We theoretically study the conducting electronic contribution to the cohesive force in a metallic nanowire irradiated under a transversely polarized external electromagnetic field at low temperatures and in the ballistic regime. In the framework of the free-electron model, we have obtained a time-dependent two-level electronic wavefunction by means of a unitary transformation. Using a thermodynamic statistical approach with this wavefunction, we have calculated the cohesive force in the nanowire. We show that the cohesive force can be divided into two components, one of which is independent of the electromagnetic field (static component), which is consistent with the existing results in the literature. The magnitude of the other component is proportional to the electromagnetic field strength. This extra component of the cohesive force is originally from the coherent coupling between the two lateral energy levels of the wire and the electromagnetic field.
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