Vacuum-induced atomic grating

Atom-field interactions, induced by the vacuum of the electromagnetic field, exhibit a variety of fundamental phenomena and effects. In this paper, we study the electromagnetically induced atomic grating due to the vacuum state of the radiation field. Using an ensemble of cold atoms, strongly coupled to an optical cavity, we show that a probe field, propagating through the atomic medium, diffracts to zeroth and first-order diffraction peaks with few photons and even by the electromagnetic vacuum field of the cavity mode. As the number of photons in the cavity increases, the intensity of the first-order diffraction peak initially rises and then exhibits a decreasing trend. Furthermore, we observe that the first-order peak intensity reaches its maximum at resonance for both the vacuum and single-photon cavity state. However, as the number of photons increases further, this peak at resonance transforms into a dip, accompanied by two side peaks at off-resonance positions. This transition from a peak to a dip may potentially be used to distinguish the quantum state of the cavity.