dc.contributor.author Grimmer, Daniel dc.date.accessioned 2020-09-16 20:40:59 (GMT) dc.date.available 2020-09-16 20:40:59 (GMT) dc.date.issued 2020-09-16 dc.date.submitted 2020-08-05 dc.identifier.uri http://hdl.handle.net/10012/16312 dc.description.abstract The dynamics of open quantum systems (i.e., of quantum systems interacting with an uncontrolled environment) forms the basis of numerous active areas of research from quantum thermodynamics to quantum computing. One approach to modeling open quantum systems is via a \textit{Collision Model. For instance, one could model the environment as being composed of many small quantum systems (ancillas) which interact with the target system sequentially, in a series of collisions''. en In this thesis I will discuss a novel method for constructing a continuous-time master equation from the discrete-time dynamics given by any such collision model. This new approach works for any interaction duration, δt, by interpolating the dynamics between the time-points t = n δt. I will contrast this with previous methods which only work in the continuum limit (as δt → 0). Moreover, I will show that any continuum-limit-based approach will always yield unitary dynamics unless it is fine-tuned in some way. Given the central role of information flow between the system and environment plays in open quantum systems, unitary models are wholly insufficient. Thus continuum limit master equations must be fine-tuned to even function as valid models of open quantum systems. For instance, it is common to find non-unitary dynamics in the continuum limit by taking an (I will argue unphysical) divergence in the interaction strengths, g, such that g^2 δt is constant as δt →0. In addition to overcoming the above limitations, the new interpolation-based approach allows for the straightforward treatment of essentially any representation of a quantum system (e.g., Hilbert space vector, density matrix, Bloch vector, probability vector, in addition to a Gaussian state's mean vector and covariance matrix). Examples of each of these representations will be given throughout this thesis. Moreover, the new interpolation-based approach allows for an order-by-order analysis of the dynamics as a series in $\delta t$. This allows us to identify which types of dynamics are fast'' and which are slow'' as well as how this speed'' depends on the interaction Hamiltonian between the system and ancilla. For instance, we can (and will) investigate under what conditions we can see purification effects at first order in δt. As I will show the speed'' of the purification effects are tied to the complexity of the interaction; Purification at first order in δt requires the interaction Hamiltonian to be at least Schmidt rank-2. A necessary condition for thermalization is also discussed. In addition to this purification study, I will present a complete analysis of Gaussian dynamics regarding which types of dynamics appear at which orders in δt under which Hamiltonians. Given a Hamiltonian (either designed or fixed by fundamental considerations e.g., the light-matter interaction) we can determine what dynamics are supported at what orders in δt. Conversely, given some dynamics (e.g., from experiments) we can determine what class of interaction Hamiltonians could support it. dc.language.iso en en dc.publisher University of Waterloo en dc.subject collision model en dc.subject repeated interactions en dc.subject finite duration en dc.subject continuum limit en dc.subject thermodynamics en dc.subject quantum thermodynamics en dc.subject thermometry en dc.subject purification en dc.subject light matter interaction en dc.subject gaussian quantum mechanics en dc.subject bloch sphere en dc.subject quantum information en dc.subject quantum physics en dc.title Interpolated Collision Model Formalism en dc.type Doctoral Thesis en dc.pending false uws-etd.degree.department Physics and Astronomy en uws-etd.degree.discipline Physics (Quantum Information) en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Doctor of Philosophy en uws.contributor.advisor Mann, Robert uws.contributor.advisor Martin-Martinez, Eduardo uws.contributor.affiliation1 Faculty of Science en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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