Spontaneous emission is a fundamental process describing the radiative decay of excited states. From a quantum electrodynamics viewpoint, it is triggered by vacuum fluctuation [1–4]. In order to tailor the spontaneous emission behavior, we need precise control of the electromagnetic (EM) density of states surrounding the emitters [5]. Following the groundbreaking works of E. M. Purcell [6], controlling the spontaneous emission rate using a cavity that confines discrete modes has been widely demonstrated from atomic to low-dimensional solid-state systems [7–11]. Recently, there has been significant research into two-dimensional semiconductors composed of transition metal dichalcogenides (TMDCs) due to their strong light-matter interactions and unique valleytronic properties [12]. The optical properties of these atomically thin TMDC layers are governed by excitons with binding energy up to few hundred meV [13–15]. The outstanding optical properties of TMDCs render them ideal candidates for photonic applications and for investigations of solid-state cavity quantum electrodynamics [16].

The weak van der Waals interactions allow heterostructure fabrication with high versatility [17]. When the stacked TMDC heterobilayers (HBLs) have a type-II band alignment, optical excitation of an individual monolayer results in layer-separated carriers and interlayer excitons (iX) with permanent electric dipole moments (∼0.5nm·e) [18–21]. iX have orders of magnitude longer lifetime of T1 ∼ few ns [22] as compared to their intralayer counterparts featuring T1 ∼ few ps [23]. The radiative recombination of iX is furthermore influenced by the twist-angle-dependent momentum space alignment between the K valleys of individual layers [24] [Fig. 1(d) inset].

Besides varying the twist-angle, the ability to gain in situ optical tunability on the excitonic dynamics is important for practical photonic applications. Recent research advances show the emerging spatial coherence and lasing phenomena of moiré iX on grating [25] and nanophotonic cavities [26,27]. The sharp emission of iX should be precisely aligned with the resonances of the underlying resonators, because the lasing threshold can be compromised in off-resonance conditions [26]. However, in reality, the moiré reconstruction [28] and inhomogeneity introduced during sample fabrication randomly shift the iX resonance away from the designed photonic energy landscape, lowering the reproducibility of high-performance devices. The cavity-iX energy detuning can be controlled via the excitonic Zeeman effect [26], while the detuning range relies on a high external magnetic field. The encapsulation with hexagonal boron nitride helps to reduce inhomogeneity [29–31], but it may reduce the spatial overlap of the iX from the EM field maxima, mitigating the cavity enhancement. A broader detuning functionality has been lacking in the above-mentioned cavity structures. In this study, we demonstrate the advantages of using a low-temperature open optical microcavity to have a much broader detuning range and robust in situ control of the iX dynamics in the weak coupling regime. Together with a thorough theoretical analysis of the cavity, our approach simultaneously provides valuable insights into more fundamental optical properties, including a free-space lifetime of 0.5 ns and an ultra-high quantum efficiency exceeding 80%. The powerful in situ tunability of our cavity can be applied to even more complex van der Waals heterostructures and devices with electronic contacts to realize more functionalities [32,33].

The schematic of the cryogenic open microcavity is shown in Fig. 1(a). Our sample is a θ=1°±1°-twisted MoSe2-WSe2 HBL deposited on a dielectric Bragg reflector (DBR) [see Fig. 1(c)]. It contains 10.5 pairs of alternating SiO2/Si3N4, resulting in a stop band centered at 940 nm. The top mirror is a 45 nm gold-layer-coated silica mesa [Fig. 1(b)]. The surface of the mesa was pre-manufactured by a focused ion beam of Ga+ to produce hemispheric lens structures. A microscope window is also etched through the gold layer, enabling us to locate the HBL on the DBR. Indeed, as we discuss later, even this window area forms an effective cavity of a low Q-factor. We can tune the cavity length by moving the top mirror vertically via a piezo-based nano-positioner. A maximum of 60 V DC voltage can be applied to the actuator to achieve a detuning length up to 1 μm with a sub-nm positioning resolution. The cavity is loaded in a dry closed-cycle cryostat (3.5 K base temperature) [34]. More details of the cavity fabrication can be found in Appendix A.2.

Photoluminescence (PL) measurements are all carried out by 750 nm laser pulses (3 ps) from a mode-locked Ti:sapphire laser with a power of 5 μW, two orders of magnitude smaller than the saturation power. The wavelength was chosen to generate iX efficiently, since it is nearly resonant with the MoSe2 intralayer exciton. Figure 1(d) compares the iX PL emissions collected through the window and a gold-coated 6 μm lens. The PL measured from the window area manifests the explicit nature of iX in our sample. The emission energy is lower than the excitonic resonances in monolayers, since it arises from the radiative recombination of the HBL’s direct band gap consisting of a valence band maximum of WSe2 and conduction band minimum of MoSe2. Moreover, due to the moiré reconstruction for heterostructures with small twist angles (θ<3°) and inhomogeneity [28], the iX PL is as wide as 140 nm. We note that the excitonic ground state in our R-type sample is the spin-singlet iX [31,35] and predominates the emission spectra [26,28,36,37]. In the band alignment inset of Fig. 1(d), the higher conduction band in MoSe2 composing spin-triplet iX is thus not shown. In contrast to this intrinsic iX spectral profile, the lens modes are more distinctive. The formation of localized Tamm-plasmon resonances in the DBR-vacuum-metal cavity yields discretized (s,p,d,f) transverse lens modes with Q-factors ∼400.

Our first experimental strategy towards in situ control of the excitonic radiation dynamics is based on the effect that even the transparent glass window in the top segment can form a resonant heterostructure. Although the cavity is very lossy (Q-factor ∼24), the local EM field density on the DBR surface can be periodically tuned to influence the iX emission in the weak coupling regime [Fig. 2(d)]. In similar configurations, the methodology to modify the emission dynamics by placing a dipole in the proximity of a dielectric interface was first discussed by Drexhage [38]. It was later applied to quantify the spontaneous emission dynamics of quantum dots [39–41], excitons in TMDC monolayers [23,42–44], and defects in hBN crystals [45]. However, thus far it has been sparsely implemented in a manner that allows for convenient in situ tuning of the dielectric interface, which here enables us to explore exactly the same emitter ensemble throughout the entire study. Figure 2(a) shows the stacked PL spectra of iX collected through the glass window versus the cavity detuning. The enhanced emission around 890 nm corresponds to two longitudinal modes tuned through the iX PL emission. The 51st and 52nd mode numbers and the effective cavity lengths (right axis) are then determined by using L=qλq/2=(q+1)λq+1/2, where λq(q+1) are the wavelengths of two adjacent longitudinal modes at the same cavity length.

We perform time-resolved photoluminescence (TRPL) measurements on the iX emission with an avalanche photodiode at different cavity detunings. Figure 2(b) shows several TRPL spectra between 40 V and 60 V, which display an acceleration of the iX decay process. We note that the TRPL traces of iX cannot be fitted by a mono-exponential function to account for a single radiative decay channel. We thus resort to a bi-exponential decay function of I(t)=Ae−t/τ1+Be−t/τ2 to minimize the fitting residual of the TRPL traces measured under different detunings (see details in Appendix A.3). We tentatively assign the slower decay process (τ1) to a non-radiative channel that is supposed to remain unaffected by the presence of a cavity resonance, and the faster decay (τ2) related to the radiative recombination of iX that can be influenced by the cavity. Indeed, an invariable slower decay process of τ1=12ns yields rational results (see Appendix A.6), while τ2 oscillates with a period of 40 V in Fig. 2(c), matching with the periodic cavity tuning of the PL intensity in Fig. 2(a). The PL maxima correspond to the anti-nodes in the lifetime measurements. A sinusoidal fit of the oscillation yields τ2=2.2ns, with a varying amplitude up to 220 ps.

The TRPL results are perfectly consistent with previous low-temperature dynamics measurements on a nearly identical HBL structure (θ=1°±0.3°), where a bi-exponential fit resulted in a similar faster (slower) decay time of 1.3 ns (∼15ns) [24]. The shorter decay processes were then verified to originate from the radiative recombination of bright iX, while the longer decay was attributed to the momentum indirect dark iX [24,36]. More straightforward evidence of the longer decay being a non-radiative process was provided in a former report by Rivera et al. [46], where only the shorter decay process depends on the highly anisotropic Purcell factors of the TE-TM modes from a photonic cavity. We neglect the contribution of spin-triplet iX to the dynamics, because the ground state in R-stacked HBL is spin-singlet iX [47], which dominates the emission with [28,36] or without [48] moiré confinement. We also do not consider the radiative recombination of dark iX since it is a second order process that needs to overcome the momentum mismatch at elevated temperatures. The constant τ1 discovered in our experiments can be explained by the weak cavity influence on the dark iX because they barely couple to light [46]. We can thus assign the slower decay process to a general long-lived non-radiative decay channel related to the momentum indirect dark iX. We discuss below that the decay time (τ2) of bright iX contains both radiative and non-radiative components. Results on an HBL of larger twist-angle are in Appendix A.3, with clear prolonged iX dynamics.

In the following, we calculate the free-space lifetime τ0 and quantum efficiency (QE) of iX. The long cavity length up to 23 μm can strongly constrain the EM modes distribution inside the cavity. This is demonstrated by the finite-difference time-domain simulations (FDTD Solutions, Lumerical). The schematic of the modelling box is shown in the left inset of Fig. 2(e). We note that in contrast to the out-of-plane electric dipole moment due to the layer separation of iX, the nature of their optical dipole moments was actually determined as 99% in-plane [26,49], so that the in-plane radiative dipole in our simulation geometry is sufficiently valid. Figure 2(e) and the right inset show the simulation of the angle- as well as the k-dependent intensity distribution of the cavity modes. The entire EM field intensity is dominated by a peak feature that can be perfectly fit by a Gaussian function. We account for this emission redistribution in the next modelling works and discard the weak intensities at the high-angle flanks, which means only the iX with center-of-mass wavevectors within the Gaussian profile can couple substantially to the cavity.

The total decay rate for emitters embedded in a cavity reads Γtot(r,ω0)=FPΓ0+Γnr, where Γ0 and Γnr are the free-space and non-radiative decay rates, respectively. The emission rate modification factor, i.e., the Purcell factor FP, is the ratio between the cavity-mediated emission rate and the free-space emission rate of iX. FP is derived as FP=3n38nfree∑σ,τ∫0π/2dθsin(θ)|uθσ,τ(z)·e∥|2FM(θ).(1)

The detailed theoretical derivations of Eq. (1) are in Appendices B and C. In short, the mode functions uθσ,τ(z) are calculated with a transfer matrix approach evaluated at the HBL position and then projected onto their in-plane component by e||. The sum runs over two polarizations σ and two propagation directions τ through the cavity structure, and we integrate over all emission angles. FM(θ) is the angular emission distribution calculated for a dipole on DBR. Since the distribution is predominated by a Gaussian-shaped feature, it is then approximated by a Gaussian function FM(θ)=e−θ2/2σ2/(2πσ) with an FWHM=4.5°, i.e., the cutoff from Fig. 2(e). Mediated by the mode functions uθσ,τ(z), the amplitude of FP changes alongside the cavity detuning, leading to the characteristic oscillations in Fig. 2(c). Hence, we can use Eq. (1) to unambiguously translate the variation of τ2 with the cavity length into a dependence of τ2 on FP.

We emphasize that our measurements do not show completely inhibited iX emission. This indicates a possible non-radiative decay channel that has a finite decay rate similar to the total decay rate mediated by the cavity, and it cannot be accurately disentangled from the bi-exponential fit. The total decay rate Γtot is thus taken as Γ2=1/τ2. The intercept of the total decay rate represents the hidden non-radiative decay rate where the emission is completely inhibited (FP=0), and the slope is actually the free-space radiative decay rate Γ0. Figure 2(f) shows the linear fit of the Γtot as a function of the derived FP, with the fitting parameters Γ0=2.025±0.162ns−1 and a second non-radiative decay rate Γnr(2)=0.376±0.006ns−1. We subsequently acquire the free-space lifetime τ0=1/Γ0=0.5±0.04ns and the decay time of the second non-radiative channel 1/Γnr(2)=2.66±0.04ns. The free-space lifetime is in excellent agreement with a former report using an electromodulation technique [50]. We notice that the 2.66 ns decay time of the second non-radiative channel is indeed close to the cavity-mediated total decay time τ2=2.2±0.11ns. So far, the newly discovered non-radiative channel is not likely due to the ultrafast charge tunneling (∼ps) as observed in a plasmonic nanocavity [51]. Its origin needs further investigation. After obtaining Γ0, the quantum efficiency of iX is then determined as 81.4%±1.4% using the formula QE=Γ0/(Γ0+Γnr(1)+Γnr(2)), where Γnr(1)=1/τ1 and Γnr(2) are rates of the two non-radiative decay channels. While Γnr(1) is obtained directly by fitting the slow component of the TRPL, Γnr(2) is deduced along with Γ0 from our transfer matrix approach to the fast TRPL component.

In order to fit the TRPL traces, an earlier work investigating H-stacked HBLs also considered three decay channels that were purely radiative processes from momentum direct bright and gray iX, and also phonon-assisted recombination of the spin-allowed momentum indirect iX [52]; the last one comprised a substantial weight of the TRPL data (lifetime up to hundreds of ns). In general, phonon-assisted recombination plays the major role in samples with larger twist angles (θ>2°) [24,36,53]. In contrast, our precisely aligned R-stacked sample (θ=1°) favors the radiative decay of the momentum direct iX whose lifetime is one to two orders of magnitude shorter than the momentum indirect ones [24,36]. The captured non-radiative processes enable us to extract the QE.

To further engineer the EM field distribution in our resonator, we resort to the integrated gold-coated hemispheric lens structures in the top segment. In conjunction with the bottom DBR that hosts the HBL, this leads to zero-dimensional localized Tamm-plasmon resonances. We then reduce the effective cavity length to approximately 5 μm and utilize a 6 μm lens. We implement the cavity detuning to scan the resonant Tamm-plasmon modes through the iX emission between 840 and 940 nm and observe clear variation of the PL intensities when optical resonances of the modes (Q-factors ∼400) are tuned through the iX emission profile [Fig. 3(a)]. To analyze the dynamics, we perform TRPL measurements by collecting emission in the spectral range of 870–890 nm.

Figure 3(b) shows three representative TRPL traces, collected for different cavity detunings. It is important to note that the resonant cavity mode for energies E2 and E3 is within the collection window, while E1 is outside the spectral window where iX dynamics are measured without the cavity effect. As the central result, we observe a significant slow-down of the iX emission in the case of the off-resonance condition at E1. More specifically, a bi-exponential fitting yields a constant τ1=18ns, and a varying τ2=7.3±0.3ns (E1), 3.2±0.03ns (E2), and 2.3±0.03ns (E3). Interestingly, the resonant decay time at E3 is in excellent agreement with the discussion in the previous section, and hints at only a weak on-resonance enhancement of the spontaneous emission, while the significant slow-down by a factor of 3.2 is unambiguous evidence of the inhibited radiative decay under off-resonance conditions.

To obtain a deeper understanding of the involved emission processes, we calculate the dynamics of a radiative dipole in confined Tamm-plasmon structure using FDTD simulations. The cavity is modeled according to the experimentally determined values for the DBR as well as the concave top mirror. A linearly polarized dipole emitter is placed on DBR and centered with respect to the top mirror. The dipole is surrounded by the HBL approximated by two dielectric slabs. Symmetric and anti-symmetric boundary conditions are applied to reduce the computational effort. Thus, only the anti-symmetric modes with respect to the dipole axis can be excited. The wavelength-dependent Purcell factor is retrieved from the power emitted by the dipole into the cavity [Fig. 3(b) inset]. We can verify the observed modest acceleration of the spontaneous emission with a Purcell factor of only one, while for the off-resonance spectral range it drops to a nearly constant value as low as 0.46, yielding the observed inhibition effect. The joint experiment-theory approach developed in our work allows us to do in situ dynamics tuning and unveil more fundamental parameters than former works [25–27,46,52]. A detailed parameter comparison of recent advances in tuning iX dynamics can be found in Table 1 (Appendix C).Table 1.

Comparison of the Current Advancement of Our Open Cavity with Other Resonator Structures in Tuning the iX Dynamics^a

Our approach of controlling the iX dynamics in van der Waals heterostructures is of great importance, both for future quantum optical studies and fundamental material related investigations. The periodic tuning of the spontaneous emission in widely tunable low-Q-factor cavities allows us to accurately extract the free-space exciton lifetime and QE of complex samples, proving itself as an ultimately powerful characterization approach. The ultra-high quantum efficiency proves the potential of MoSe2-WSe2 interlayer excitons for high-efficiency lasers and even quantum photonic applications of nonclassical light sources [54]. We expect that the engineering of the inhibition of radiation from moiré excitons in low-Q cavities is also a promising method to steer their thermalization and relaxation behavior. This approach of photonic engineering of excitons will have a profound impact on the transport and the dynamics of moiré excitons, and especially on their collective response [55], such as the capability to condense in coherent states.

Acknowledgment. The project is funded by Deutsche Forschungsgemeinschaft (DFG) in the framework of SPP 2244 and is also partially funded by the QuantERA II European Union’s Horizon 2020 research and innovation programme under the EQUAISE project. B.H. acknowledges Alexander von Humboldt-Stiftung for the fellowship grant and NFSC. M.S. and S.S. acknowledge funding from the Bundesministerium für Bildung und Forschung (BMBF) within the project tubLAN Q.0. M.E. acknowledges funding from the Carl von Ossietzky Universität Oldenburg through a Carl von Ossietzky Young Researchers’ Fellowship. F.E. acknowledges support by DFG SFB 1375 (NOA) and BMBF FKZs 16KISQ087K and 13XP5053A.