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In this work we analytically investigate the ionization of an atomic system in a quantum electromagnetic field. A new theoretical approach based on the eigenstates of a free electron in a quantized electromagnetic field is developed. Squeezed vacuum state and coherent state of light are considered and special features of ionization in squeezed light are established. Analytical expressions for the ionization rate for various multiphoton channels are found and the angular distribution of the electron emission during ionization is analyzed.