Abstract:
Starting with a thermal squeezed state defined as a conventional thermal state based on an appropriate hamiltonian, we show how an important physical property, the signal-to-noise ratio, is degraded, and propose a simple model of thermalization (Kraus thermalization).

Abstract:
We analyze the properties of nonclassical number states, specifically squeezed number states D(a)S(z)|n >, and find their maximum signal-to-quantum noise ratio. It is shown that the optimal signal-to-quantum noise ratio for these states decreases as 1/(2n+1)2, where n is the photon number, from the optimal value as derived by Yuen.

Abstract:
We investigate the dynamics of a four-photon Jaynes-Cummings model for large photon number. It is shown that at certain times the cavity field is in a pure state which is a superposition of two Kerr states, analogous to the Schr\"{o}dinger cat state (superposition of two coherent states) which occurs in the one and two photon cases.

Abstract:
A state in quantum mechanics is defined as a positive operator of norm 1. For finite systems, this may be thought of as a positive matrix of trace 1. This constraint of positivity imposes severe restrictions on the allowed evolution of such a state. From the mathematical viewpoint, we describe the two forms of standard dynamical equations - global (Kraus) and local (Lindblad) - and show how each of these gives rise to a semi-group description of the evolution. We then look at specific examples from atomic systems, involving 3-level systems for simplicity, and show how these mathematical constraints give rise to non-intuitive physical phenomena, reminiscent of Bohm-Aharonov effects. In particular, we show that for a multi-level atomic system it is generally impossible to isolate the levels, and this leads to observable effects on the population relaxation and decoherence.

Abstract:
For a 3-qubit Heisenberg model in a uniform magnetic field, the pairwise thermal entanglement of any two sites is identical due to the exchange symmetry of sites. In this paper we consider the effect of a non-uniform magnetic field on the Heisenberg model, modeling a magnetic impurity on one site. Since pairwise entanglement is calculated by tracing out one of the three sites, the entanglement clearly depends on which site the impurity is located. When the impurity is located on the site which is traced out, that is, when it acts as an external field of the pair, the entanglement can be enhanced to the maximal value 1; while when the field acts on a site of the pair the corresponding concurrence can only be increased from 1/3 to 2/3.

Abstract:
A necessary and sufficient condition for the maximal entanglement of bipartite nonorthogonal pure states is found. The condition is applied to the maximal entanglement of coherent states. Some new classes of maximally entangled coherent states are explicited constructed; their limits give rise to maximally entangled Bell-like states.

Abstract:
We study the constraints imposed on the population and phase relaxation rates by the physical requirement of completely positive evolution for open N-level systems. The Lindblad operators that govern the evolution of the system are expressed in terms of observable relaxation rates, explicit formulas for the decoherence rates due to population relaxation are derived, and it is shown that there are additional, non-trivial constraints on the pure dephasing rates for N>2. Explicit experimentally testable inequality constraints for the decoherence rates are derived for three and four-level systems, and the implications of the results are discussed for generic ladder-, Lambda- and V-systems, and transitions between degenerate energy levels.

Abstract:
We show that a quantum control procedure on a two-level system including dissipation gives rise to a semi-group corresponding to the Lie algebra semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in the Bloch ball.

Abstract:
A dynamical group for the single-particle (non-interacting) Quantum Hall Effect is found, and used to describe the Landau levels and determine the transverse (Hall) current.

Abstract:
We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the $\eta$-pairing operators introduced by C.N.Yang, and define coherent pairing states, which are combinations of eigenfunctions of $\eta$-operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing ODLRO to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.