Inter-layer excitons (IXs) in hetero-bilayers of transition metal dichalcogenides (TMDs) represent an exciting emergent class of long-lived dipolar composite bosons in an atomically thin, near-ideal two-dimensional (2D) system. The long-range interactions that arise from the spatial separation of electrons and holes can give rise to novel quantum, as well as classical multi-particle correlation effects. Indeed, first indications of exciton condensation have been reported recently. In order to acquire a detailed understanding of the possible many-body effects, the fundamental interactions between individual IXs have to be studied. Here, we trap a tunable number of dipolar IXs (N_IX ~ 1–5) within a nanoscale confinement potential induced by placing a MoSe₂–WSe₂ hetero-bilayer (HBL) onto an array of SiO₂ nanopillars. We control the mean occupation of the IX trap via the optical excitation level and observe discrete sharp-line emission from different configurations of interacting IXs. The intensities of these features exhibit characteristic near linear, quadratic, cubic, quartic and quintic power dependencies, which allows us to identify them as different multiparticle configurations with N_IX ~ 1–5. We directly measure the hierarchy of dipolar and exchange interactions as N_IX increases. The interlayer biexciton (N_IX = 2) is found to be an emission doublet that is blue-shifted from the single exciton by ΔE = (8.4 ± 0.6) meV and split by 2J = (1.2 ± 0.5) meV. The blueshift is even more pronounced for triexcitons ((12.4 ± 0.4) meV), quadexcitons ((15.5 ± 0.6) meV) and quintexcitons ((18.2 ± 0.8) meV). These values are shown to be mutually consistent with numerical modelling of dipolar excitons confined to a harmonic trapping potential having a confinement lengthscale in the range \(\ell \approx 3\) nm. Our results contribute to the understanding of interactions between IXs in TMD hetero-bilayers at the discrete limit of only a few excitations and represent a key step towards exploring quantum correlations between IXs in TMD hetero-bilayers.

过渡金属二硫属化合物（TMDs）异质双层中的层间激子（IXs）代表了原子稀薄，近乎理想的二维（2D）系统中长寿命的偶极复合玻色子的令人兴奋的新兴类。由电子和空穴的空间分离引起的远距离相互作用可以产生新的量子以及经典的多粒子相关效应。实际上，最近已经报道了激子凝聚的最初迹象。为了获得对可能的多体效应的详细了解，必须研究各个IX之间的基本相互作用。在这里，我们陷阱可调数目偶极IXS的（Ñ _IX 通过将感应的纳米级限制潜在内〜1-5）一个摩西₂ -WSe ₂异质双层（HBL）形成SiO ₂纳米柱阵列。我们通过光学激发能级控制IX陷阱的平均占有率，并观察到来自相互作用IX的不同配置的离散尖锐线发射。这些特征的强度表现出接近线性，二次方，三次方，四次和五次方的幂相关性，这使我们能够将它们标识为N _{IX〜1–5的}不同多粒子配置 。随着N _IX的增加，我们直接测量偶极和交换相互作用的层次。发现层间双激子（N _IX  = 2）是发射双峰，从单激子蓝移了ΔE =（8.4±0.6）meV，并除以2 J  =（1.2±0.5）meV。对于三Exexcitons（（12.4±0.4）meV），Quadexcitons（（15.5±0.6）meV）和quintexcitons（（18.2±0.8）meV）的蓝移更为明显。这些值显示为与偶极激子的数值模型相互一致，偶极子激子的数值模型被限制在谐波俘获电势中，其限制长度标度在\（\ ell \大约3 \） nm范围内。我们的研究结果有助于理解TMD异质双分子层中IX之间相互作用的离散离散极限，并且仅是探索TMD异质双分子层中IX之间的量子相关性的关键一步。