Quantum decoherence in finite size exciton-phonon systems

Exciton-phonon dynamics on complex networks: Comparison between a perturbative approach and exact calculations

A method combining perturbation theory with a simplifying ansatz is used to describe the exciton-phonon dynamics in complex networks. This method, called PT^{*}, is compared to exact calculations based on the numerical diagonalization of the exciton-phonon Hamiltonian for eight small-sized networks. It is shown that the accuracy of PT^{*} depends on the nature of the network, and three different situations were identified. For most graphs, PT^{*} yields a very accurate description of the dynamics. By contrast, for the Wheel graph and the Apollonian network, PT^{*} reproduces the dynamics only when the exciton occupies a specific initial state. Finally, for the complete graph, PT^{*} breaks down. These different behaviors originate in the interplay between the degenerate nature of the excitonic energy spectrum and the strength of the exciton-phonon interaction so that a criterion is established to determine whether or not PT^{*} is relevant. When it succeeds, our study shows the undeniable advantage of PT^{*} in that it allows us to perform very fast simulations when compared to exact calculations that are restricted to small-sized networks.

Exciton-phonon system on a star graph: A perturbative approach

Based on the operatorial formulation of the perturbation theory, the properties of an exciton coupled with optical phonons on a star graph are investigated. Within this method, the dynamics is governed by an effective Hamiltonian, which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud whereas the phonons are clothed by virtual excitonic transitions. In spite of the coupling with the phonons, it is shown that the energy spectrum of the dressed exciton resembles that of a bare exciton. The only differences originate in a polaronic mechanism that favors an energy shift and a decay of the exciton hopping constant. By contrast, the motion of the exciton allows the phonons to propagate over the graph so that the dressed normal modes drastically differ from the localized modes associated to bare phonons. They define extended vibrations whose properties depend on the state occupied by the exciton that accompanies the phonons. It is shown that the phonon frequencies, either red shifted or blue shifted, are very sensitive to the model parameter in general, and to the size of the graph in particular.

A qubit coupled with confined phonons: the interplay between true and fake decoherence

The decoherence of a qubit coupled with the phonons of a finite-size lattice is investigated. The confined phonons no longer behave as a reservoir. They remain sensitive to the qubit so that the origin of the decoherence is twofold. First, a qubit-phonon entanglement yields an incomplete true decoherence. Second, the qubit renormalizes the phonon frequency resulting in fake decoherence when a thermal average is performed. To account for the initial thermalization of the lattice, the qua- ntum Langevin theory is applied so that the phonons are viewed as an open system coupled with a thermal bath of harmonic oscillators. Consequently, it is shown that the finite lifetime of the phonons does not modify fake decoherence but strongly affects true decoherence. Depending on the values of the model parameters, the interplay between fake and true decoherence yields a very rich dynamics with various regimes.

Vibrons in finite size molecular lattices: a route for high-fidelity quantum state transfer at room temperature

A communication protocol is proposed in which vibron-mediated quantum state transfer takes place in a molecular lattice. We consider two distant molecular groups grafted on each side of the lattice. These groups form two quantum computers where vibrational qubits are implemented and received. The lattice defines the communication channel along which a vibron delocalizes and interacts with a phonon bath. Using quasi-degenerate perturbation theory, vibron-phonon entanglement is taken into account through the effective Hamiltonian concept. A vibron is thus dressed by a virtual phonon cloud whereas a phonon is clothed by virtual vibronic transitions. It is shown that three quasi-degenerate dressed states define the relevant paths followed by a vibron to tunnel between the computers. When the coupling between the computers and the lattice is judiciously chosen, constructive interference takes place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperature range.