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Towards large-scale entanglement with neutral atoms in optical lattices

Final Activity Report Summary - ENTANGLED ATOMS (Towards large-scale entanglement with neutral atoms in optical lattices)

The laws of quantum mechanics are a challenge to our everyday intuition. At a microscopic level, they are verified to an unprecedented level of accuracy. However, some key concepts are hardly compatible with our experience. Among them is the uncertainty relation, which prevents the position and velocity of a quantum object to be perfectly defined at the same time, or the wave-particle duality. They seem even more paradoxical when applied to large objects, such as the famous Schrodinger cat which, if behaving as a quantum system, can be put in a state where it stays suspended between life and death.

The predictions of quantum mechanics for such large ensembles of particles can be tested to a high accuracy using atomic gases held in a ultra-high-vacuum environment and cooled within a few billionths of degrees above the absolute zero. At such extremely cold temperatures, tiny droplets known as Bose-Einstein condensates behave as a quantum fluid: the atoms forming the condensate lose their individuality and display striking wave-like behaviour. In particular, they can be trapped in optical lattices, a periodic, three-dimensional landscape of alternating hills and valleys. Atoms close to the absolute zero accumulate in the valleys, forming a periodic density distribution. When the condensate is released from this periodic landscape, it develops a striking interference pattern, implying that the gaseous droplet can also behave as a 'giant matter wave' However, in certain cases where the repulsion between the atoms is very strong, they force this quantum fluid to turn into another form of quantum matter, characterized by a regular pattern with (almost) exactly an integer number of atoms per lattice site. This is a spectacular example where repulsive interactions are able to turn an extremely cold and dilute gaseous sample into a nearly perfect 'atomic crystal' maintained by the laser light. Because the same repulsive interactions also inhibit the flow of matter across the lattice potential, this ordered state is termed a Mott insulator.

In this Mott insulator, the wave behaviour seems essentially absent. The interference pattern is no longer observed, as it was for a Bose-Einstein condensate. However, we have been able to show that a clever measurement scheme was able to reveal this interference where it is seemingly absent. The key step was to measure the probability to find two atoms a certain distance apart after they have been released from the trap. For most distances, nothing particular is observed, but for specific, regularly spaced spots that are related to the initial regular distribution of the atoms, sharp peaks were observed in close analogy with the interference pattern produced by a condensate. This correlated behaviour implies that the atoms try to maintain a certain pattern as they expand, a consequence of the initial regular distribution of the atoms. We believe that this method can be applied to detect even more exotic forms of quantum matter. Additionally, we have discovered that a Mott insulator actually displayed some wave behaviour under precise circumstances, and have shown this to be a fundamental feature of these systems. Our study provides further insight into this peculiar state of matter.

Further insights into the puzzling rules of the quantum mechanical world were obtained in other experiments, where quantum superpositions of atom pairs induced by inter-atomic collisions were investigated in detail. Apart from fundamental studies, these experiments allow to characterize the collision between the two atoms forming the pair to an amazing accuracy. In addition, they pave the way to the creation of entangled states of many-atoms, where the gaseous droplet is found in a completely counter-intuitive situation.