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• W1617331407 abstract "In this thesis we investigate the entanglement ofSchrodinger cat states that derive from harmonic oscillatormodels. In order to extend the finite dimensional framework ofentanglement to the in finite dimensional case we consider onlyinitial conditions that have some type of symmetry. Systems withsymmetry usually have fewer important parameters. In our case,symmetry allows us to discard the bulk of the Hilbert space asirrelevant to our particular entanglement problem. We are then leftwith an effectively finite dimensional Hilbert space, and thedeveloped entanglement framework can therefore be followed. Thedimension we derive for the reduced Hilbert space in eachsubsystem is equal to the number of coherent states in theSchrodinger cat superposition. We investigate the entanglement vs.time of our Schrodinger cat state for closed and open systems. Forclosed systems, we place no limit on the number of coherentlysummed linearly independent coherent states. So the dimension ofour effective Hilbert space can be quite high. We also place norestriction on the number of subsystems (or parties).Consequently, we use the entanglement measure developed by Barnum,Knill, Ortiz, and Viola (BKOV). This is the only measure to ourknowledge that has no restriction on the dimension of the Hilbertspace or the number of subsystems. We also place no constraint onthe magnitude of our coherent states. The coherent value may bequite large, or quite small. We find that the entanglement of theSchrodinger cat state has nontrivial dependence on the abovementioned three variables. That is, the entanglement is anon-separable function of the values of the coherent states, thenumber of coherent states in the superposition, and the number ofpartitions of the Hilbert space. For open systems, we model thereservoir as a harmonic oscillator zero temperature bath. Due tothe interactions with the bath the Schrodinger cat state becomes amixed density matrix. To investigate the time dependententanglement of our density matrix, we apply the convex roofextension of the BKOV measure. This required development of analgorithm to search the space of decompositions of the densitymatrix. The time dependence depends on the symmetry of the system,naturally splitting the Hilbert space into a direct sum of twosubspaces. One subspace interacts strongly with the bath resultingin rapid decoherence. The other complimentary subspace does notinteract at all with the bath and is decoherence free. For initialstates in the decohering subspace we find that for large values ofthe coherent state, the decay of entanglement corresponds to thedecay rate of correlations in the bath. We are able to derive thisresult analytically. For small values of the coherent states, theloss of entanglement corresponds to the decay of the coherentstate amplitude. Finally, we consider initial states that live inthe combined Hilbert space. Decoherence then provides a means ofengineering a new state through decay of the component…" @default.
• W1617331407 created "2016-06-24" @default.
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• W1617331407 date "2009-01-01" @default.
• W1617331407 modified "2023-09-24" @default.
• W1617331407 title "Study of continuous variable entanglement in multipartite harmonic oscillator systems" @default.
• W1617331407 hasPublicationYear "2009" @default.
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