Collapse in ultracold Bose Josephson junctions

Abstract

We investigate how ultracold atoms in double-well potentials can be used to study and put bounds on models describing wave-function collapse. We refer in particular to the continuous spontaneous localization (CSL) model, which is the most well studied among dynamical reduction models. It modifies the Schr\"odinger equation in order to include the collapse of the wave function in its dynamics. We consider Bose Josephson junctions, where ultracold bosons are trapped in a double-well potential, since they can be experimentally controlled with high accuracy and are suited and used to study macroscopic quantum phenomena on a scale of microns, with a number of particles typically ranging from $\ensuremath{\sim}{10}^{2}--{10}^{3}$ to $\ensuremath{\sim}{10}^{5}--{10}^{6}$. We study the CSL dynamics of three atomic states showing macroscopic quantum coherence: the atomic coherent state, the superposition of two atomic coherent states, and the NOON state. We show that for the last two states, the suppression of quantum coherence induced by the CSL model increases exponentially with the number of atoms. We observe that in the case of optically trapped atoms, the spontaneous photon emission of the atoms induces a dynamics similar to the CSL one, and we conclude that magnetically trapped atoms may be more convenient to experimentally test the CSL model. Finally, we discuss decoherence effects in order to provide reasonable estimates on the bounds that it is (or will be) possible to obtain for the parameters of the CSL model in such class of experiments. As an example, we show that a NOON state with $N\ensuremath{\sim}{10}^{3}$ with a coherence time of $\ensuremath{\sim}1$ s can constrain the CSL parameters in a region where the other systems presently cannot.