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Degree of electron-nuclear entanglement in the E x e Jahn-Teller system

Marie Ericsson, Erik Sjöqvist, Osvaldo Goscinski

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

Jahn-Teller systems exhibit strong coupling between the electronic and nuclear degrees of freedom. We analyse how linear and quadratic coupling affect the electron-nuclear entanglement in the $E\otimes \epsilon$ system. A measure of quantum entanglement, recently developed by Shimony [Ann. New York Acad. Sci. 755, 675 (1995)], is used. States in the adiabatic regime with quadratic coupling are analysed. The electron-nuclear entanglement in vibronic states of the linear Exe model is calculated numerically. The physical significance of electron-nuclear entanglement is discussed in terms of reduction factors and magnetic vibrational circular dichroism.

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Jahn-Teller systems exhibit strong coupling between the electronic and nuclear degrees of freedom. We analyse how linear and quadratic coupling affect the electron-nuclear entanglement in the E⊗ϵE\otimes \epsilonE⊗ϵ system. A measure of quantum entanglement, recently developed by Shimony [Ann. New York Acad. Sci. 755, 675 (1995)], is used. States in the adiabatic regime with quadratic coupling are analysed. The electron-nuclear entanglement in vibronic states of the linear Exe model is calculated numerically. The physical significance of electron-nuclear entanglement is discussed in terms of reduction factors and magnetic vibrational circular dichroism.
The degree of electron–nuclear entanglement in molecular states is analyzed. This entanglement has, generally, two sources: delocalization of the electronic and nuclear wave functions and vibronic coupling. For a diatomic molecular ground-state with a single potential energy minimum, it is demonstrated that the entanglement is a function of the product of the vibrational energy and the Born–Huang potential energy correction evaluated at the minimum. In the case of a double-well potential energy surface, the deviation from maximal entanglement is determined by the overlap of the electronic and nuclear wave functions evaluated at and around the two minima. The adiabatic states of the E⊗ϵ Jahn–Teller model are shown to be maximally entangled and a relation between the degree of entanglement and Ham's reduction factor for this model is derived. Numerical calculations in the E⊗ϵ model demonstrate a nontrivial relation between entanglement and vibronic coupling. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 526–533, 2000
Abstract We explore quantum correlations, in particular, quantum entanglement, among vibrational phonon modes as well as between electronic and vibrational degrees of freedom in molecular systems, described by Jahn-Teller mechanism. Specifically, to isolate and simplify the phonon- electron interactions in a complex molecular system, the basis of our discussions is taken to be the proposal of simulating two-frequency Jahn- Teller systems using superconducting circuit quantum electrodynamics systems (circuit QED) by Tekin Dereli and co-workers in 2012. We evaluate the quantum correlations, in particular entanglement between the vibrational phonon modes, and present analytical explanations using a single privileged Jahn-Teller mode picture. Furthermore, spin-orbit entanglement or quantum correlations between electronic and vibrational degrees of freedom are examined. We conclude by discussing experimental feasibility to detect such quantum correlations, considering the dephasing and decoherence in state-of-the-art superconducting two-level systems (qubits).
We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The $E\ensuremath{\bigotimes}\ensuremath{\beta}$ system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the $E\ensuremath{\bigotimes}\ensuremath{\epsilon}$ models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the $E\ensuremath{\bigotimes}\ensuremath{\beta}$ system, the ground states of the $E\ensuremath{\bigotimes}\ensuremath{\epsilon}$ model always exhibit entanglement. For the $E\ensuremath{\bigotimes}\ensuremath{\beta}$ case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the $E\ensuremath{\bigotimes}\ensuremath{\epsilon}$ case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.
We discuss the ground state entanglement of the E⊗ϵE\otimes\epsilonE⊗ϵ Jahn-Teller model in the presence of a strong transverse magnetic field as a function of the vibronic coupling strength. A complete characterization is given of the phenomenon of entanglement sharing in a system composed by a qubit coupled to two bosonic modes. Using the residual III-tangle, we find that three-partite entanglement is significantly present in the system in the parameter region near the bifurcation point of the corresponding classical model.
We discuss the ground state entanglement of the $E\ensuremath{\bigotimes}ϵ$ Jahn-Teller model in the presence of a strong transverse magnetic field as a function of the vibronic coupling strength. A complete characterization is given of the phenomenon of entanglement sharing in a system composed by a qubit coupled to two bosonic modes. Using the residual III tangle, we find that three-partite entanglement is significantly present in the system in the parameter region near the bifurcation point of the corresponding classical model.
Abstract We study the linear E ⊗ ε Jahn–Teller effect in which a doubly degenerate fermionic (electron) level is coupled to a pair of degenerate oscillators. Because of the relative simplicity of the model, and since a complete numerical solution has been known for a long time, theorists have had at their disposal an excellent proving ground for a variety of calculational efforts. Here we apply the recently developed canonical sequence method (CSM) of Šamaj et al. J Phys 1997, A30, 1741 to investigate the ground state of this system. Comparisons are then made with other calculation schemes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005