Theory of voltage oscillations in ultra-small capacitance Josephson junctions

"In ultra-small capacitance Josephson junctions, where the junction charging energy Eq =(2e)2 /2C is comparable to or larger than the junction coupling energy EJ, the quantum mechanical nature of the phase of the superconducting order parameter becomes important. Such quantum effects lead to novel behavior in the junction dynamics-supplying a constant current I to such a junction produces voltage or ""Bloch"" oscillations with a frequency WB = 211""1 /2e, which are the result of the periodic transfer a Cooper pair of charge 2e across the junction. This thesis examines certain theoretical aspects of these Bloch oscillations. Chapters 1 and 2 contain an introduction to the physics of Josephson junctions and Bloch oscillations. Chapter 3 introduces a phenomenological Hamiltonian which models the dissipation due to unpaired electrons in the junction as a resistive shunt R across the junction. Calculations of the junction dynamics using the phenomenological model are in Chapter 4. Using a path integral approach, the translational properties of the phase are treated using a winding number description, and it is shown that for ohmic dissipation the phase may be treated as an extended coordinate. It is then shown that the Bloch oscillations persist in the presence of dissipation, provided that the dissipation satisfies R > 2Rq, where Rq =h/4e2 =6.4k!l. The behavior in the presence of an additional applied AC current of frequency W is also studied, and it is argued that the DC voltage across the junction should pass through zero whenever the applied DC current is an integer multiple of I = 2ew/211"". Chapter 5 considers the effects of interband or ""Zener"" transitions by introducing a simple model to study how dissipation affects the rate of interband transitions. Chapter 6 is a synopsis of some experiments which may indirectly provide evidence of Bloch oscillations. Finally, Chapter 7 concludes with some possible extensions of this work to other problems, and lists some open questions which require further theoretical consideration."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2011

Author dc:creator

• Dorsey, Alan Thomas

Contributors dc:contributor

• Leggett, Anthony J.

• voltage oscillations
• ultra-small capacitance Josephson junctions
• junction dynamics

Statement dc:rights

• 1987 Alan Thomas Dorsey

Language dc:language

en

Identifier

1853990

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23887