Transformation design and nonlinear Hamiltonians

Brougham, Thomas and Chadzitaskos, Goce and Jex, Igor (2009) Transformation design and nonlinear Hamiltonians. Journal of Modern Optics, 56 (14). pp. 1588-1597. ISSN 0950-0340

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Abstract

We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple 'beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.