitting, respectively. The additional information of the sample fabrication and the detailed linear optical properties of the sample are described in our previous literature.²⁶⁾

Zoom In Zoom Out Reset image size

4.2. Nonlinear spectroscopy

The ΔT/T spectrum, at a delay time t = 0 ps measured in scheme (a), is shown in Fig. 5 as a dashed-dotted line. The ΔT/T was negative at around 1.03 eV. We consider this to be an observation of the photoinduced absorption in the energy region, which corresponds to the vacuum Rabi splitting energy of the sample. We also performed the same experiment to the naked Lemke/PMMA thin film as shown by the solid line in Fig. 5. The ΔT/T was almost zero; therefore, the naked Lemke did not have the state that can be excited with this experiment. We also confirmed that the transmission intensity of the naked Lemke thin film does not change significantly depending on the delay time in this experiment. These experiments indicate that the observed photoinduced absorption results from transition from the LP state to the new state formed by the interaction in the microcavity, probably the UP state.

Zoom In Zoom Out Reset image size

Next, we measured the time dependence of the ΔT/T , as shown by the open circles in Fig. 6. The relaxation time of the observed photoinduced absorption was estimated to be a few picoseconds. If this photoinduced absorption results from the transition between the polariton branches, it would be observed while the LP state was populated. If there is no transition related to a level other than the LP, UP, and ground states, the relaxation time is determined by that of the LP. To investigate the relaxation time of the excitation of the LP state, we performed the mono-color pump-probe spectroscopy, namely, scheme (b). The time-dependent ${\rm{\Delta }}T/T$ at 1.96 eV in scheme (b) is shown by the closed circle in Fig. 6. The ΔT/T became positive after pumping, due to the absorption saturation of the LP state. The relaxation time of the absorption saturation of the LP state was also a few picoseconds, and it was almost the same as that of the photoinduced absorption observed in scheme (a). This correspondence is reasonable if the transition between the polariton branches occurs, as described above.

Zoom In Zoom Out Reset image size

As mentioned above, transition between the polariton branches is usually forbidden. Both of them are linear combinations of the one-photon state of the cavity field and the first excited state of the matter;³⁶⁾ thus, they have wave functions with the same parity. Matrix elements for transitions between the states with the same parity are zero, and they are generally forbidden, but this selection rule breaks down in highly asymmetric systems, because the parity of their wave function cannot be categorized as perfectly odd or even. The Lemke dye is highly asymmetric as it has a push-pull structure. Thus, the polariton branches may not have the parity categorized as perfectly odd or even, and the selection rule may break down in the microcavity containing Lemke dye.

However, the observed vacuum Rabi splitting energy is the sum of contributions from multiple molecules.^15,26) The vacuum Rabi splitting might be small if the interaction is between a single molecule and the light field. Thus, it might be reasonable to assume that light with a photon energy corresponding to the vacuum Rabi splitting energy cannot induce the transition between the polariton branches when the transition occurs in a single molecule. We discuss the following from this point of view.

First, we consider the proposition that the transition might occur in the intra-molecule. If the spectrum of the single molecule has a relatively large linewidth, the transition between the tails of the polariton branches can occur. The linewidth of polariton branches is the weighted average of that of the cavity and matter.¹⁶⁾ Thus, the spectral linewidth of each branch in the cavity polariton, produced by the matter with large spectral linewidth, becomes large. Moreover, vibrational levels exist in the inhomogeneously broadened spectrum of the Lemke dyes. When a single molecule interacts with the light field, middle polariton branches may be formed.^3,41,42) In this case, the energy difference between the UP and LP branches would become larger than that it would be without middle polariton branches. Therefore, the probe pulse may possibly excite to the UP state in scheme (a) (see Fig. 2) when considering the vibrational levels buried in the inhomogeneous broadening.

Next, we consider the idea that the energy might be transferred between the molecules when the transition occurs. It is known that the polariton in crystal propagates as a hybrid wave of the excitation of the matter and the light field. In the microcavity containing organic dyes, the excitation might also be transferred among the molecules. Thus, the transition between polariton branches also can be observed in scheme (a) if the energy transfer between the molecules with different transition or Rabi splitting energiess occurs. In this case, the transition from the LP to UP does not occur in a single molecule but might occur across multiple molecules.

We cannot categorically conclude that the transition from the LP to UP state caused the photoinduced absorption of the sample, but the results of our experiment strongly imply that it is the potent origin of the observed photoinduced absorption.

We fabricated an ultrastrongly coupled metal planar microcavity containing Lemke dyes and investigated its ultrafast nonlinear optical properties. We performed a dual-color pump-probe spectroscopy to pump the LP state and to probe with the pulse having the photon energy corresponding to the vacuum Rabi splitting energy of the sample. Photoinduced absorption with a few picoseconds' relaxation time was observed. This was not found when using the naked Lemke dye; therefore, it appeared to result from the transition from the LP state to that formed by the interaction in the microcavity, probably the UP state. On the other hand, because we predicted that the relaxation time of the LP state would dominate that of the excitation to the UP state from the LP state, we measured the relaxation time of the bleaching of the LP state using the mono-color pump-probe spectroscopy for the cavity sample. The measured relaxation time was, indeed, comparable with that of the photoinduced absorption of the cavity sample. Although there may be other possible origins of the photoinduced absorption, the results of our experiment lead us to conclude that the most reasonable one is the transition between the polariton branches.

The authors acknowledge Prof. Fusao Shimokawa, Mr. Keiji Uzumi, and Ms. Xinping Yu at Kagawa University for their contribution to the observation of the ultrastrong coupling regime. The authors would like to thank Prof. Shyun Koshiba in Kagawa University who lent us the multi-channel spectrometer [NIR-I (λ:1.7)]. This study was supported by the Kagawa Nanofabrication Platform in the Nanotechnology Platform Project sponsored by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. The authors are deeply grateful to the technical staff, especially Mr. Hisao Higa, in the Kagawa Nanofabrication Platform for advice on the sample fabrication. This study was also supported by JSPS KAKENHI Grant Numbers JP15K04697 and JP16J11890. The authors would like to thank Enago (www.enago.jp) for the extremely amazing English language review.