A thesis submitted December 19, 2014 for the degree of Doctor of Philosophy and defended February 12, 2015.
The PhD School of Science
Faculty of Science, Niels Bohr Institute, Theoretical Quantum Optics, University of Copenhagen, Denmark
Anders S. Sørensen
Dissipative preparation of entanglement in quantum optical and solid state systems
Quantum mechanics is an immensely successful theory which is essential for the explanation of numerous phenomena in atomic physics, solid state physics, nuclear physics and elementary particle physics. Quantum theory also involves effects which have no analogy in the classical world. In particular, quantum entanglement is a correlation predicted by quantum mechanics, but not by classical physics. As an observable property it is indispensable for our understanding of nature. In addition, entangled states are important in quantum computation, quantum communication and quantum measurement protocols. Entangled states are, however, sensitive to interactions with the environment, which are present in any open system. Here, in particular decoherence, i.e. loss of coherence, and dissipation, i.e. loss of energy, destroy the desired correlations. The novel approach of “dissipative quantum computing” and “dissipative state engineering” suggests to use the interaction with the environment to perform quantum information tasks. Here, decay processes are no longer undesirable, but play an integral part in the dynamics. Following this approach, we consider the dissipative preparation of two-particle and multi-particle entangled states in several concrete physical systems such as optical cavities, trapped ions, and superconducting qubits. To study the dynamics of open quantum systems, we first develop an operator formalism which allows us to identify the effective interactions. Eliminating the decaying states from the dynamics of a weakly driven system, we derive an effective master equation which reduces the evolution to the ground states. We obtain simple expressions for the effective operators which can be directly applied to reach effective equations of motion for the ground states, as is demonstrated considering several widely used example systems.
Using this operator formalism we identify the effective interactions in the physical systems under consideration and engineer them to prepare a desired entangled target state. This state is then reached regardless of the initial state of the system and stabilized as the unique steady state of the dissipative time evolution. In this way, we develop theoretical schemes for the generation of two-particle entangled states in optical cavities, superconducting systems and trapped ions. For optical cavities, we harness the natural decay processes of cavity photon loss and spontaneous emission to prepare the maximally entangled singlet state of the system. We analytically derive the optimal parameters, the error and the speed of convergence of our protocols and find a qualitative improvement of the error as compared to previous methods.
A similar scheme is presented for two superconducting qubits in a circuit QED setup. Combining resonator photon loss, a dissipative process already present in the setup, with an effective two-photon microwave drive, we engineer an effective decay mechanism which prepares a maximally entangled state of two qubits. We find that high fidelities with the target state can be achieved both with state-of-the-art three-dimensional, as well as with the more commonly used two-dimensional transmon qubits.