An attempt is made to measure the vibron-phonon coupling strength in a finite size lattice of H-bonded peptide units. Within a finite temperature density matrix approach, we compare separately the influence of both the vibron-phonon coupling and the dipole-dipole interaction on the coherence between the ground state and a local one-vibron state. Due to the confinement, it is shown that the vibron-phonon coupling yields a series of dephasing-rephasing mechanisms that prevents the coherence to decay. Similarly, the dipole-dipole interaction gives rise to quantum recurrences for specific revival times. Nevertheless, intense recurrences are rather rare events so that the coherence behaves as a random variable whose most probable value vanishes. By comparing the degree of the coherence for each interaction, a critical coupling chi*(L) is defined to discriminate between the weak and the strong coupling limits. Its size dependence indicates that the smaller the lattice size is, the weaker the vibron-phonon coupling relative to the dipole-dipole interaction is.
The exciton-phonon system in a confined environment is revisited within standard perturbation theory. Special attention is paid to describing the time evolution of the excitonic coherences at finite temperature. To proceed, the system involving an exciton dressed by a single phonon mode is considered. Owing to its simplicity, it is solved exactly so that the relevance of the perturbation theory is checked. Within the nonadiabatic weak-coupling limit, it is shown that several time scales govern the coherence dynamics. In the short-time limit, the coherences behave as if the exciton was insensitive to the phonon bath. Then, quantum decoherence takes place. Finally the coherences recur almost periodically at specific revival times. Coherence decay and revival strongly depend on the nature of the excitonic states. In particular, for odd lattice sizes, the coherence of the state exactly located at the band center survives over a very long-time scale. Therefore, confinement-induced decoherence softening favors high-fidelity quantum-state transfer and allows to encode the information on a quantum bit almost insensitive to quantum decoherence.
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.
The ground state of a one-dimensional electron-phonon system is studied by means of a small-crystal approach: an exact solution of a two-site cluster with two electrans and periodic boundary conditions.A single electron band is considered in the tight-binding approximation, together with two-electron interactions between electrons in the same site (Hubbard model); the electrons are coupled to longitudinal acoustic phonons through a bilinear interaction.The problem is isomorphic with that of the homopolar diatomic molecule with a vibronic degree of freedom and coupling between the electronic and vibronic modes.In the adiabatic (large ionic mass, small vibrational frequency) limit there is an analytical solution which indicates that the transition between the non-distorted (weak coupling) and the distorted (strong coupling) phases can be either continuous or discontinuous, depending on whether the value of the electron-electron interaction is larger or smaller than a critical value.In the extremely high-frequency limit (ionic mass M ~ 0 ) it is also possible to find an analytical solution (for M = 0) that shows that the system remains undistorted for any value of the electron-phonon coupling and the electron-electron interaction.In the intermediate case (finite, nonvanishing M) numerical solutions exhibit a continuous transition from the non-distorted to the distorted phase.
The ground state of a one-dimensional electron-phonon system is studied by means of a small-crystal approach: an exact solution of a two-site cluster with two electrons and periodic boundary conditions. A single electron band is considered in the tight-binding approximation, together with two-electron interactions between electrons in the same site (Hubbard model); the electrons are coupled to longitudinal-acoustic phonons through a bilinear interaction. The problem is isomorphic with that of the homopolar diatomic molecule with a vibronic degree of freedom and coupling between the electronic and vibronic modes. In the adiabatic (large-ionic-mass, small-vibrational-frequency) limit there is an analytical solution which indicates that the transition between the nondistorted (weak-coupling) and the distorted (strong-coupling) phases can be either continuous or discontinuous, depending on whether the value of electron-electron interaction is smaller or larger than a critical value. In the extremely-high-frequency limit (ionic mass M\ensuremath{\rightarrow}0) it is also possible to find an analytical solution (for M=0) that shows that the system remains undistorted for any value of the electron-phonon coupling and the electron-electron interaction. In the intermediate case (finite, nonvanishing M), numerical solutions exhibit a continuous transition from the nondistorted to the distorted phase.
We explore the ground-state properties of a few bosons with dipole-dipole interactions in a one-dimensional optical lattice. For comparatively strong interactions, a transition from a Mott-insulator state to a crystal state occurs. Herein, we provide a detailed characterization and a detection protocol for the resulting crystal state. Using the eigenvalues of the reduced one-body density matrix, we define an order parameter that characterizes all the emergent states occurring in the finite-sized ensemble and agrees with the signatures obtained from the analysis of the one- and two-body densities. We further demonstrate that these few-body emergent states can be detected experimentally using the variance of single-shot measurements.
We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction
f of sites, while keeping a finite
U on the remaining ones. Through quantum Monte Carlo simulations for several values of
f and
U and for system sizes ranging from $8\ifmmode\times\else\texttimes\fi{}8$ to $16\ifmmode\times\else\texttimes\fi{}16$, we have calculated the configurational averages of the equal-time pair structure factor
Ps and, for a more restricted set of variables, the helicity modulus ${\ensuremath{\rho}}_{s}$, as functions of temperature. Two finite-size scaling Ans\"atze for
Ps have been used: one for zero temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration
fc, which increases with
U, at least up to
U=4 (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of
f shows a maximum near $f\ensuremath{\sim}0.07$ for $2\ensuremath{\lesssim}U\ensuremath{\lesssim}6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of
f for
U=3, 4, and 6: they also show maxima near $f\ensuremath{\sim}0.07$, with the highest
Tc increasing with
U in this range. We argue that, overall, the observed behavior results from both the breakdown of charge-density-wave-superconductivity degeneracy and the fact that free sites tend to ``push'' electrons toward attractive sites; the latter effect being more drastic at weak couplings.