We show how atomic coherence can lead to entanglement between two thermal fields at a temperature T. We first show that the passage of a three-level atom in V configuration without coherence cannot create entanglement. However, if the excited states are driven by a microwave field, the resulting atomic coherence can lead to entanglement between the thermal fields. We show that, no matter how high the temperature of the fields is, the thermal fields can always be entangled in the presence of atomic coherence.Atomic coherence ͓1͔, which results from a coherent superposition of different states of a single atom, can lead to many different quantum optical phenomena. These include correlated spontaneous emission laser ͓2͔, lasing without inversion ͓3͔, electromagnetically induced transparence ͓4͔ and spontaneous emission cancellation ͓5͔. Atomic coherence has recently been shown to play a key role in quantum thermodynamics. For example, Scully et al. showed that mechanical work may be extracted from a single heat bath via vanishing atomic coherence ͓6͔.Another feature of quantum systems is entanglement that refers to quantum correlation among subsystems that share a common quantum state. Quantum entanglement plays an essential role in quantum information processing such as quantum computation ͓7͔, quantum teleportation ͓8͔, and quantum cryptography ͓9͔.In this paper we discuss an important application where atomic coherence plays a crucial role in creating entanglement between two modes of the electromagnetic field inside a doubly resonant cavity at temperature T, which are coupled to two transitions of an atom in V configuration. The two important concepts, entanglement and atomic coherence, are shown to be closely related.In earlier studies on the interaction of thermal fields with the atomic systems, it has been shown that atom-field ͓10͔ and atom-atom ͓11͔ entanglement can be generated in such systems. In these studies, at least, one subsystem is initially in a pure state. The entanglement appears only when the atom and the field are not in thermal equilibrium. Here we show that atomic coherence is the unique resource of creating entanglement between two cavity modes in thermal state even at arbitrarily high temperature.The model under consideration is shown in Fig. 1. We consider the interaction of an atom in the V configuration with the fields inside a cavity at temperature T. Here we assume that the transitions between the upper levels ͉a͘ and ͉b͘ to the ground state ͉c͘ are dipole allowed and these transitions are coupled resonantly with the modes inside the cavity. The transition between the upper levels ͉a͘ and ͉b͘ is dipole forbidden, while the coherence between level ͉a͘ and level ͉b͘ could be created by applying a classical magnetic field between these two levels. The interaction picture Hamiltonian of the system is given bywhere â 1 ͑â 1 † ͒ and â 2 ͑â 2 † ͒ are the annihilation ͑creation͒ operators for the two cavity modes and g 1,2 are coupling constants of the atom with the fields.We consider the init...
