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

Abstract

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 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 × N v and 3 × 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 × N v case), taking as an example a coupling between the a 3 Σ + 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 × 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 Σ + u (6s, 6s), 0 − g (6s, 6p 3/2 ), and 0 − g (6s, 5d) electronic states, which are coupled by a non-adiabatic radial coupling and a sequence of chirped laser pulses.

Measures of electronic-vibrational entanglement and quantum coherence in a molecular system

“…We consider the entanglement between electronic and vibrational degrees of freedom created by vibronic couplings in a diatomic molecule described in the Born-Oppenheimer (BO) approximation [19]. Neglecting the rotational degree of freedom, we focus on a pure entangled stateρ 2 el,vib =ρ el,vib of the Hilbert space H=H el H vib :…”

Non-Markovian dynamics of the electronic subsystem in a laser-driven molecule: Characterization and connections with electronic-vibrational entanglement and electronic coherence

“…Therefore, it appears that the non-Markovian character of the dynamics is strengthened when the transfer of population between the two electronic channels is such as the larger population decreases (i.e., the smaller electronic population increases). This condition, describing an evolution oriented to the equalization of the electronic populations, is in fact a condition indicating the increase of the electronic-vibrational entanglement, which becomes maximum when the electronic populations are equal [58]. This observation will be developed in the following sections.…”

“…We begin by describing the theoretical model of a diatomic molecule driven by a coupling between electronic states, such that several electronic states could be populated. The intramolecular dynamics of such a molecule is characterized by electronic-vibrational entanglement and electronic coherence [58,59]. Subsequently, we will deduce the canonical form of the master equation for a 2-dimensional electronic subsystem, building the non-Markovianity measures from the canonical decoherence rates.…”

“…A detailed description of the molecular model can be found in previous papers [58,59], where we have analyzed entanglement and coherence of pure states |Ψ el,vib (t) > created by laser pulses. The molecular state |Ψ el,vib (t) > has the form…”

“…ρ el (t) describes an electronic subsystem which is entangled with the vibrational environment [58]. For N el populated states, the linear entropy L(t) = 1 − Tr el (ρ 2 el (t)) of the electronic-vibrational entanglement has the expression [59]:…”