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 $\mathcal{H}$$=$$\mathcal{H}$${}_{el}$$⨂$$\mathcal{H}$${}_{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 $2\times N_v$ and $3\times N_v$ cases of the bipartite entanglement, where 2 and 3 are the dimensions of the electronic Hilbert space $\mathcal{H}$${}_{el}$, and $N_v$ is the dimension of $\mathcal{H}$${}_{vib}$. We study the entanglement dynamics for two electronic states coupled by a laser pulse (a $2\times N_v$ 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 $3\times N_v$ 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 non-adiabatic radial coupling and a sequence of chirped laser pulses.

30 pages, 8 figures

References in corpus (11)

• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• 'Designer atoms' for quantum metrology
• Essential entanglement for atomic and molecular physics
• Quantum entanglement between electronic and vibrational degrees of freedom in molecules
• Entanglement in helium
• Dynamical entanglement and chaos: the case of Rydberg molecules
• Tailoring many-body entanglement through local control
• The entanglement of few-particle systems when using the local-density approximation
• Molecular Feshbach dissociation as a source for motionally entangled atoms
• Efficient formation of strongly bound ultracold cesium molecules by photoassociation with tunneling
• Modeling and control of entanglement dynamics in laser cooling of trapped atoms

Cited by in corpus (3)

• Quantum phenomena in attosecond science
• Sub-femtosecond optical control of entangled states
• Non-Markovian dynamics of the electronic subsystem in a laser-driven molecule: Characterization and connections with electronic-vibrational entanglement and electronic coherence