{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23887"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23887","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Theory of voltage oscillations in ultra-small capacitance Josephson junctions","abstract":"\"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.\"","abstract_html":""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."","abstract_has_math":false,"creators":["Dorsey, Alan Thomas"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Leggett, Anthony J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-16T19:00:22Z","date_published":"2011-05-16T19:00:22Z","updated_at":"2026-07-22T22:25:22Z","subjects":["voltage oscillations","ultra-small capacitance Josephson junctions","junction dynamics"],"languages":["en"],"rights":["1987 Alan Thomas Dorsey"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["1853990"],"render_values":[{"text":"1853990","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23887","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leggett, Anthony J."]},{"key":"dc:creator","label":"Author","values":["Dorsey, Alan Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-16T19:00:22Z","10000-01-01","1987"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["voltage oscillations","ultra-small capacitance Josephson junctions","junction dynamics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1987 Alan Thomas Dorsey"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["1853990","http://hdl.handle.net/2142/23887"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"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.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-16T19:00:22Z No. of bitstreams: 1 1987_dorsey.pdf: 5075999 bytes, checksum: e173b13387b71a49a21245bfa774eeff (MD5)","Made available in DSpace on 2011-05-16T19:00:22Z (GMT). No. of bitstreams: 1 1987_dorsey.pdf: 5075999 bytes, checksum: e173b13387b71a49a21245bfa774eeff (MD5) Previous issue date: 1987","Restriction data tranferred 2014-07-01T11:13:26-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-16T19:00:22Z Item is restricted indefinitely.","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Theory of voltage oscillations in ultra-small capacitance Josephson junctions"]}]}],"canonical_facts":{"dc:contributor":["Leggett, Anthony J."],"dc:creator":["Dorsey, Alan Thomas"],"dc:date":["2011-05-16T19:00:22Z","10000-01-01","1987"],"dc:description":["\"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.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-16T19:00:22Z No. of bitstreams: 1 1987_dorsey.pdf: 5075999 bytes, checksum: e173b13387b71a49a21245bfa774eeff (MD5)","Made available in DSpace on 2011-05-16T19:00:22Z (GMT). No. of bitstreams: 1 1987_dorsey.pdf: 5075999 bytes, checksum: e173b13387b71a49a21245bfa774eeff (MD5) Previous issue date: 1987","Restriction data tranferred 2014-07-01T11:13:26-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-16T19:00:22Z Item is restricted indefinitely.","Thesis","U of I Only"],"dc:identifier":["1853990","http://hdl.handle.net/2142/23887"],"dc:language":["en"],"dc:rights":["1987 Alan Thomas Dorsey"],"dc:subject":["voltage oscillations","ultra-small capacitance Josephson junctions","junction dynamics"],"dc:title":["Theory of voltage oscillations in ultra-small capacitance Josephson junctions"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:22Z"}