Entanglement between electronic and vibrational degrees of freedom in a laser-driven molecular system

We investigate the entanglement between electronic and vibrational degrees of freedom produced by a vibronic coupling in a molecular system described in the Born-Oppenheimer approximation. Entanglement in a pure state of the Hilbert space H = H-el circle times H-vib is quantified using the von Neumann entropy of the reduced density matrix and the reduced linear entropy. Expressions for these entanglement measures are derived for the 2 x N-v and 3 x N-v cases of the bipartite entanglement, where 2 and 3 are the dimensions of the electronic Hilbert space H-el, and N-v is the dimension of H-vib. We study the entanglement dynamics for two electronic states coupled by a laser pulse (a 2 x N-v case), taking as an example a coupling between the a(3)Sigma(+)(u)(6s, 6s) and 1(g) (6s, 6p(3/2)) states of the Cs-2 molecule. The reduced linear entropy expression obtained for the 3 x N-v case is used to follow the entanglement evolution in a scheme proposed for the control of the vibronic dynamics in a Cs-2 cold molecule, implying the a(3)Sigma(+)(u)(6s, 6s), 0(g)(-)(6s, 6p(3/2)), and 0(g)(-)(6s, 5d) electronic states, which are coupled by a nonadiabatic radial coupling and a sequence of chirped laser pulses.