The paper discusses the creation of synthetic magnetic fields for ultracold neutral atoms using a spatially-dependent optical coupling between internal states of the atoms, which generates a Berry's phase. This approach circumvents the limitations of rotating systems, such as technical issues with maximum rotation velocity and metastability, and allows for the creation of large synthetic magnetic fields. The authors demonstrate the synthesis of a magnetic field by observing the appearance of vortices in a Bose-Einstein condensate (BEC) of $^{87}$Rb atoms. The synthetic magnetic field is engineered by dressing the atoms with an optical field that couples different spin states, creating a Hamiltonian with a spatially-dependent vector potential. The synthetic magnetic field is uniform near the center of the BEC and varies with the detuning gradient. The study shows that the system can reach the quantum Hall regime, potentially enabling the exploration of topological quantum computation. The paper also includes experimental details on the preparation of the dressed state and numerical simulations to verify the results.The paper discusses the creation of synthetic magnetic fields for ultracold neutral atoms using a spatially-dependent optical coupling between internal states of the atoms, which generates a Berry's phase. This approach circumvents the limitations of rotating systems, such as technical issues with maximum rotation velocity and metastability, and allows for the creation of large synthetic magnetic fields. The authors demonstrate the synthesis of a magnetic field by observing the appearance of vortices in a Bose-Einstein condensate (BEC) of $^{87}$Rb atoms. The synthetic magnetic field is engineered by dressing the atoms with an optical field that couples different spin states, creating a Hamiltonian with a spatially-dependent vector potential. The synthetic magnetic field is uniform near the center of the BEC and varies with the detuning gradient. The study shows that the system can reach the quantum Hall regime, potentially enabling the exploration of topological quantum computation. The paper also includes experimental details on the preparation of the dressed state and numerical simulations to verify the results.