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Physical Review B

Bloch-Zener oscillations of strongly correlated electrons

Stefano Longhi

Published Aug 23, 2012• 23 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.86.075144

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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.
We study the dynamics of bound pairs in the extended Hubbard model driven by a linear external field. It is shown that two interacting bosons or singlet fermions with nonzero on-site and nearest-neighbor interaction strengths can always form bound pairs in the absence of an external field. There are two bands of bound pairs, one of which may have incomplete wave vectors when it has an overlap with the scattering band, referred to as an imperfect band. In the presence of the external field, the dynamics of the bound pair in the perfect band exhibits distinct Bloch-Zener oscillation (BZO), while in the imperfect band the oscillation presents a sudden death. The pair becomes uncorrelated after the sudden death and the BZO never comes back. Such dynamical behaviors are robust even for the weak-coupling regime and thus can be used to characterize the phase diagram of the bound states.
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.
The correlated motion of electrons in a one-dimensional system with an externally applied longitudinal electric field is discussed. Within the tight-binding model we show that in addition to the well-known Bloch oscillations, the electron-electron interaction induces time-dependent oscillations of the mobility whose period depends on the strength and range of the coupling only. The oscillations involve transitions between bands of bound and unbound states. The case of two electrons is solved in detail and an extension of the results to more particles is discussed.
It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two subbands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunneling between the subbands, a Bloch-Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian, a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker-Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach-Zehnder interferometer is briefly discussed. PACS numbers: 03.65.-w, 03.75.Be, 03.75.LmBloch-Zener oscillations 2 1.
It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two sub-bands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunnelling between the sub-bands, a Bloch–Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian which is a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker–Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach–Zehnder interferometer is briefly discussed.
Coherent transport of quantum particles in binary superlattices driven by an ac force can realize a kind of quantum walk (QW) that can be referred to as Bloch–Zener QW. In this regime, the particle wavepacket undergoes a sequence of Zener tunnelling events that mimic a discrete QW on a lattice, provided that the impulse of the ac force over one semi-cycle of oscillation is properly adjusted. In the Bloch–Zener QW, the coin states are related to the particle occupation of the two minibands, and thus it does not require any internal degrees of freedom of the particle.