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Laser Physics Letters

Tunneling current-induced entanglement between electronic and vibrational modes in coupled molecules

N. S. Maslova, Vladimir N. Mantsevich, P. I. Arseyev, Igor Michailovitsch Sokolov

Published Jan 8, 2021• 0 citations
Publisher

Abstract

Abstract The formation of entanglement between the electronic and vibrational subsystems of two interacting molecules localized between tunneling contact leads was theoretically analyzed using the Keldysh diagram technique. The time evolution of concurrence after ‘switching on’ the coupling between the molecules was investigated. It was revealed that non-zero concurrence can be present in the system in the resonant case, even if the molecules are connected by the leads. It was also shown that the stationary value of concurrence can be directly expressed by the stationary tunneling current. It reveals non-monotonic behavior with increasing coupling between the molecule’s electronic states. In the regime of small tunneling rates between the molecules and the leads, ‘switching on and off’ the coupling between molecules multiple times, while detecting one of the molecules’ charge states after each ‘on’ and ‘off’ cycle, results in the appearance of non-classical phonon statistics and opens the possibility of creating a vibrational mode in a Fock state.

DOI
10.1088/1612-202x/abd5b6

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Abstract The formation of entanglement between the electronic and vibrational subsystems of two interacting molecules localized between tunneling contact leads was theoretically analyzed using the Keldysh diagram technique. The time evolution of concurrence after ‘switching on’ the coupling between the molecules was investigated. It was revealed that non-zero concurrence can be present in the system in the resonant case, even if the molecules are connected by the leads. It was also shown that the stationary value of concurrence can be directly expressed by the stationary tunneling current. It reveals non-monotonic behavior with increasing coupling between the molecule’s electronic states. In the regime of small tunneling rates between the molecules and the leads, ‘switching on and off’ the coupling between molecules multiple times, while detecting one of the molecules’ charge states after each ‘on’ and ‘off’ cycle, results in the appearance of non-classical phonon statistics and opens the possibility of creating a vibrational mode in a Fock state.
In the present work we theoretically analyze the emergence appearance of entanglement between electronic and vibrational states in a system of two coupled molecules after switching on the interaction between them. In the framework of the adiabatic approach this effect appears because the equilibrium position of one of the molecules is sensitive to its electron occupation. The time evolution of the system shows multiple changes between its entangled and unentangled states. If this evolution starts from a pure coherent vibrational mode state and a state of a single electron localized in one of the molecules, the Schr\"odinger-cat states can appear during the system's time evolution. The Schr\"odinger-cat states can arise as a quantum superposition of distinct coherent states of molecule vibrational mode. Such states are entangled with empty and singly occupied electronic states of the molecule. The presence of entanglement between electronic and vibrational molecule states can be revealed by measuring the electron occupation (charge) of a particular molecule.
Non-Markovian quantum evolution of the electronic subsystem in a laser-driven molecule is characterized through the appearance of negative decoherence rates in the canonical form of the electronic master equation. For a driven molecular system described in a bipartite Hilbert space H=Hel⨂Hvib\mathcal{H}={\mathcal{H}}_{el}⨂{\mathcal{H}}_{\mathrm{vib}}H=Hel​⨂Hvib​ of dimension $2\ifmmode\times\else\texttimes\fi{}{N}_{v}$, we derive the canonical form of the electronic master equation, deducing the canonical measures of non-Markovianity and the Bloch volume of accessible states. We find that one of the decoherence rates is always negative, accounting for the inherent non-Markovian character of the electronic evolution in the vibrational environment. Enhanced non-Markovian behavior, characterized by two negative decoherence rates, appears if there is a coupling between the electronic states g,eg,\phantom{\rule{0.16em}{0ex}}eg,e, such that the evolution of the electronic populations obeys d(PgPe)/dt>0d({P}_{g}{P}_{e})/dt>0d(Pg​Pe​)/dt>0. Non-Markovianity of the electronic evolution is analyzed in relation to temporal behaviors of the electronic-vibrational entanglement and electronic coherence, showing that enhanced non-Markovian behavior accompanies entanglement increase. Taking as an example the coupling of two electronic states by a laser pulse in the Cs2{\mathrm{Cs}}_{2}Cs2​ molecule, we analyze non-Markovian dynamics under laser pulses of various strengths, finding that the weaker pulse stimulates the bigger amount of non-Markovianity. Our results show that increase of the electronic-vibrational entanglement over a time interval is correlated to the growth of the total amount of non-Markovianity calculated over the same interval using canonical measures and connected with the increase of the Bloch volume. After the pulse, non-Markovian behavior is correlated to electronic coherence, such that vibrational motion in the electronic potentials which diminishes the nuclear overlap, implicitly increasing the linear entropy of entanglement, brings a memory character to dynamics.
In this work, we show how electron-vibrational mode coupling can be used to drive maximally entangled states. The physical system consists of two pairs of quantum dots, each pair with a single electron able to tunnel between the dots, thus encoding a qubit. The electron-vibrational mode coupling, described by the strength parameter ggg, yields to an effective electron-electron interaction, responsible for the formation of a maximally entangled quantum state. Both the formation time and the relative phase of the aforementioned state are strongly dependent on ggg. The quantum dynamics exhibits a nonmonotonic behavior as ggg increases, an effect explained through an effective Hamiltonian that takes into account high-order transition processes.
In this thesis, we will analyze quantum entanglement phenomena in systems composed of quantum molecules, considering two different models. In the first, N molecules, each with a single excess electron, interact via Coulomb coupling. This interaction is restricted to the first neighbors. In the second system, electrons from distinct molecules interact with each other through the electron-phonon coupling. Considering the N-molecule system, we broadened our studies started in the master’s degree to verify the characteristics of the energy spectrum and eigenstates for the molecule system. We focus on the scalability of the system and its effect on entanglement, showing that some specific eigenstates are systematically associated with the maximally entangled GHZ states, regardless of the number of molecules. In the second part of the work, we explore the entanglement of both the electronic subsystem and the phonon subsystem, defining a new base composed of Bell’s electronic states associated with the excitation states in vibrational modes, which allows rewriting the Hamiltonian to the composite system. From this point of view, it is possible to determine a set of 4 ⊗ 4 matrix subspaces that elucidated the study of the entanglement behavior in both subsystems, allowing the determination of distinct sets of parameters effective in generating highly entangled states in the electronic subsystem and now in the phononic subsystem.
The dynamics of tripartite entanglement and intramolecular energy for one harmonic- and two anharmonic-vibrational modes in a symmetric trimer molecule is studied for various initial states, where the entanglement is quantified in terms of concurrence and the interacting energy among three modes is calculated to establish a link between entanglement and energy. It is shown that the concurrence and the interacting energy behave dominantly positive correlation for the localized state in the anharmonic-vibrational mode, while they are dominantly anti-correlated for the localized state in the harmonic-vibrational mode. The relation between bipartite entanglement and the energy in a subsystem is discussed as well. Those are useful for quantum computing and quantum information in high dimensional states prepared in polyatomic molecules.
We theoretically investigate the formation of W states in a tripartite system composed of three charge qubits coupled to vibrational modes. The electromechanical coupling is responsible for second-order virtual processes that result in an effective electron-electron interaction between neighbor qubits, which leads to the formation of W states. Based on the Lang-Firsov transformation and perturbation theory, we analytically solve the quantum dynamics, providing a mathematical expression for the maximally entangled W state. Dephasing is also taken into account, paying particular attention to the robustness of bipartite entanglement against local dephasing processes.