The Non-linear Quantum Dynamics of Superconducting Circuitry
Over the last few decades, it has been established that the Josephson junction's (JJ) non-linear nature can be used to manufacture novel quantum Hamiltonians. The uneven spacing in the energy levels of circuits containing one or more Josephson junctions means that they can be thought of as form...
| Main Author: | |
|---|---|
| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/74656/ |
| _version_ | 1848800877772537856 |
|---|---|
| author | Morley, Grace |
| author_facet | Morley, Grace |
| author_sort | Morley, Grace |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Over the last few decades, it has been established that the Josephson junction's (JJ) non-linear nature can be used to manufacture novel quantum Hamiltonians. The uneven spacing in the energy levels of circuits containing one or more Josephson junctions means that they can be thought of as forming something like an atom. These artificial atoms, when connected to one or more quantum harmonic oscillators formed by microwave cavities, can then be used to study the interaction of light and matter in a new field called circuit quantum electrodynamics (cQED).
A subset of these systems, which combine a voltage biased Josephson junction in series with a cavity, bring together charge dynamics with microwave photonics in an interesting way. In these devices, Cooper pairs can tunnel through the circuity only when the energy supplied by the voltage matches that of a transition within the microwave cavity. When this condition is met, the Cooper pair tunnelling evolves from incoherent to coherent tunnelling as the Josephson energy of the junction is increased.
In this thesis, we will explore the dynamics of a JJ-cavity system voltage biased such that each Cooper pair has energy equal to half that of the transition in one of the cavity modes, this being the simplest possible case of super harmonic driving. We find that the presence of the cavity mode promotes tunnelling of the Cooper pairs at the same time. We use a second order rotating wave approximation to derive an effective time-independent Hamiltonian that describes this behaviour and we use it to explore how the state of the cavity mode evolves as the Josephson energy of the junction is increased. We also explore the way in which charge is transported through the system, identifying regimes of both incoherent and coherent double Cooper pair tunnelling.
This thesis will also examine the dynamics of a Josephson junction cavity system where more then one mode can play an important role, know as the Josephson laser. We will start by examining the behaviour of a system with a very large number of modes. We find that in this case the system exhibits a wide range of dynamical behaviour as a function of the strength of the applied drive. Surprisingly it can take an extremely long time for the system to reach a stable regime (beyond any transient behaviour). We also explore the behaviour in cases where a relatively small number of modes are included. Here the pattern is less complex, but still very interesting. We show how this system undergoes a discrete time symmetry breaking transition as the drive strength increases, and how this transition can occur in two different ways, continuous and discontinuous. We prove that the conditions that determine if the transition will be continuous or discontinuous are related to the destabilization of the zero amplitude solution, which in turn is dependent on the relationship between the number of modes present and the voltage. |
| first_indexed | 2025-11-14T20:58:33Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-74656 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:58:33Z |
| publishDate | 2023 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-746562024-08-15T11:54:55Z https://eprints.nottingham.ac.uk/74656/ The Non-linear Quantum Dynamics of Superconducting Circuitry Morley, Grace Over the last few decades, it has been established that the Josephson junction's (JJ) non-linear nature can be used to manufacture novel quantum Hamiltonians. The uneven spacing in the energy levels of circuits containing one or more Josephson junctions means that they can be thought of as forming something like an atom. These artificial atoms, when connected to one or more quantum harmonic oscillators formed by microwave cavities, can then be used to study the interaction of light and matter in a new field called circuit quantum electrodynamics (cQED). A subset of these systems, which combine a voltage biased Josephson junction in series with a cavity, bring together charge dynamics with microwave photonics in an interesting way. In these devices, Cooper pairs can tunnel through the circuity only when the energy supplied by the voltage matches that of a transition within the microwave cavity. When this condition is met, the Cooper pair tunnelling evolves from incoherent to coherent tunnelling as the Josephson energy of the junction is increased. In this thesis, we will explore the dynamics of a JJ-cavity system voltage biased such that each Cooper pair has energy equal to half that of the transition in one of the cavity modes, this being the simplest possible case of super harmonic driving. We find that the presence of the cavity mode promotes tunnelling of the Cooper pairs at the same time. We use a second order rotating wave approximation to derive an effective time-independent Hamiltonian that describes this behaviour and we use it to explore how the state of the cavity mode evolves as the Josephson energy of the junction is increased. We also explore the way in which charge is transported through the system, identifying regimes of both incoherent and coherent double Cooper pair tunnelling. This thesis will also examine the dynamics of a Josephson junction cavity system where more then one mode can play an important role, know as the Josephson laser. We will start by examining the behaviour of a system with a very large number of modes. We find that in this case the system exhibits a wide range of dynamical behaviour as a function of the strength of the applied drive. Surprisingly it can take an extremely long time for the system to reach a stable regime (beyond any transient behaviour). We also explore the behaviour in cases where a relatively small number of modes are included. Here the pattern is less complex, but still very interesting. We show how this system undergoes a discrete time symmetry breaking transition as the drive strength increases, and how this transition can occur in two different ways, continuous and discontinuous. We prove that the conditions that determine if the transition will be continuous or discontinuous are related to the destabilization of the zero amplitude solution, which in turn is dependent on the relationship between the number of modes present and the voltage. 2023-12-12 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/74656/2/Grace_Thesis.pdf Morley, Grace (2023) The Non-linear Quantum Dynamics of Superconducting Circuitry. PhD thesis, University of Nottingham. Nonlinear Dynamics Josephson Junction single photon Quantum circuits superconducting circuits quantum electrodynamics |
| spellingShingle | Nonlinear Dynamics Josephson Junction single photon Quantum circuits superconducting circuits quantum electrodynamics Morley, Grace The Non-linear Quantum Dynamics of Superconducting Circuitry |
| title | The Non-linear Quantum Dynamics of Superconducting Circuitry |
| title_full | The Non-linear Quantum Dynamics of Superconducting Circuitry |
| title_fullStr | The Non-linear Quantum Dynamics of Superconducting Circuitry |
| title_full_unstemmed | The Non-linear Quantum Dynamics of Superconducting Circuitry |
| title_short | The Non-linear Quantum Dynamics of Superconducting Circuitry |
| title_sort | non-linear quantum dynamics of superconducting circuitry |
| topic | Nonlinear Dynamics Josephson Junction single photon Quantum circuits superconducting circuits quantum electrodynamics |
| url | https://eprints.nottingham.ac.uk/74656/ |