Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum

We generalize the momentum average (MA) approximation to study the properties of models with momentum-dependent electron-phonon coupling. As in the case of the application of the original MA to the Holstein model, the results are analytical, numerically trivial to evaluate, exact for both zero bandwidth and for zero electron-phonon coupling, and are accurate everywhere in parameter space. Comparison with available numerical data confirms this accuracy. We then show that further improvements can be obtained based on variational considerations, using the one-dimensional breathing-mode Hamiltonian as a specific example. For example, by using this variational MA, we obtain ground state energies within at most 0.3% error of the numerical data.Comment: 15 pages, 10 figure

Quantum nanostructures in strongly spin-orbit coupled two-dimensional systems

Recent progress in experimental studies of low-dimensional systems with strong spin-orbit coupling poses a question on the effect of this coupling on the energy spectrum of electrons in semiconductor nanostructures. It is shown in the paper that this effect is profound in the strong coupling limit. In circular quantum dots a soft mode develops, in strongly elongated dots electron spin becomes protected from the effects of the environment, and the lower branch of the energy spectrum of quantum wires becomes nearly flat in a wide region of the momentum space.Comment: 5 pages, 1 figur

Small polarons in dilute gas Bose-Einstein condensates

A neutral impurity atom immersed in a dilute Bose-Einstein condensate (BEC) can have a bound ground state in which the impurity is self-localized. In this small polaron-like state, the impurity distorts the density of the surrounding BEC, thereby creating the self-trapping potential minimum. We describe the self-localization in a strong coupling approach

Poynting's theorem and energy conservation in the propagation of light in bounded media

Starting from the Maxwell-Lorentz equations, Poynting's theorem is reconsidered. The energy flux vector is introduced as S_e=(E x B)/mu_0 instead of E x H, because only by this choice the energy dissipation can be related to the balance of the kinetic energy of the matter subsystem. Conservation of the total energy as the sum of kinetic and electromagnetic energy follows. In our discussion, media and their microscopic nature are represented exactly by their susceptibility functions, which do not necessarily have to be known. On this footing, it can be shown that energy conservation in the propagation of light through bounded media is ensured by Maxwell's boundary conditions alone, even for some frequently used approximations. This is demonstrated for approaches using additional boundary conditions and the dielectric approximation in detail, the latter of which suspected to violate energy conservation for decades.Comment: 5 pages, RevTeX4, changes: complete rewrit

Electromagnetic wave refraction at an interface of a double wire medium

Plane-wave reflection and refraction at an interface with a double wire medium is considered. The problem of additional boundary conditions (ABC) in application to wire media is discussed and an ABC-free approach, known in the solid state physics, is used. Expressions for the fields and Poynting vectors of the refracted waves are derived. Directions and values of the power density flow of the refracted waves are found and the conservation of the power flow through the interface is checked. The difference between the results, given by the conventional model of wire media and the model, properly taking into account spatial dispersion, is discussed.Comment: 17 pages, 11 figure

Sub-nanosecond delay of light in (Cd,Zn)Te crystal

We study excitonic polariton relaxation and propagation in bulk CdZnTe using time- resolved photoluminescence and time-of-flight techniques. Propagation of picosecond optical pulses through 0.745 mm thick crystal results in time delays up to 350 ps, depending on the photon energy. Optical pulses with 150 fs duration become strongly stretched. The spectral dependence of group velocity is consistent with the dispersion of the lower excitonic polariton branch. The lifetimes of excitonic polariton in the upper and lower branches are 1.5 and 3 ns, respectively.Comment: 5 pages, 4 figure

Optical Properties of Crystals with Spatial Dispersion: Josephson Plasma Resonance in Layered Superconductors

We derive the transmission coefficient, $T(\omega)$, for grazing incidence of crystals with spatial dispersion accounting for the excitation of multiple modes with different wave vectors ${\bf k}$ for a given frequency $\omega$. The generalization of the Fresnel formulas contains the refraction indices of these modes as determined by the dielectric function $\epsilon(\omega,{\bf k})$. Near frequencies $\omega_e$, where the group velocity vanishes, $T(\omega)$ depends also on an additional parameter determined by the crystal microstructure. The transmission $T$ is significantly suppressed, if one of the excited modes is decaying into the crystal. We derive these features microscopically for the Josephson plasma resonance in layered superconductors.Comment: 4 pages, 2 figures, epl.cls style file, minor change

A Variational Approach to Nonlocal Exciton-Phonon Coupling

In this paper we apply variational energy band theory to a form of the Holstein Hamiltonian in which the influence of lattice vibrations (optical phonons) on both local site energies (local coupling) and transfers of electronic excitations between neighboring sites (nonlocal coupling) is taken into account. A flexible spanning set of orthonormal eigenfunctions of the joint exciton-phonon crystal momentum is used to arrive at a variational estimate (bound) of the ground state energy for every value of the joint crystal momentum, yielding a variational estimate of the lowest polaron energy band across the entire Brillouin zone, as well as the complete set of polaron Bloch functions associated with this band. The variation is implemented numerically, avoiding restrictive assumptions that have limited the scope of previous assaults on the same and similar problems. Polaron energy bands and the structure of the associated Bloch states are studied at general points in the three-dimensional parameter space of the model Hamiltonian (electronic tunneling, local coupling, nonlocal coupling), though our principal emphasis lay in under-studied area of nonlocal coupling and its interplay with electronic tunneling; a phase diagram summarizing the latter is presented. The common notion of a "self-trapping transition" is addressed and generalized.Comment: 33 pages, 11 figure

Quantum simulation of small-polaron formation with trapped ions

We propose a quantum simulation of small-polaron physics using a one-dimensional system of trapped ions acted upon by off-resonant standing waves. This system, envisioned as an array of microtraps, in the single-excitation case allows the realization of the anti-adiabatic regime of the Holstein model. We show that the strong excitation-phonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonon-dressed excitation.Comment: accepted for publication in Phys. Rev. Let