  We introduce low regularity exponential-type integrators for nonlinear
Schr\"odinger equations for which first-order convergence only requires the
boundedness of one additional derivative of the solution. More precisely, we
will prove first-order convergence in $H^r$ for solutions in $H^{r+1}$
($r>d/2$) of the derived schemes. This allows us lower regularity assumptions
on the data in the energy space than for instance required for classical
splitting or exponential integration schemes. For one dimensional quadratic
Schr\"odinger equations we can even prove first-order convergence without any
loss of regularity. Numerical experiments underline the favorable error
behavior of the newly introduced exponential-type integrators for low
regularity solutions compared to classical splitting and exponential
integration schemes.
