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Physical Review B

Correlated super-Bloch oscillations

Stefano Longhi, Giuseppe Della Valle

Published Aug 23, 2012• 33 citations
Publisher

Abstract

The coherent dynamics of two strongly interacting electrons hopping on a one-dimensional lattice and driven by combined dc-ac fields is theoretically investigated in the framework of the Hubbard model. It is shown that, under appropriate forcing conditions in the strong-field regime, super-Bloch oscillations (SBOs) can be observed for the bound particle state, but not for unpaired electrons that remain frozen in the lattice. As compared to single-particle SBOs, SBOs of correlated particles are generally quasiperiodic.

DOI
10.1103/physrevb.86.075143

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The coherent dynamics of two strongly interacting electrons hopping on a one-dimensional lattice and driven by combined dc-ac fields is theoretically investigated in the framework of the Hubbard model. It is shown that, under appropriate forcing conditions in the strong-field regime, super-Bloch oscillations (SBOs) can be observed for the bound particle state, but not for unpaired electrons that remain frozen in the lattice. As compared to single-particle SBOs, SBOs of correlated particles are generally quasiperiodic.
It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.
Several recent studies have investigated the dynamics of cold atoms in optical lattices subject to ac forcing; the theoretically predicted renormalization of the tunneling amplitudes has been verified experimentally. Recent observations include global motion of the atom cloud, such as giant ``super--Bloch oscillations'' (SBOs). We show that, in order to understand unexplained features of SBOs, in addition to the renormalization of the tunneling, a new and important phase correction must be included. For fermionic systems with strong attractive interactions, one may engineer different types of collisions and recollisions between bound-pairs and unpaired atoms.
The onset of Bloch oscillations (BOs) for two correlated anyons hopping on a one-dimensional lattice is theoretically investigated in the framework of the anyon-Hubbard model. It is shown that, even in the absence of on-site particle interaction, BOs are degraded for a nonvanishing statistical phase exchange owing to the nonlocal quasiparticle nature of anyons. A remarkable exception is found for pseudofermions, i.e., particles that, although they are bosons on site, behave as fermions off site. In this case, if the ratio of forcing to the hopping rate is smaller than $\ensuremath{\sim}$0.50.50.5, in the absence of on-site interaction long-lived BOs are observed at a frequency which is half the BO frequency of single particles. This is notably distinct from results for previously investigated BOs of two strongly correlated bosons or fermions, in which particle correlation leads to a doubling of the BO frequency.
We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.
We consider one-dimensional chains of two-level quantum systems coupled via tunneling. The chain is driven by the superposition of dc and ac fields in the strong coupling regime. Based on the fundamental principles of electrodynamics and quantum theory, we have developed a generalized model of quantum dynamics for such interactions, free of rotating-wave approximation. The system of equations of motion was studied numerically. We analyzed the dynamics and spectra of the inversion density, dipole current density, and tunneling current density. In the case of resonant interaction with the ac component, the particle dynamics exhibits itself in the oscillatory regime, which may be interpreted as a combination of Rabi and Bloch oscillations with their strong mutual influence. Such scenario for an obliquely incident ac field dramatically differs from the individual picture of both types of oscillations due to the interactions. This effect is counterintuitive because of the existence of markedly different frequency ranges for such two types of oscillations. These dynamics manifest themselves in multiline spectra in different combinations of Rabi and Bloch frequencies. The effect is promising as a framework of a new type of spectroscopy in nanoelectronics and electrical control of nanodevices.
We study the dynamics of few interacting bosons in a one-dimensional lattice with dc bias. In the absence of interactions the system displays single-particle Bloch oscillations. For strong interaction the Bloch oscillation regime re-emerges with fractional Bloch periods which are inversely proportional to the number of bosons clustered into a bound state. The interaction strength affects the oscillation amplitude. Excellent agreement is found between numerical data and a composite particle dynamics approach. For specific values of the interaction strength, a particle will tunnel from the interacting cloud to a well-defined distant lattice location.