Quadrupolar and Dipolar Excitons in Bilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mi>H</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mrow><mml:mi>MoSe</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We report the experimental observation of quadrupolar exciton states in the reflectance contrast spectrum of 2H-stacked bilayer MoSe_{2}. The application of a vertical electric field results in a quadratic energy redshift of these quadrupolar excitons, in contrast to the linear energy splitting observed in the coexisting dipolar excitons within the bilayer MoSe_{2}. We perform helicity-resolved reflectance contrast measurements to investigate the spin and valley configurations of the quadrupolar exciton states as a function of applied vertical electric and magnetic fields. Comparing our results with a phenomenological coupled-oscillator model indicates that the electric- and magnetic-field dependence of the quadrupolar exciton states can be attributed to the intra- and intervalley hybridization of spin-triplet interlayer excitons with opposite permanent dipole moments, mediated by interlayer hole tunneling. These results position naturally stacked MoSe_{2} bilayers as a promising platform to explore electric-field-tunable many-body exciton phenomena.