We present a unified theory of polaron and soliton dynamics by combining time-dependent variational methods recently applied to the theory of Davydov solitons with partial-dressing methods well known from polaron theory. We focus on the simplest partial-dressing assumption, applying a common dressing fraction to all phonon modes. Our fundamental result is a system of nonlinear evolution equations in which the tendency of a system to form Davydov solitons is balanced against its tendency to form small polarons. We subsequently apply time-independent variational methods to determine the optimal dressing fraction in a mean-field manner. The characterization of the partially dressed soliton states that results is complete with respect to the system parameter space. Consistent with prior works from polaron theory, we find a self-trapping transition that is only weakly modified by our inclusion of nonlinearities, and we reinterpret this transition in terms of our newly obtained soliton states. Applying our results to a central problem in bioenergetics, we obtain results markedly different from well-known results of Davydov’s theory.

We study self-trapping of electrons (excitons) in one-dimensional systems with three realistic types of coupling with phonons, applying a variational procedure valid for the whole range of system parameters. Various types of self-trapped states are identified and mapped in the parameter space. Our results are compared to the results of previous studies. The particular case of biological systems is studied and it is shown that the Davydov-soliton concept can be used for the description of electron transport in biological systems, but not for the energy transfer in terms of amide-I vibrations (CO stretching vibration mode).

We present a generalization of small-polaron band theory based on methods used in the study of Davydov solitons. The eigenstates of the small-polaron band are found to be stationary solutions of our equations of motion; however, among the nonstationary solutions can be found a family of soliton states. The soliton solutions we obtain differ from Davydov solitons in fundamental ways, but are fully consistent with the theory of small polarons.

Quantum bits (qubits) are at the heart of quantum information processing schemes. Currently, solid-state qubits, and in particular the superconducting ones, seem to satisfy the requirements for being the building blocks of viable quantum computers, since they exhibit relatively long coherence times, extremely low dissipation, and scalability. The possibility of achieving quantum coherence in macroscopic circuits comprising Josephson junctions, envisioned by Legett in the 1980’s, was demonstrated for the first time in a charge qubit; since then, the exploitation of macroscopic quantum effects in low-capacitance Josephson junction circuits allowed for the realization of several kinds of superconducting qubits. Furthermore, coupling between qubits has been successfully achieved that was followed by the construction of multiple-qubit logic gates and the implementation of several algorithms. Here it is demonstrated that induced qubit lattice coherence as well as two remarkable quantum coherent optical phenomena, i.e., self-induced transparency and Dicke-type superradiance, may occur during light-pulse propagation in quantum metamaterials comprising superconducting charge qubits. The generated qubit lattice pulse forms a compound ”quantum breather” that propagates in synchrony with the electromagnetic pulse. The experimental confirmation of such effects in superconducting quantum metamaterials may open a new pathway to potentially powerful quantum computing.