Dynamics of Bloch oscillations

Hartmann, T.; Keck, Frédéric; Korsch, Hans Jürgen; Mossmann, S.

doi:10.1088/1367-2630/6/1/002

Cited by 225 publications

(263 citation statements)

References 48 publications

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“…This expression is exactly the same as the period of Bloch oscillations [23]. In summary, we have shown that two paired and initially undimerized polyacetylene chains has an electronic energy band with a gap.…”

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confidence: 67%

Electronic oscillations in paired polyacetylene chains

Muniz

Filho

2010

Solid State Communications

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An interacting pair of polyacetylene chains are initially modeled as a couple of undimerized polymers described by a Hamiltonian based on the tight-binding model representing the electronic behavior along the linear chain, plus a Dirac's potential double well representing the interaction between the chains. A theoretical field formalism is employed, and we find that the system exhibits a gap in its energy band due to the presence of a mass-matrix term in the Dirac's Lagrangian that describes the system. The Peierls instability is introduced in the chains by coupling a scalar field to the fermions of the theory via spontaneous symmetry breaking, to obtain a kink-like soliton, which separates two vacuum regions, i.e., two spacial configurations (enantiomers) of the each molecule. Since that mass-matrix and the pseudo-spin operator do not commute in the same quantum representation, we demonstrate that there is a particle oscillation phenomenon with a periodicity equivalent to the Bloch oscillations. Quantum mechanical particles moving under the influence of a constant electric field and submitted to a periodic potential oscillate instead of moving with uniform acceleration. This phenomenon is called Bloch oscillations and were predicted theoretically by F. Bloch in 1928 [1]. Such oscillations have never been observed in a natural lattice because the characteristic times of the electrons scattering by the lattice defects, or impurities, are much shorter than the Bloch period. As a consequence, during a long time these oscillations were seen like a mere theoretical curiosity to demonstrate the strange properties of matter, according to quantum mechanics principles. However, they have been recently observed experimentally in semiconductor superlattices [2,[4][5][6]8] and with larger periods, of the order of ten seconds, in strontium atoms trapped by laser beams, cooled at temperatures close to absolute zero. In the former case, the dependence of the Bloch frequency on the electric field makes the oscillations tunable, yielding a potential source of coherent high frequency radiation and, in latter case, the constant external force was the terrestrial gravitational field itself [3].These oscillations can play an effective and important role in quantum electronics, due to development of the physics of quasi-unidimensional molecular structures, as polyacetylene [9] and graphene ribbons [10,11]. Polyacetylene consists of a linear chain of carbon atoms, coupled to each other with alternating simple and double chemical bonds, that can be obtained via acetylene polymerization. It is an organic polymer with special electronic properties. Thin films of this polymer produced under special doping conditions are excellent conductors that can be used to develop electronic devices in the nanometer scale [14]. Due to its dimensionality we can model the undimerized polyacetylene as a linear chain of carbon atoms with periodic boundary conditions and a Hamiltonian based on the tight binding model. In this approach, the valence electron...

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confidence: 67%

Electronic oscillations in paired polyacetylene chains

Muniz

Filho

2010

Solid State Communications

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“…8 we show the evolution of an initial bare Gaussian wave packet, when the detuning oscillates as δ(t) = δ 0 cos(ωt). But since the initial detuning is rather large, the state has dressed features also when the detuning is small, which is seen in the oscillations of the wave packet, see [9,10]. From the lower plot one notes that the oscillations of the inversion die out (compared to the stable adiabatic solution (25)), which is due to the non-adiabatic evolution of the wave packet.…”

Section: Figmentioning

confidence: 95%

“…This is due to the adiabatic transition between bare states with different group velocities vg. The oscillations in the wave packet are typical for Gaussian dressed states [9,10]. In the lower plot, the atomic inversion is shown from the numerical simulation (solid line) and for the adiabatic result (25) (dotted line).…”

Section: Figmentioning

confidence: 99%

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Level crossings in a cavity QED model

Larson

2006

Phys. Rev. A

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In this paper I study the dynamics of a two-level atom interacting with a standing wave field. When the atom is subjected to a weak linear force, the problem can be turned into a time dependent one, and the evolution is understood from the band structure of the spectrum. The presence of level crossings in the spectrum gives rise to Bloch oscillations of the atomic motion. Here I investigate the effects of the atom-field detuning parameter. A variety of different level crossings are obtained by changing the magnitude of the detuning, and the behaviour of the atomic motion is strongly affected due to this. I also consider the situation in which the detuning is oscillating in time and its impact on the atomic motion. Wave packet simulations of the full problem are treated numerically and the results are compared with analytical solutions given by the standard Landau-Zener and the three-level Landau-Zener models.

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“…21 we consider a 1D TB system. To account for the time-dependence of the electric field, we use a recently developed numerical method 22 , which is based on the time-dependent non-equilibrium Green's function (TDNEGF) formalism 23,24 in combination with an auxiliary-mode expansion 25 .…”

Section: Introductionmentioning

confidence: 99%

Emergence of Bloch oscillations in one-dimensional systems

Popescu

2017

Phys. Rev. B

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Electrons in periodic potentials exhibit oscillatory motion in presence of an electric field. Such oscillations are known as Bloch oscillations. In this article we theoretically investigate the emergence of Bloch oscillations for systems where the electric field is confined to a finite region, like in typical electronic devices. We use a one-dimensional tight-binding model within the single-band approximation to numerically study the dynamics of electrons after a sudden switching-on of the electric field. We find a transition from a regime with direct current to Bloch oscillations when increasing the system size or decreasing the field strength. We propose a pump-probe scheme to observe the oscillations by measuring the accumulated charge as a function of the pulse-length.

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Dynamics of Bloch oscillations

Cited by 225 publications

References 48 publications

Electronic oscillations in paired polyacetylene chains

Electronic oscillations in paired polyacetylene chains

Level crossings in a cavity QED model

Emergence of Bloch oscillations in one-dimensional systems

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