Bloch-Like Oscillations in Finite Quantum Structures

Inspired by several attempts to generate Bloch-like oscillations in different fields of physics [1,2], we examine a multitude of oscillator systems and interactions that lead to Bloch oscillations in finite quantum structures. A general requirement is the existence of a common period in the time dependence of different eigenstates which is guaranteed if eigenenergies are distributed in, e.g., a Stark ladder.

We show that one possibility to create a Stark ladder is to vary the individual well widths in a chain of quantum wells. For this system we study the effect of permuting the positions of individual quantum wells and changing the coupling strength as a function of position. It is, furthermore, demonstrated that the application of a magnetic field to a structure of quantum wells may lead to the observation of Bloch oscillations (similar to Bloch oscillations stemming from the Stark effect) and derive rather general mathematical relations between quantum systems that allow the existence of Bloch oscillations.

References:

[1]: G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, and R. Osellame, Nature Communications 4, 1555 (2013)

[2]: H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sanchez-Dehesa, PRL 98, 134301 (2007)