Spin squeezing is a bulk, non-classical effect that can occur in spin systems and occurs when fluctuations between two observables are redistributed while still maintaining the minimum uncertainty product. Planar-quantum squeezing is a similar phenomenon where there are decreased spin variances in two orthogonal spin components. In the work that follows, we consider specifically the realization of a spin-j system, a collection of N = 2j two-level atoms, in accordance with the famous Dicke model for such a system. Both spin and planar-quantum squeezing act as entanglement witnesses. This means that where we observe spin squeezing we should also observe entanglement. This does not hold in the opposite direction, however, observing entanglement does not necessarily imply the presence of spin squeezing in a system. In this thesis, we investigate spin squeezing and planar-quantum squeezing for a variety of increasingly exotic quantum states. We also examine states resulting from the action of a multitude of angular momentum operators on these states. A major goal of the research is to identify those locations in state space, as represented via the Bloch Sphere, at which spin and planar-squeezing (a) exists and (b) is optimal for each of the states we consider. The areas of maximal squeezing imply that we should expect a high degree of entanglement in the same areas. To corroborate this, we calculate the state purity as a well-known quantifier of the degree of entanglement in a global system comprised of two interacting subsystems. This choice necessarily restricts our entanglement study of each category of state we consider to the j = 1 (N = 2 atoms) "toy model" case. Still, we expect to gain important input into the spin squeezing/entanglement connection even for more complex cases in which unique entanglement measures are, so far, lacking. Other calculations that we perform for each state include the excitation statistics, which we relate to quantum interference, as well as the intensity of spontaneous emission which can lead to future work to study topics such as superradiance from collections of two-level atoms in the non-classical states we study here.

Publication Date


Document Type


Student Type


Degree Name

Physics (MS)

Department, Program, or Center

Physics and Astronomy, School of


College of Science


Edwin Hach

Advisor/Committee Member

Gregory Howland

Advisor/Committee Member

Michael Pierce


RIT – Main Campus