Strongly bound excitons determine light-matter interactions in van der Waals heterostructures of two-dimensional semiconductors. Unlike fundamental particles, quasiparticles in condensed matter, such as excitons, can be tailored to alter their interactions and realize emergent quantum phases. Here, using a WS₂ /WSe₂ /WS₂ heterotrilayer, we create a quantum superposition of oppositely oriented dipolar excitons-a quadrupolar exciton-wherein an electron is layer-hybridized in WS₂ layers while the hole localizes in WSe₂ . In contrast to dipolar excitons, symmetric quadrupolar excitons only redshift in an out-of-plane electric field. At higher densities and a finite electric field, the nonlinear Stark shift of quadrupolar excitons becomes linear, signalling a transition to dipolar excitons resulting from exciton-exciton interactions, while at a vanishing electric field, the reduced exchange interaction suggests antiferroelectric correlations between dipolar excitons. Our results present van der Waals heterotrilayers as a field-tunable platform to engineer light-matter interactions and explore quantum phase transitions between spontaneously ordered many-exciton phases.