Infinite volume and atoms at the bottom of the spectrum

Let $G$ be a higher rank simple real algebraic group, or more generally, any semisimple real algebraic group with no rank one factors and $X$ the associated Riemannian symmetric space. For any Zariski dense discrete subgroup $\mathrm{\Gamma }<G$, we prove that $\mathrm{Vol}(\mathrm{\Gamma }\mathrm{\backslash }X)=\mathrm{\infty }$ if and only if no positive Laplace eigenfunction belongs to $L^2(\mathrm{\Gamma }\mathrm{\backslash }X)$, or equivalently, the bottom of the $L^2$-spectrum is not an atom of the spectral measure of the negative Laplacian. This contrasts with the rank one situation where the square-integrability of the base eigenfunction is determined by the size of the critical exponent relative to the volume entropy of $X$.