Propagation and Reduction of Coherent States in Bargmann Spaces
Coherent states are special types of wavefunctions that minimize a generalized uncertainty principle for a suitable pair of operators. Equivalently, they are eigenstates of an appropriate annihilation operator. Their applications are extensive throughout physics including in quantum optics, nuclear physics, quantum field theory, path integral formulations, and quantum information through the study of entanglement and quantum measurement. This thesis explores two main topics. First, we consider
... he Schrödinger evolution of a Gaussian coherent state under a non-Hermitian Hamiltonian. We develop a symbol calculus and use it to construct an approximate solution to the time-dependent Schrödinger equation. We find the evolution equations of the center and the Gaussian matrix of the coherent state, which form a system. This result generalizes the previously-known case where the classical Hamiltonian is quadratic. In the second part of the thesis, we apply a quantum version of dimensional reduction to construct Gaussian coherent states in the Bargmann space of complex projective space. The semiclassical properties of these reduced states are controlled by a suitable notion of symbol. Making use of these properties, we provide norm estimates and a propagation result for Hermitian Hamiltonians. As a special case of these reduced states, we define and examine spin-squeezed states that live naturally in the Bargmann space of the Riemann sphere.