  In this work, we implement a new method for imaging ultracold atoms with
subwavelength resolution capabilities and determine its regime of validity. It
uses the laser driven interaction between excited states to engineer hyperfine
ground state population transfer in a three-level system on scales much smaller
than the optical resolution. Subwavelength imaging of a quantum gas is atypical
in the sense that the measurement itself perturbs the dynamics of the system.
To avoid induced dynamics affecting the measurement, one usually measures
"rapidly" the wavefunction in a so-called strong imaging regime. We
experimentally illustrate this regime using a thermal gas ensemble, and
demonstrate subwavelength resolution in quantitative agreement with a fully
analytical model. Additionally, we show that, counter-intuitively, the opposite
weak imaging regime can also be exploited to reach subwavelength resolution. As
a proof of concept, we demonstrate that this regime is a robust solution to
select and spatially resolve a 30 nm wide wavefunction, which was created and
singled out from a tightly confined 1D optical lattice. Using a general
dissipation-included formalism, we derive validity criteria for both regimes.
The formalism is applicable to other subwavelength methods.
