Persistent entanglement of valley exciton qubits in transition metal dichalcogenides integrated into a bimodal optical cavity

We report dissipative dynamics of two valley excitons residing in the $K$ and ${K}^{\ensuremath{'}}$ valleys of a bare ${\mathrm{WSe}}_{2}$ monolayer and the one being integrated into a bimodal optical cavity. In the former, only when the exciton-field detunings in the $K$ and ${K}^{\ensuremath{'}}$ valleys are rigorously equal (resonant detuning) can partially entangled stationary states be created. Otherwise, the concurrence of exciton qubits turns to zero. Remarkably, in the latter (the ${\mathrm{WSe}}_{2}$ monolayer in a bimodal optical cavity), the transfers of entanglement from one subsystem (exciton/light) to the other (light/exciton) take place. Hence a finite stationary concurrence of exciton qubits is always generated, independent of whether the exciton-field detuning in two valleys is resonant or nonresonant. In addition, it can even reach as high as 1 (maximally entangled state of two valley excitons). Since there no real system which has a strictly resonant detuning, an immersion of the ${\mathrm{WSe}}_{2}$ monolayer in a bimodal optical cavity provides an opportunity to overcome the challenge facing by the bare ${\mathrm{WSe}}_{2}$, opening a novel realm of potential qubits.