Quantum coherence and correlations in cold atom systems

Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical" and "quantum" can be made for systems composed of many particles when the properties of the ensemble are determined by the correlations between the constituents. The issue of grasping the nature of entanglement (i.e. quantum correlations) lies in its formal, discriminative definition: "if state is not classical then it is entangled". A possible remedy would be to approach the problem from the utilitarian point of view. The idea is that certain tasks can be performed better when entangled states are used instead of states that are only classically correlated. An example of such task is an entanglement-enhanced interferometer utilizing ensembles of ultra-cold atoms. This line of reasoning leads to the concept of classification of entanglement by the degree of usefulness and allows to relate it to certain well-defined physical properties of the state. The aim of this work is to formalize this abstraction and build upon it an intuitive picture which can help us understand what the entanglement is.