Hybrid entanglement in a triple-quantum-dot shuttle device

We study the H-3xN hybrid entanglement between charge and vibrational modes in a triple-quantum-dot shuttle system. Three quantum dots are linearly connected, with the outer dots fixed and the central dot oscillating, described as a quantum harmonic oscillator with oscillation modes that are entangled with the electronic states of the quantum dots. The entangled states are characterized by the Schmidt number as a function of the parameters of the system: detuning and inverse tunneling length. We show that at steady state, as a function of detuning, the excited states of lower energy present Bell-type entanglement 2 x N, with the participation of two quantum dots, while the more energetic excited states present 3 x N entanglement, with the participation of three quantum dots. In the stationary regime, we find qualitative relationships between the maxima of the electronic current and the Schmidt number. Also, the time evolution of the degree of entanglement for a particular initial condition is studied in the presence of a time-dependent electric field and we evaluate the effects on entanglement of the condition of coherent destruction of tunneling.