physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...

, a Super Bloch oscillation describes a certain type of motion of a particle in a lattice potential under external periodic driving. The term super refers to the fact that the amplitude in position space of such an oscillation is several orders of magnitude larger than for 'normal'

Bloch oscillations Bloch oscillation is a phenomenon from solid state physics. It describes the oscillation of a particle (e.g. an electron) confined in a periodic potential when a constant force is acting on it. It was first pointed out by Felix Bloch and Clarence Z ...

Bloch oscillations vs. Super Bloch oscillations

Normal Bloch oscillations and Super Bloch oscillations are closely connected. In general,

are a consequence of the periodic structure of the lattice potential and the existence of a maximum value of the

Bloch wave In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential take the form of a plane wave modulated by a periodic function. The theorem is named after the physicist Felix Bloch, who di ...

vector

k_\text

. A constant force

F_0

results in the acceleration of the particle until the edge of the first

Brillouin zone In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice ...

is reached. The following sudden change in velocity from

+\hbar k_\text/m

-\hbar k_\text/m

can be interpreted as a

Bragg scattering In physics and chemistry , Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a crystal lattice. It encompasses the superposition of wave ...

of the particle by the lattice potential. As a result, the velocity of the particle never exceeds

, \hbar k_\text/m,

but oscillates in a saw-tooth like manner with a corresponding periodic oscillation in position space. Surprisingly, despite of the constant acceleration the particle does not translate, but just moves over very few lattice sites. Super Bloch oscillations arise when an additional periodic driving force is added to

F_0

, resulting in:

F(t) = F_0 + \Delta F \sin(\omega t + \varphi)

The details of the motion depend on the ratio between the driving frequency

\omega

and the Bloch frequency

\omega_B

. A small detuning

\omega-\omega_B

results in a beat between the Bloch cycle and the drive, with a drastic change of the particle motion. On top of the Bloch oscillation, the motion shows a much larger oscillation in position space that extends over hundreds of lattice sites. Those Super Bloch oscillations directly correspond to the motion of normal Bloch oscillations, just rescaled in space and time. A quantum mechanical description of the rescaling can be found here. An experimental realization is demonstrated in these. A theoretical analysis of the properties of Super-Bloch Oscillations, including dependence on the phase of the driving field is found here.

References

{{reflist Concepts in physics Oscillation