Two-vibron bound states lifetime in a one-dimensional molecular lattice coupled to acoustic phonons

The lifetime of two-vibron bound states in the overtone region of a one-dimensional anharmonic molecular lattice is investigated. The anharmonicity, introduced within an attractive Hubbard Hamiltonian for bosons, is responsible for the formation of bound states which belong to a finite linewidth band located below the continuum of two-vibron free states. The decay of these bound states into either bound or free states, is described by considering the coupling between the vibrons and a thermal bath formed by a set of low frequency acoustic phonons. The relaxation rate is expressed in terms of the spectral distribution of the vibron/phonon coupling and of the two-vibron Green operator which is calculated exactly by using the number states method. The behavior of the two-vibron bound states relaxation rate is analyzed with a special emphasis on the influence of the anharmonicity. It is shown that the rate exhibits two distinct regimes depending on the thermal bath dimension. When the bath dimension is equal to unity, the rate increases with the anharmonicity and the decay of the two-vibron bound states into the other bound states appears as the main contribution of the rate. By contrast, when the bath dimension is equal to 2 and 3, the rate decreases as the anharmonicity increases indicating that the two-vibron bound states decay into the two-vibron free states continuum.Comment: January 200

Quantum decoherence in finite size exciton-phonon systems

International audienceBased on the operatorial formulation of the perturbation theory, the properties of a confined exciton coupled with phonons in thermal equilibrium is revisited. 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. Special attention is thus paid for describing the time evolution of the excitonic coherences at finite temperature. As in an infinite lattice, temperature-enhanced quantum decoherence takes place. However, it is shown that the confinement softens the decoherence. The coherences are very sensitive to the excitonic states so that the closer to the band center the state is located, the slower the coherence decays. In particular, for odd lattice sizes, the coherence between the vacuum state and the one-exciton state exactly located at the band center survives over an extremely long time scale. A superimposition involving the vacuum and this specific one-exciton state behaves as an ideal qubit insensitive to its environment

Vibrons in alpha-helix proteins: influence of the inhomegenous mass distribution in the amino acid sequence

submitted to Phys. Rev. EThe influence of the inhomogeneous mass distribution in the amino acid sequence on the amide-I vibrons in protein is addressed within the small polaron approach. It is shown that inhomogeneities in the sequence favor a randomness in the polaron Hamiltonian via the dressing mechanism. The polaron dynamics is thus described by a 1D tight binding model with correlated off-diagonal disorder. At low temperature, the polaron hopping constants exhibit small fluctuations around a rather large average value so that the polaron Hamiltonian appears weakly disordered. Extended states occur over a wide range of energies around the band center whereas the states close to the band edges appear localized. By contrast, at biological temperature, a stronger disorder takes place which originates in a drastic decrease of the average hopping constant. The number of localized states increases but few states close to the band center exhibit a localization length about to or greater than the lattice size. The extended nature of the states at the band center is attributed to the existence of short range correlations in the random hopping constants

Two-polaron energy diffusion in a one-dimensional lattice of hydrogen bounded peptide units

A generalized Pauli master equation is established for describing the vibrational energy flow in a 1D lattice of hydrogen bounded peptide units. A Lang-Firsov transformation is applied so that the relevant excitations are small polarons corresponding to vibrational excitons dressed by virtual phonons. A special attention is thus paid to characterize the energy transfer mediated by two polarons. At biological temperature, it is shown that the polaron-phonon coupling is sufficiently strong to prevent any coherent motion. The polaron-polaron interaction occurring in such a nonlinear lattice does not affect the long time behavior of the energy flow which results from the diffusion of two independent polarons

Vibron-polaron critical localization in a finite size molecular nanowire

The small polaron theory is applied to describe the vibron dynamics in an adsorbed nanowire with a special emphasis onto finite size effects. It is shown that the finite size of the nanowire discriminates between side molecules and core molecules which experience a different dressing mechanism. Moreover, the inhomogeneous behavior of the polaron hopping constant is established and it is shown that the core hopping constant depends on the lattice size. However, the property of a lattice with translational invariance is recovered when the size of the nanowire is greater than a critical value. Finally, it is pointed out that these features yield the occurrence of high energy localized states which both the nature and the number are summarized in a phase diagram in terms of the relevant parameters of the problem (small polaron binding energy, temperature, lattice size).Comment: 17 pages, 10 figure

Vibrational exciton-mediated quantum state transfert: a simple model

13A communication protocol is proposed in which quantum state transfer is mediated by a vibrational exciton. We consider two distant molecular groups grafted on the sides of a lattice. These groups behave as two quantum computers where the information in encoded and received. The lattice plays the role of a communication channel along which the exciton propagates and interacts with a phonon bath. Special attention is paid for describing the system involving an exciton dressed by a single phonon mode. The Hamiltonian is thus solved exactly so that the relevance of the perturbation theory is checked. Within the nonadiabatic weak-coupling limit, it is shown that the system supports three quasi-degenerate states that define the relevant paths followed by the exciton to tunnel between the computers. When the model parameters are judiciously chosen, constructive interferences take place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperature range

Energy transfer in finite-size exciton-phonon systems : confinement-enhanced quantum decoherence

Based on the operatorial formulation of the perturbation theory, the exciton-phonon problem is revisited for investigating exciton-mediated energy flow in a finite-size lattice. Within this method, the exciton-phonon entanglement is taken into account through a dual dressing mechanism so that exciton and phonons are treated on an equal footing. In a marked contrast with what happens in an infinite lattice, it is shown that the dynamics of the exciton density is governed by several time scales. The density evolves coherently in the short-time limit whereas a relaxation mechanism occurs over intermediated time scales. Consequently, in the long-time limit, the density converges toward a nearly uniform distributed equilibrium distribution. Such a behavior results from quantum decoherence that originates in the fact that the phonons evolve differently depending on the path followed by the exciton to tunnel along the lattice. Although the relaxation rate increases with the temperature and with the coupling, it decreases with the lattice size, suggesting that the decoherence is inherent to the confinement

Transport quantique dans les réseaux nanoscopiques

DEACe cours, destiné aux étudiants de Master 2, présente une introduction à l'étude des phénomènes de transport dans les réseaux moléculaires de basse dimension. Les outils de base pour étudier le transfert d'énergie à l'échelle nanométrique sont présentés : Modèle de liaisons fortes, Opérateur d'évolution, Fonction de Green, Théorie de la réponse linéaire). Les méthodes des fonctions de des matrice de transfert sont exposées pour aboutir finalement à la définition de la conductance quantique selon Landauer. Les derniers chapitres introduisent les notions importantes de localisation d'Anderson et de couplage avec un environnement

Theoretical Fluctuations of Conductance in Stretched Monatomic Nanowire

Recent experiments showed that the last, single channel conductance step in monatomic gold contacts exhibits significant fluctuations as a function of stretching. From simulations of a stretched gold nanowire linked to deformable tips, we determine the distribution of the bond lengths between atoms forming the nanocontact and analyze its influence on the electronic conductance within a simplified single channel approach. We show that the inhomogeneous distribution of bond lengths can explain the occurrence and the 5% magnitude of conductance fluctuations below the quantum conductance unit $g_{o}= 2e^2/h$