Investigation of one- and two-dimensional vibrational density of states using two-phonon infrared absorption spectroscopy

Two-exciton bound state quantum self-trapping in an extended star graph

The attractive Bose-Hubbard model is applied for describing the quantum self-trapping in an extended star graph. In the strong coupling limit and when two excitons are created on the core of the star, the dynamics is dominated by pair states whose properties is governed by the branch number $N$. When $N=2$, the star reduces to a linear chain so that the energy does not self-localize. Conversely, when $N\geq3$, a restructuring of the eigenstates arises and a low-energy state occurs describing a pair localized on the core of the star. Preferentially excited, this localized state gives rise to a quantum self-trapping of the energy, a process that intensifies as $N$ increases.

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.

Quantum decoherence in finite size exciton-phonon systems

Based 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.

Parametric resonance-induced time-convolutionless master equation breakdown in finite size exciton-phonon systems

A detailed analysis is performed to show that the second order time-convolutionless master equation fails to describe the exciton-phonon dynamics in a finite size lattice. To proceed, special attention is paid to characterizing the coherences of the exciton reduced density matrix. These specific elements measure the ability of the exciton to develop superimpositions involving the vacuum and the one-exciton states. It is shown that the coherences behave as wavefunctions whose dynamics is governed by a time-dependent effective Hamiltonian defined in terms of the so-called time-dependent relaxation operator. Due to the confinement, quantum recurrences provide to the relaxation operator an almost periodic nature, so the master equation reduces to a linear system of differential equations with almost periodic coefficients. We show that, in accordance with the Floquet theory, unstable solutions emerge due to parametric resonances involving specific frequencies of the relaxation operator and specific excitonic eigenfrequencies. These resonances give rise to an unphysical exponential growth of the coherences, indicating the breakdown of the second order master equation.

Relaxation channels of two-vibron bound states in alpha-helix proteins

Relaxation channels for two-vibron bound states in an anharmonic alpha-helix protein are studied. According to a recently established small polaron model [V. Pouthier, Phys. Rev. E 68, 021909 (2003)], it is shown that the relaxation originates in the interaction between the dressed anharmonic vibrons and the remaining phonons. This interaction is responsible for the occurrence of transitions between two-vibron eigenstates mediated by both phonon absorption and phonon emission. At biological temperature, the relaxation rate does not significantly depend on the nature of the two-vibron states involved in the process. The lifetime for both bound and free states is of the same order of magnitude and ranges between 0.1 and 1.0 ps for realistic parameter values. By contrast, the relaxation channels strongly depend on the nature of the two-vibron states which is a consequence of the breatherlike behavior of the two-vibron bound states.

Two-vibron bound states in alpha-helix proteins: the interplay between the intramolecular anharmonicity and the strong vibron-phonon coupling

The influence of the intramolecular anharmonicity and the strong vibron-phonon coupling on the two-vibron dynamics in an alpha-helix protein is studied within a modified Davydov model. The intramolecular anharmonicity of each amide-I vibration is considered, and the vibron dynamics is described according to the small polaron approach. A unitary transformation is performed to remove the intramolecular anharmonicity, and a modified Lang-Firsov transformation is applied to renormalize the vibron-phonon interaction. Then a mean field procedure is realized to obtain the dressed anharmonic vibron Hamiltonian. It is shown that the anharmonicity modifies the vibron-phonon interaction, which results in an enhancement of the dressing effect. In addition, both the anharmonicity and the dressing favor the occurrence of two different bound states whose properties strongly depend on the interplay between the anharmonicity and the dressing. This dependence was summarized in a phase diagram which characterizes the number and the nature of the bound states as a function of the relevant parameters of the problem. For a significant anharmonicity, the low-frequency bound states describe two vibrons trapped onto the same amide-I vibration, whereas the high-frequency bound states refer to the trapping of the two vibrons onto nearest neighbor amide-I vibrations.