Constraints on the spontaneous collapse mechanism: theory and experiments

Quantum mechanics, with the usual orthodox interpretation, leads to the problem of macroscopic linear superpositions: to avoid them the wave-function collapse postulate was introduced, forcing an arbitrary distinction between the microscopic (the system) and the macroscopic (the measurement apparatus). To resolve this issue, spontaneous collapse models suggest to combine the Schrödinger evolution with the wave-function collapse in a single dynamical law: in the microscopic regime we reobtain the predictions of quantum mechanics, within experimental errors, while for macroscopic objects we obtain a classical dynamics. In particular, the Schrödinger equation is modified by non-linear interaction terms with a noise field. However, this has led to a multitude of different collapse models and model dependent experimental tests. In this thesis we asked the following two natural questions: can we single out, with theoretical arguments, a particular collapse model (part I) and is there a model independent experimental test (part II)? In part I we have considered a generic Gaussian diffusion process describing guiding the wave function. We have then considered the following constraints: (i) probabilistic interpretation (trace conservation), (ii) the state vector evolves towards an eigenstate of the collapse operator, (iii) translational covariance and (iv) stationary initial conditions of the noise field. We have then successfully characterized the existing collapse models in terms of the additional requests imposed on top of the basic requests (i)-(iv): color (non-Markovian) and dissipation. Besides conditions (i)-(iv) we considered two additional reasonable constraints: (v) the noise is a field over physical space and the dissipation leads to (vi) an asymptotic Gibbs state. In particular, we have shown that from the requests (i)-(vi) we identify a single dynamical map (CD) for the statistical operator: in the appropriate limits the map reduces to the colored (cCSL) and dissipative (dCSL) continuous spontaneous localization (CSL) maps. However, the request (vi) breaks Galilean boost covariance of the dynamical map: we discuss the relation between dissipation and boost covariance and argue that the noise field could have a cosmological origin. In addition, we have proposed a novel collapse model, namely the colored and dissipative CSL (cdCSL), that generalizes the cCSL and dCSL evolution for the state vector: the corresponding dynamical map is by construction the CD map. Based on the previous results, in part II we have considered the theoretical predictions of the CD map for interferometry experiments: these offer a direct test of the superposition principle and thus a direct test of the collapse mechanism. We have shown that, unlike other experiments, the results are unaffected by color and dissipation and thus provide a model-independent test. In particular, we have analyzed in the detail the CD map theoretical predictions for the far field and near field Kapitza Dirac Talbot Lau (KDTL) experiments. We have obtained the exclusion diagram for the collapse mechanism parameters: the upper bounds are obtained from the KDTL experiment, while the lower bounds are estimated by requiring a quick localization of a thin graphene disk. This analysis, apart from the relevance for collapse models phenomenology, is also important for the larger scientific community interested in the experimental limits of the superposition principle.