Master Thesis Defense by Luca Dellantonio – University of Copenhagen

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Master Thesis Defense by Luca Dellantonio

Spin squeezing is a fundamental instrument for beating the standard quantum limit in measurement precision. Experimentally, it has already been achieved and tested, proving its advantage with respect to classical systems. From an elementary point of view, there are two key features of these experiments: the creation and the detection of entanglement. For the latter, the squeezing parameter is the most used criterion: it consists of a simple inequality that can be easily veri?fied. It represents a powerful, suffi?cient criterion for proving the existence of quantum correlation in an ensemble of atoms. Moreover, in terms of measurement, it involves only the mean and variance of the collective spin operator in the z and x direction respectively.

However, in a typical experiment atoms are generally not equally illuminated by the probing beam, and thus we can suppose they do not contribute equally to the measurement. It is thus important to understand the eff?ect of this on the squeezing parameter, to make the entanglement measures suitable to realistic situations. In this thesis, we fi?rst point out the necessity of the creation of a new entanglement criterion, showing the failure of the squeezing parameter in experiments involving ensembles of particles. Later on, we introduce this new criterion and generalize it for the detection of multi-partite entanglement. Finally, we apply the theory we developed to analyse experimental data, establishing more than 2-particle entanglement in an atomic ensemble.