  Laser induced transitions between internal states of atoms have been playing
a fundamental role to manipulate atomic clouds for many decades. In absence of
interactions each atom behaves independently and their coherent quantum
dynamics is described by the Rabi model. Since the experimental observation of
Bose condensation in dilute gases, static and dynamical properties of
multicomponent quantum gases have been extensively investigated. Moreover, at
very low temperatures quantum fluctuations crucially affect the equation of
state of many-body systems. Here we study the effects of quantum fluctuations
on a Rabi-coupled two-component Bose gas of interacting alkali atoms. The
divergent zero-point energy of gapless and gapped elementary excitations of the
uniform system is properly regularized obtaining a meaningful analytical
expression for the beyond-mean-field equation of state. In the case of
attractive inter-particle interaction we show that the quantum pressure arising
from Gaussian fluctuations can prevent the collapse of the mixture with the
creation of a self-bound droplet. We characterize the droplet phase and
discover an energetic instability above a critical Rabi frequency provoking the
evaporation of the droplet. Finally, we suggest an experiment to observe such
quantum droplets using Rabi-coupled internal states of $^{39}$K atoms.
