Chinese Optics Letters, Volume. 22, Issue 10, 103602(2024)

Strong light–matter coupling between excitons and chiral quasi-bound states in the continuum in van der Waals metasurfaces

Zhonghong Shi, Houjiao Zhang, and Zhang-Kai Zhou*
Author Affiliations
  • State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-sen University, Guangzhou 510275, China
  • show less

    The study of strong coupling between photonic cavities and excitons has brought about significant advances, varying from fundamental physics to applied science. However, there are several challenges hindering its further development, including obtaining photonic modes with both low room-temperature loss and high electric field (EF) enhancements, the difficulty of precisely transferring exciton materials into the photonic cavity, and the urgent need for additional manipulation approaches. In order to overcome these challenges simultaneously, we present a theoretical strong coupling system based on the chiral metasurfaces that are built by the excitonic van der Waals material of WSe2 and can support the quasi-bound states in the continuum (q-BIC) mode. The q-BIC mode can sustain EF enhancements over 80 times with loss smaller than 10 meV, and the strong coupling between q-BIC mode and WSe2 excitons can be naturally realized without material transferring. Furthermore, a large chirality beyond 0.98 can be obtained in this strong coupling system, making the circular polarization of excitation light an effective parameter to control the generation of coherent states in this metasurface system. Our results can benefit the further development of strong coupling research, shedding light onto the exploration of new quantum devices.

    Keywords

    1. Introduction

    The strong coupling of cavity–photon and exciton at room temperature has garnered significant research attention due to its potential in fundamental physics, such as superfluidity and Bose–Einstein condensation, as well as practical applications, including various quantum logic devices, low-threshold lasers, quantum computing, quantum information processing, and storage[1]. Especially, with the developments of various novel photonic modes and excitonic materials employed into the study of strong coupling, such as the gap plasmons[2,3], bound states in the continuum (BIC) mode[48], and various hybrid photonic modes[912], as well as the graphene[13], and the van der Waals materials of transition metal dichalcogenides (TMDCs)[1417], remarkable advances have been demonstrated, including the realization of strong coupling at the quantum limit[18,19] and ultrastrong coupling at room temperature[13].

    Despite these achievements, there still exist three important problems hindering the further development of strong coupling. First, in order to prolong the coherent time of a strong coupling system, finding suitable photonic modes with low room-temperature loss and large electric field (EF) enhancements is of great importance. However, for the majority of photonic nanocavities, their room-temperature losses are usually over 100 meV[2023]. Although in some cases such as the dielectric grating[24], Tamm–plasmon photonic microstructures[9,10], and distributed Bragg reflector mirrors[25,26], their losses can be relatively low, these modes also sustain smaller EF enhancements due to their weaker ability in confining optical fields. Therefore, it is highly desirable to find a photonic mode with both low loss and large EF enhancements. The second problem is exciton transferring. Since the EF enhancements are mainly confined inside photonic modes, a large amount of effort has to be devoted into placing the excitons inside nanocavities, which is apparently a difficult task for experiments. Third, with the requirement for actively manipulating quantum bits[27] for obtaining advanced room-temperature quantum logic devices, it is also necessary to explore effective ways for controlling quantum states in strong coupling systems.

    Therefore, we propose a system that we call chiral quasi-bound states in the continuum (q-BIC) metasurfaces built by excitonic TMDCs to overcome the above-mentioned problems. First, the optical loss of the q-BIC mode is determined only by the controllable radiation leakage[28], which can be easily suppressed within 10 meV. Meanwhile, it is found that the EF enhancements of this q-BIC can be more than 80 times, which is highly beneficial for the construction of strong coupling systems. Second, since the q-BIC metasurfaces are made by the excitonic material of TMDCs (we choose WSe2), the excitons are naturally locating in the q-BIC mode[6,15,29], saving the process of transferring excitons inside photonic structures. With the rapid development of two-dimensional (2D) material processing technology[30], there are already TMDCs-based grating structures[29], nanoresonators[31], and metasurfaces[6,32] that have been used to study the interaction between light and matter, which confirms the feasibility of this scheme. Third, it is of great significance to add a new chiral dimension to the light–matter interaction systems, which not only enriches the general principle of light–matter interaction, but also provides guidance for the design of chiroptical devices[3336]. The circular dichroism (CD) of our metasurfaces can be as large as 0.985 in this system, indicating that the generation of quantum states induced by strong coupling can be effectively manipulated by changing the circular polarization of the excitation light. The reversible energy exchange process in strong coupling can be used to coherently transfer quantum information between excitons and photons. The chiral response of coherent states provides a new approach for the design of quantum logic devices, which can be manipulated by the circular polarization of excitation light. Our findings can not only deepen the understanding of novel strong coupling systems, but also pave the way toward the development of room-temperature quantum logic devices with more dimensions of manipulation.

    2. Structure and Design

    Consider an achiral array constructed by the planar lattice of a pair of parallel rectangular dielectric pillars on SiO2 substrate, shown in Fig. 1(a), which supports the symmetry-protected BIC mode. The vanishing resonance means that there is no leakage of energy from the bound state to free space, proving the existence of the BIC state [the lower panel of Fig. 1(a)]. By introducing perturbations, such as in-plane symmetry breaking or out-of-plane symmetry breaking, the pure BIC mode of the symmetrical lattice could be converted into a leaky q-BIC mode with the electromagnetic field distribution slightly deviating from the BIC[28,37]. To be specific, as shown in Fig. 1(b), a q-BIC mode can be obtained by breaking the out-of-plane symmetry (i.e., manipulating the height difference ΔH between the two rectangle pillars). The right panel of Fig. 1(b) shows the gradual evolution, demonstrating that the BIC mode changes to q-BIC mode as ΔH increases from 0 to 70 nm, and showing obvious transmission valley. In Fig. 1(c), another q-BIC mode is obtained by breaking the in-plane rotational symmetry (i.e., changing the angle 2θ between the two rectangle pillars). Similar to the evolution in Fig. 1(b), it is clear that the BIC mode turns to the q-BIC mode with θ increasing from 0° to 15°.

    Schematic diagram of the evolution process from BIC to chiral q-BIC. (a) The unit cell of a metasurface with a pair of parallel rectangular dielectric pillars that support BIC mode, the lower panel is its transmission spectrum; (b) metasurface with a pair of rectangular dielectric pillars that support a q-BIC mode after introducing the height difference ΔH. The right panel is its transmission spectrum as a function of ΔH. (c) Metasurface with a pair of rectangular dielectric pillars that support a q-BIC mode after breaking the in-plane rotational asymmetry. The right panel is its transmission spectrum as a function of θ. (d) Metasurfaces with a pair of rectangular dielectric pillars that support a chiral q-BIC mode after combining the out-of-plane symmetry-breaking perturbation with the in-plane one. The bottom panel is its transmission spectra under the excitations with opposite circularly polarized lights.

    Figure 1.Schematic diagram of the evolution process from BIC to chiral q-BIC. (a) The unit cell of a metasurface with a pair of parallel rectangular dielectric pillars that support BIC mode, the lower panel is its transmission spectrum; (b) metasurface with a pair of rectangular dielectric pillars that support a q-BIC mode after introducing the height difference ΔH. The right panel is its transmission spectrum as a function of ΔH. (c) Metasurface with a pair of rectangular dielectric pillars that support a q-BIC mode after breaking the in-plane rotational asymmetry. The right panel is its transmission spectrum as a function of θ. (d) Metasurfaces with a pair of rectangular dielectric pillars that support a chiral q-BIC mode after combining the out-of-plane symmetry-breaking perturbation with the in-plane one. The bottom panel is its transmission spectra under the excitations with opposite circularly polarized lights.

    Although the q-BIC mode only induced by out-of-plane or in-plane asymmetry is achiral, combining the out-of-plane and in-plane asymmetry together (i.e., applying the parameter changing of ΔH and 2θ simultaneously) can lead to the q-BIC mode with large chirality, bringing about chiral q-BIC metasurfaces[3335]. By precisely adjusting the values of θ and ΔH, appropriate parameters can be determined such that kΔH/2=θ, where the metasurfaces only couple to the incident light with a specific chirality, while the light with opposite chirality is completely transmitted. For the structure in Fig. 1(d), the metasurfaces can be excited by the right circularly polarized (RCP) light to produce a q-BIC mode, while the left circularly polarized (LCP) light is almost completely transmitted, which is defined as the R-structure. The L-structure with completely opposite chiral responses can be obtained by swapping the positions of the two rectangle pillars.

    Following the understanding of origins about the q-BIC mode and its chirality supported by the metasurfaces, we turn to detailed investigations about the manipulations of q-BIC mode and chirality based on changing structure parameters. Here, we take the R-structure as an example; it is composed of a material with a refractive index of 4.24. As shown in Fig. 2(a), there are nine structure parameters defining our metasurfaces, which are the array periods (Px and Py), pillar length (L), widths (WR and WL), heights (HR and HL), as well as the rotation angle and center spacing of the two rectangle pillars (θ and W). The two pillars have the same length L because we need to avoid the introduction of additional in-plane symmetry breaking, which will increase the complexity of this system.

    (a) Schematic diagram of the R-structure that supports a chiral q-BIC mode with periods of Px = 475 nm and Py = 350 nm. For the two rectangle pillars, HR = 110 nm, HL = 70 nm, WR = 70 nm, WL = 110 nm, L = 234 nm. (b) Maximum CD as a function of the rotation angle θ (red line) and the spacing of two pillars W (blue line); (c) transmission spectra depending on the period in the x-direction (Px) under the excitation of LCP (red lines) and RCP (blue lines), for both the R-structure (lower panel) and L-structure (upper panel). Px was changed from 445 to 705 nm in steps of 10 nm. (d) ℏΓq-BIC as a function of Px (red dot) and λq-BIC as a function of Px (blue dot). The solid lines are the fitting results. (e) CD values at different Px, and the inset is the corresponding EF distributions.

    Figure 2.(a) Schematic diagram of the R-structure that supports a chiral q-BIC mode with periods of Px = 475 nm and Py = 350 nm. For the two rectangle pillars, HR = 110 nm, HL = 70 nm, WR = 70 nm, WL = 110 nm, L = 234 nm. (b) Maximum CD as a function of the rotation angle θ (red line) and the spacing of two pillars W (blue line); (c) transmission spectra depending on the period in the x-direction (Px) under the excitation of LCP (red lines) and RCP (blue lines), for both the R-structure (lower panel) and L-structure (upper panel). Px was changed from 445 to 705 nm in steps of 10 nm. (d) ℏΓq-BIC as a function of Px (red dot) and λq-BIC as a function of Px (blue dot). The solid lines are the fitting results. (e) CD values at different Px, and the inset is the corresponding EF distributions.

    Among those parameters, six of them are preset. First, we should set the volume of one rectangle pillar. In order to make the resonant wavelength (λq-BIC) of q-BIC mode located around the exciton energy of 1.645 eV (i.e., 754nm), we set L, WR, and HR as 234, 70, and 110 nm according to the simulation results in Fig. 1. Second, since the BIC mode can only appear when the two rectangle pillars have the antiparallel dipole moments p1=p2[37,38], for the left rectangle pillar, we set L, WL, and HL as 234, 110, and 70 nm. Third, considering that varying Py cannot linearly change λq-BIC, we set Py=350nm. There are three variable parameters (θ, W, and Px), which can be applied to manipulate the chirality and resonance wavelength (λq-BIC) of q-BIC modes. On one hand, by adjusting the values of θ and W with fixed Px=475nm and Py=350nm, maximum CD values 0.985 and 0.981 of the chiral q-BIC metasurfaces can be obtained, and the corresponding parameters are θ=6.5° and W=125nm, respectively [Fig. 2(b)]. Here, CD is defined as CD=TRTLTR+TL,where TR represents the transmission intensity under the excitation of RCP while TL represents the transmission intensity under the excitation of LCP.

    On the other hand, it should also be noted that the resonance wavelength of q-BIC mode (λq-BIC) can be manipulated by changing Px. For both R-structure [lower panel in Fig. 2(c)] and L-structure [upper panel in Fig. 2(c)], by changing Px from 445 to 705 nm in steps of 10 nm, the λq-BIC can be tuned from 730 to 760 nm. Also, as depicted in the simulation results [Fig. 2(d)], one can even find the λq-BIC linearly redshifts with the increasing of Px, while the linewidth of the q-BIC modes (Γq-BIC, i.e., the mode loss) reduces exponentially as Px increases. Moreover, it is excited to find that Γq-BIC decreases with the increasing of Px, changing from about 14 to about 4 meV.

    Figure 2(e) presents the EF enhancements and chirality of the chiral q-BIC metasurfaces. Due to parameter optimizations of Px, one can see that the CD values are all over 0.935, meaning that the intrinsic chirality of the structure is well maintained over a wide band. More importantly, different from most photonic modes, which can hardly exhibit small loss and large EF enhancements simultaneously, the metasurfaces can sustain EF enhancements over 80. Due to the advantages of high chirality, small loss, and large EF enhancements, it is believed that the chiral q-BIC metasurfaces are ideal platforms for building strong coupling systems.

    TMDCs are a promising class of van der Waals materials for strong light–matter coupling, as they host strongly bounded excitons that are stable up to room temperature, enabling strong coupling without relying on a cryogenic environment. Furthermore, the 2D geometry of these materials results in large in-plane dipole moments in the interaction area, significantly increasing coupling with the cavity mode. Since bulk TMDCs are dielectric materials and possess a high refractive index, they can be used to fabricate various subwavelength structures that support different modes. Compared to several other materials in TMDCs, the energy difference between the A exciton and the B exciton of WSe2 is quite large, which can reduce the interference and facilitate our analysis of the results, since we focus on the manipulation of strong coupling coherent states by structural chirality; and so we chose WSe2 as the design material for the metasurfaces. To study the strong coupling between the uncoupled q-BIC mode and WSe2 excitons, we need to change the dielectric of the bulk WSe2 from a constant to a dielectric function described by the Lorentzian oscillator as[39,40]ε=ε0+f0ωex2ωex2ω2iγexω,where ε0=18 is the background permittivity due to higher energy transitions, f0=0.655 is the oscillator strength, ωex=1.645eV, and γex=90meV is the full width of the excitons. These parameters were obtained by comparing the calculated results with the experimental data in Ref. [40]. For background index-only material in Fig. 2, the value of the refractive index is obtained by setting f0 to zero. In this work, we use excitons from bulk WSe2 (with a thickness of more than 70 nm) at room temperature. To the best of our knowledge, when TMDCs are thinned down to a monolayer, the inversion symmetry is explicitly broken, giving rise to a valley-contrasting optical selection rule. The effects are expected only in thin films with an odd number of layers, since inversion symmetry is preserved in bulk and in thin films with an even number of layers[41]. Although, the spin-valley coupling in TMDCs leads to spin polarization in bilayers, which also gives circular polarization in the optical process[42], one can hardly find the evidence to prove that the same can occur in bulk crystals of the 2H phase. In addition, even for TMDCs with monolayers, there is a temperature dependence on the degree of circular polarization under circularly polarized excitation. The degree of circular polarization originating from the contrasting selection rules for optical transitions in the K and K valleys at room temperature is small[43] compared to our CD values. Therefore, we have not considered the valley properties of bulk WSe2 here.

    3. Results and Discussions

    Based on the results of Fig. 3, two important features that can benefit the study of strong coupling are found. For one thing, it is found that large chirality (i.e., large CD) of the metasurfaces can promote the active manipulation of quantum states in a strong coupling system. Taking the R-structure as an example, we present three systems with different CD values of 0.946, 0.41, and 0. In the first case, the spectral difference under LCP and RCP excitations can be clearly seen. As the CD value decreases to 0.41, the spectral difference becomes smaller, whereas at CD=0, there is no difference between LCP and RCP excitations. Specifically, when CD=0.946 [Fig. 3(a)], the coupling of q-BIC to an exciton can occur only when the incident light is RCP. Three valleys are formed in the spectrum in this case, corresponding to the upper polariton (UP), exciton absorption band, and the lower polariton (LP), which illustrates the formation of hybrid states. Benefiting from the giant intrinsic chirality of the structure, when the incident light is LCP, no q-BIC mode is generated, and there is only one valley on the transmission spectrum, which corresponds to the absorption of the exciton itself. The decrease in CD value means that the q-BIC mode is formed under the excitation of both LCP and RCP, resulting in a splitting line shape in both cases, so that the spectral difference is smaller at CD=0.41 [Fig. 3(b)]. Further, for the metasurfaces with CD=0 [Fig. 3(c)], the same transmission spectra are produced under both LCP and RCP excitations. These results demonstrate that the quantum states of the strong coupling system with large chirality can be switched by selecting different circularly polarized lights for excitation, which introduces a new dimension of manipulation for future applications.

    The transmission spectra of the hybrid system with CD values of 0.946 (a), 0.41 (b), and 0 (c), respectively. The red line represents the results under RCP excitation, while the blue line represents that under excitation of LCP. (d) The difference in transmission spectra of the CD values of 0, 0.41, and 0.946, represented by the black, orange, and violet lines, respectively; (e) the transmission spectra of the L-structure under the excitation of RCP and LCP and (f) their difference.

    Figure 3.The transmission spectra of the hybrid system with CD values of 0.946 (a), 0.41 (b), and 0 (c), respectively. The red line represents the results under RCP excitation, while the blue line represents that under excitation of LCP. (d) The difference in transmission spectra of the CD values of 0, 0.41, and 0.946, represented by the black, orange, and violet lines, respectively; (e) the transmission spectra of the L-structure under the excitation of RCP and LCP and (f) their difference.

    For another, one can also find that the system with a CD value close to 1 has the function of removing the inherent spectral background of the strong coupling system. The existence of exciton absorption bands on the absorption spectrum is a common problem in the study of strong coupling using bulk 2D materials, which greatly interferes with the analysis of spectral Rabi splitting[6,15,29]. Since the strong coupling requires large EF enhancements, it is common to find that only excitons near the hot spots (i.e., the place with large EF enhancements) can strongly couple with photonic modes. Therefore, a large number of excitons that are not involved in strong coupling will bring about the emergence of distinct exciton absorption bands on the transmission spectrum. Previous reports have shown a strong absorption caused by uncoupled excitons in the spectra[6,7,15] and demonstrated that the uncoupled excitons will not affect the evolution process of strong coupling and the formation of coherent quantum states. In our system, the Rabi splitting spectrum can be obtained by subtracting the transmission spectrum under the excitation of LCP from the transmission spectrum under the excitation of RCP, as the transmission spectrum excitation by LCP is derived from exciton absorption. In Fig. 3(d), the violet line displays the transmittance difference with CD=0.946, revealing clear spectra for UP and LP, respectively. In addition, it can be seen from the EF distribution map that both UP and LP have strong EF enhancements, which leads to the emergence of absorption valleys, while for the wavelength corresponding to the position of the absorption bands, there are no obvious EF enhancements, indicating that the spectral valley of the R-structure under the excitation of the LCP is derived from exciton absorption. At the same time, the black line of Fig. 3(d) gives the transmittance difference corresponding to the strong coupling system with CD=0 in Fig. 3(c), which has a value of 0. For the metasurfaces with CD=0.41 [orange line in Fig. 3(d)], the line shape of the transmission difference changes compared to the case with CD=0.946. This is due to the presence of splitting under the excitation of both LCP and RCP, making it impossible to determine the pure spectral background. Figures 3(e) and 3(f) are the transmission spectra and the transmission difference of the L-structure with CD=0.946, respectively, which have the same performance as the R-structure.

    Figure 3 mainly focuses on the spectra of the strong coupling system on resonance (i.e., λq-BIC=λex, and λex is the absorption wavelength of the exciton). Next, we go further to show the anticrossing dispersion relationship of our chiral q-BIC metasurfaces. Figure 4(a) displays the simulated transmission spectra of five representative cases after subtracting the uncoupled excitons, where the λq-BIC is varied by changing Px but the λex is stable. The anticrossing dispersion of the chiral q-BIC metasurfaces is extracted from the transmission spectra, and the solid symbols are simulated data obtained by reading those transmission peaks.

    (a) Transmission spectra of the hybrid system with Px varying from 445 to 505 nm; (b) simulation results (symbols) of the anticrossing dispersion relationship extracted from (a). Red and blue dots represent the UP and LP, and the corresponding lines are theoretical fitting results. (c) Polariton branch mixing of WSe2 exciton (green line) and q-BIC (red line) for LP and UP branches; (d) Rabi splitting (ℏΩR) as a function of oscillator strength f.

    Figure 4.(a) Transmission spectra of the hybrid system with Px varying from 445 to 505 nm; (b) simulation results (symbols) of the anticrossing dispersion relationship extracted from (a). Red and blue dots represent the UP and LP, and the corresponding lines are theoretical fitting results. (c) Polariton branch mixing of WSe2 exciton (green line) and q-BIC (red line) for LP and UP branches; (d) Rabi splitting (ℏΩR) as a function of oscillator strength f.

    To fit the results from numerical simulations in Fig. 4(b) and evaluate the coupling mechanism quantitatively, a hybrid system described as an interaction between a two-level system and a quantized light field is introduced, the Hamiltonian of which can be expressed as H=(Eq-BICiΓq-BIC2ggEexiΓex2),where Eq-BIC, Eex and Γq-BIC, Γex are the uncoupled q-BIC mode and exciton energies and their decay rates, respectively. g denotes the coupling strength of the hybrid system. Upon diagonalization, this Hamiltonian yields energies of the two states, E±=Eq-BIC+Eex2±g2+(Eq-BICEex+i(Γq-BICΓex)2)2iΓq-BIC+Γex4.

    Under the condition of zero detuning, i.e., Eq-BIC=Eex, Rabi splitting can be written as ΩR=2g2((Γq-BICΓex)4)2.

    The detuning between Eq-BIC and Eex varies with λq-BIC, from which the anticrossing dispersion of the hybrid system can be clearly observed [Fig. 4(a)]. By introducing parameters Γq-BIC=8meV and Γex=90meV, and setting the coupling strength g as a free input parameter, we can obtain g under the zero-detuning condition by fitting the simulation and theoretical calculations.

    Based on Eq. (4), the anticrossing dispersion can be fitted by the two curves corresponding to the UP (red color) and the LP (blue color) branches. In the case of g=83meV, the calculated dispersion curves match the simulated spectra very well, while the Rabi splitting ΩR reaches 161 meV, which is far beyond the strong coupling criterion ΩR>(Γq-BIC+Γex)/2=49meV. Diagonalization of the Hamiltonian in Eq. (4) yields the Hopfield coefficients α and β. The |α|2 and |β|2 describe the relative mixing fraction of the q-BIC mode and the exciton in the hybrid polaritons, which satisfy |α|2+|β|2=1. As illustrated in Fig. 4(c), the curves representing the contribution of q-BIC and WSe2 are, respectively, marked by red and green lines. The presence of hybrid states further confirms the realization of strong coupling between the q-BIC mode and WSe2 excitons. In order to verify the robustness of the hybrid system, the relation between the Rabi splitting and materials with different parameters was calculated by varying the oscillator strength f. The results show that the strong coupling criterion is satisfied over a wide range, changing from 0.15 to 1 [Fig. 4(d)].

    Static spectra cannot provide further information on the dynamic energy exchange process when strong coupling occurs, limiting understanding of the internal mechanism[44,45]. Therefore, we study the properties of Rabi oscillations in the time domain by calculating the probability amplitudes of each state. The wave function of the hybrid system in the interaction picture can be written as[46,47]|ψ(t)=n(Ce(t)|e,n+Cc(t)|c,n+1),where Ce(t) and Cc(t) are the probability amplitude of the excited exciton state and cavity q-BIC mode, respectively. |e,n is the state where emitter is in the excited state, while |c,n+1 is the state of the q-BIC mode. After bringing Eq. (6) into the Schrödinger equation to solve Eq. (3), one can obtain the probability amplitude of the exciton and the q-BIC mode. Considering that a single photon and the exciton are in an excited state at the initial time, the probability of the system in the excited state (Pe) and in the cavity q-BIC mode (Pc) can be written as Pe(t)=|ce(t)|2=eΓq-BIC+Γex2t|iΓq-BIC+Γex+2iΔ2ΩRsin(ΩR2t)+cos(ΩR2t)|2,Pc(t)=|cc(t)|2=eΓq-BIC+Γex2t|i2gΩRsin(ΩR2t)|2,where Δ=Eq-BICEex is the detuning between the uncoupled q-BIC mode and the exciton. The equation given above shows that the probabilities oscillate sinusoidally with an exponential decay envelope, which is determined by two key parameters: the exponential decay time τ1 (the time when the total probability decays to 1/e) and the oscillation period τ2. This can be derived from Eqs. (7) and (8) such that τ1=2Γq-BIC+Γex,and τ2=2πΩR.

    Therefore, the time-domain dynamics of Rabi oscillation can be quantified by the above two parameters.

    With zero detuning and a Rabi splitting width of 161 meV, the probabilities of the excited state (Pe) and the q-BIC (Pc) are plotted in Fig. 5(a). The obtained probability amplitudes show an exponential decay time of τ1=20fs and clear Rabi oscillations with a period of τ2=39fs. The amplitude decays to 0 after more than 100 fs, which is significantly longer than that of the typical plasmon systems[47,48] as well as dielectric Mie nanoresonators[31]. The longer decay extends the lifetime of coherent states, which is significant for manipulating quantum states and future applications in quantum computing and quantum information processing[49,50].

    Rabi oscillation obtained from Eqs. (6) and (7) with different Rabi splitting, ℏΩR = 161 meV (a) and ℏΩR = 100 meV (b). The other parameters are set to ℏΓq-BIC = 8 meV and ℏΓex = 90 meV, Δ = 0. Inset in (a): τ1 as a function of γex (red line), and τ2 as a function of ℏΩR (blue line). (c) Rabi oscillation with ℏΩR = 161 meV, ℏΓex = 45 meV, and ℏΓq-BIC = 8 meV. The evolution process of excited states under the excitation of RCP (d) and LCP (e), respectively. Three important interaction times (corresponding to the π/2, π, and 2π) are indicated.

    Figure 5.Rabi oscillation obtained from Eqs. (6) and (7) with different Rabi splitting, ℏΩR = 161 meV (a) and ℏΩR = 100 meV (b). The other parameters are set to ℏΓq-BIC = 8 meV and ℏΓex = 90 meV, Δ = 0. Inset in (a): τ1 as a function of γex (red line), and τ2 as a function of ℏΩR (blue line). (c) Rabi oscillation with ℏΩR = 161 meV, ℏΓex = 45 meV, and ℏΓq-BIC = 8 meV. The evolution process of excited states under the excitation of RCP (d) and LCP (e), respectively. Three important interaction times (corresponding to the π/2, π, and 2π) are indicated.

    Based on Eqs. (9) and (10), one can see that the exponential decay time τ1 is only related to Γex in the case of a certain Γq-BIC, and the oscillation period τ2 is only related to ΩR. In order to clearly illustrate the relationship between them, a trend graph has been inserted in Fig. 5(a). As Γex decreases, τ1 increases, while τ2 becomes smaller as ΩR increases. As the results calculated in Fig. 4(d), the oscillator strength affects the rate of Rabi oscillations. For WSe2, the oscillator strengths generally take values above 0.6 or 0.7[14]. However, even in the case of f=0.3 (corresponding to a Rabi splitting of 100 meV), more than one oscillation period can still exist with the same decay time as in Fig. 5(a), which again shows the robustness of our system [Fig. 5(b)]. The coherent energy exchange efficiency can be obtained from the evolution of time-domain exchange oscillations[51]. The maximum energy transfer efficiency at time τ2/2 is about 40% [Fig. 5(a)], which is significantly affected by the splitting width [Fig. 5(b)] and damping [Fig. 5(c)]. More importantly, since the exciton loss is much larger than that of the uncoupled q-BIC mode, the lifetime of the coherent state is mainly limited by the exciton loss. Figure 5(c) gives the oscillation curves for ΩR=161meV and Γex=45meV, clearly showing that the decay time can be extended if excitons with smaller loss are employed.

    Unlike the weak coupling regime of irreversible emission, strong coupling is a reversible process that can be used to transfer quantum information between excitons and photons in a coherent manner[52]. In other words, strong coupling between excitons and localized photonic modes provides a more effective link between propagating qubits encoded in the light and the stationary qubits encoded in the emitters, and the exchange of photons between emitters can also lead to photon-mediated interactions between them, which can be harnessed for building two-qubit entangling gates or serve as a basis of new analog quantum simulators[53]. Due to the large intrinsic chirality of the structure, we propose a new coherent state control method, which is expected to provide a new solution for the development of room-temperature quantum logic devices. As shown in Fig. 5(d), the system is in the strong coupling regime under RCP excitation. At the initial moment, the exciton is prepared to the excited state, and when ΩRt=π, the final state reads |c,n+1. The system has undergone an evolutionary process from the initial state |e,n to the entangled state 12(|e,n+|c,n+1) and then to the final state |c,n+1, and the exchange between quantum states has been realized. By changing the circular polarization of the excitation light to LCP, the system can be taken out of the strong coupling regime. In this case, the exciton emission process is irreversible, and the exchange of quantum states cannot be read [Fig. 5(e)], but only the decay of the excited states. This chiral response of coherent states provides a new approach for the design of quantum logic devices, which can be manipulated by the circular polarization of excitation light.

    Then, we simulated another system consisting of a monolayer WSe2 under the q-BIC array, as shown in Fig. 6(a). Figure 6(b) shows transmittance difference spectra of the hybrid structure depending on the Px, and anticrossing LP and UP are obtained. However, after fitting it to the results of the calculations of Eq. (4), the Rabi splitting ΩR=36.5  meV<(Γq-BIC+Γex)/2=49  meV was obtained, suggesting that the criterion for strong coupling is not satisfied. In a more detailed discussion of strong coupling, the system belongs to the intermediate strong coupling regime, where the level splitting occurs but the spectral Rabi splitting can be seen in the absorption only from the quantum emitters’ channel[54]. The poor coincidence between the optical modes of the cavity and the exciton position of monolayer WSe2 may be the reason for the weaker coupling. Additionally, the coupling strength also decreases when light–matter interaction occurs only via the evanescent fields around the BIC resonators[6]. This result also proves the superiority of the self-hybrid strong coupling system proposed above.

    (a) Schematic of the coupled system with a WSe2 monolayer on the bottom of the array of silicon pillars; (b) transmission spectra of the hybrid system with Px varying from 462.5 to 472.5 nm. (c) Simulation results (symbols) of the anticrossing dispersion relationship extracted from (b); red and blue dots represent the UP and LP, and the corresponding lines are theoretical fitting results. (d) Schematic of the coupled system with perovskite pillars array; (e) transmission spectra of the hybrid system with Px varying from 325 to 365 nm. (f) Simulation results (symbols) of the anticrossing dispersion relationship extracted from (e); red and blue dots represent the UP and LP, and the corresponding lines are theoretical fitting results.

    Figure 6.(a) Schematic of the coupled system with a WSe2 monolayer on the bottom of the array of silicon pillars; (b) transmission spectra of the hybrid system with Px varying from 462.5 to 472.5 nm. (c) Simulation results (symbols) of the anticrossing dispersion relationship extracted from (b); red and blue dots represent the UP and LP, and the corresponding lines are theoretical fitting results. (d) Schematic of the coupled system with perovskite pillars array; (e) transmission spectra of the hybrid system with Px varying from 325 to 365 nm. (f) Simulation results (symbols) of the anticrossing dispersion relationship extracted from (e); red and blue dots represent the UP and LP, and the corresponding lines are theoretical fitting results.

    To demonstrate the universality of our strong coupling system, we calculated the case when replacing the exciton material of the self-hybrid system with perovskite, as shown in Fig. 6(d). Here, we use phenethylammonium lead iodide (PEPI) perovskite with the chemical formula (C6H5C2H4NH3)2PbI4 as an example. Its parameters are derived from Ref. [55] and include a linewidth of 30 meV and an exciton energy of 2.394 eV. The simulation [Fig. 6(e)] and fitting results [Fig. 6(f)] show that the Rabi splitting ΩR reaches 165 meV, suggesting that the criterion for strong coupling is satisfied. It should be noted that the dispersion curve of LP gradually becomes unclear in the simulation, which is similar to the results of strong coupling systems with q-BIC cavities in previous reports[7,56]. The results presented above demonstrate that even though the material constituting the pillars is replaced with perovskite, the strong coupling system proposed can still achieve the desired performance. Nevertheless, while perovskites have been successfully fabricated into simple structures with relatively large sizes, such as one-dimensional gratings[57] and waveguides[58], the fabrication of fine micro-nano structures remains a challenge. In contrast, 2D materials have been demonstrated to fabricate fine micro-nano structures as small as 90 nm[6]. Given the size limitations, the relatively mature process makes WSe2 a more suitable candidate for our self-hybrid strong coupling system. The difficulty in fabricating this structure is that the height of the two pillars is different, but similar structures can already be fabricated using the multistep nanofabrication approach[59] or G-EBL technology[60]. Therefore, there is reason to believe that the self-hybrid strong coupling system proposed in this paper can be fabricated by a well-designed process.

    In recent years, we have noted that the TMDCs sustain valley excitons that can also have chiral responses in a cryogenic environment[61]. In contrast, the chirality in our system is derived from the structure’s response to incident light with different circular polarizations, rather than the valley polarization of the 2D material. Therefore, there are no restrictions on temperature or the layer number of 2D material in our solution if one wants to realize the function of control quantum states by excitation polarizations. Also, as mentioned in Fig. 3, our system enables a new method to remove the influence of an uncoupled exciton on the observed spectra by subtracting transmission spectra under different polarized excitations. Such function should be enabled by a large CD response, which cannot be reached by weak chirality strong coupling systems. Furthermore, even comparing with the reported room-temperature chiral strong coupling systems based on excitonic molecules[62,63], the value of γcav/2+γex/2 ranges from 170 to 220 meV, while the value in our system is only 49 meV. This fact means that our system has a longer state lifetime at ambient temperature and can support more oscillation periods during the decay time. The ultrafast oscillation period and extended polariton state lifetime indicate that our system has great potential for exploring future ultrafast integrated logic circuits at room temperature.

    4. Conclusion

    In conclusion, we have theoretically investigated the strong coupling between the WSe2 excitons and chiral q-BIC mode supported by WSe2 metasurfaces. The q-BIC mode can exhibit large EF enhancements over 80 times together with mode loss smaller than 10 meV, which is an important feature for enhancing light–matter interactions. By tuning the structural parameters, we obtained the anticrossing behavior, which is a typical feature of strong coupling between WSe2 exctions and the q-BIC mode. The Rabi splitting energy up to 161 meV is observed in the transmission spectra of the hybrid structure. More importantly, due to the intrinsic large chirality of metasurfaces (CD value as high as 0.985), we theoretically demonstrate that the generation of coherent quantum states can be effectively controlled by the circular polarization of excitation, and the function of purifying Rabi splitting spectra in this chiral q-BIC metasurfaces. Furthermore, a new coherent state control method has been proposed based on the large intrinsic chirality of the structure, which is expected to provide a new solution for the development of room-temperature quantum logic devices. Our study about the chiral q-BIC metasurfaces built by the excitonic van der Waals material of WSe2 can not only deepen the understanding of the mechanism of strong coupling, but also pave the way toward future exciton–polariton devices with more controllable dimensions.

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    Zhonghong Shi, Houjiao Zhang, Zhang-Kai Zhou, "Strong light–matter coupling between excitons and chiral quasi-bound states in the continuum in van der Waals metasurfaces," Chin. Opt. Lett. 22, 103602 (2024)

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    Paper Information

    Category: Nanophotonics, Metamaterials, and Plasmonics

    Received: Mar. 20, 2024

    Accepted: May. 15, 2024

    Published Online: Oct. 12, 2024

    The Author Email: Zhang-Kai Zhou (zhouzhk@mail.sysu.edu.cn)

    DOI:10.3788/COL202422.103602

    CSTR:32184.14.COL202422.103602

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