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Qubit-controlled displacements in Markovian environments

Tufarelli, T.; (2012) Qubit-controlled displacements in Markovian environments. Doctoral thesis , UCL (University College London).

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Abstract

We study a particular form of interaction Hamiltonian between qubits and quantum harmonic oscillators, whose closed system dynamics results in qubit controlled displacement operations. This simple mechanism has the potential for many applications, such as the preparation of nonclassical states of one or more quantum oscillators, and the possibility to read out the density matrix of quantum oscillator networks in full detail. These possibilities can be of great interest both in the development of Quantum Technologies such as Quantum Information, and in the investigation of the foundations of Quantum Mechanics. We show how this particular form of interaction is realizable in many setups, including nanomechanical systems, ion traps, cavity QED and circuit QED. To make our model more realistic, and study its applicability to real experimental setups, we include in our calculations typical decoherence mechanisms resulting from the coupling of the qubits and oscillators to a thermal Markovian environment, and we investigate the robustness of our protocols with respect to the strength of such unwanted environmental noise. We show how to solve analytically the full master equation of the system, thanks to a hybrid representation in wich the standard Hilbert space formalism is used for the qubits, while the harmonic oscillators are treated via phase-space. In all parts of our work, we make reference to state-of-the-art experimental data to investigate the feasibility of our proposals with present technology.

Type: Thesis (Doctoral)
Title: Qubit-controlled displacements in Markovian environments
Language: English
Additional information: Permission for digitisation not received
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI: https://discovery.ucl.ac.uk/id/eprint/1344094
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