Library of Congress Cataloging-in-Publication Data Metcalf, Harold J.Laser cooling and trapping / H.J. Metcalf, P. van der Straten. p. cm. -(Graduate texts in contemporary physics) Includes bibliographical references and index.

We present the zero-temperature phase diagram of bosonic atoms in an optical lattice, using two different mean-field approaches. The phase diagram consists of various insulating phases and a superfluid phase. We explore the nature of the insulating phase by calculating both the quasiparticle and quasihole dispersion relation. We also determine the parameters of our single band Bose-Hubbard model in terms of the microscopic parameters of the atoms in the optical lattice.

Using the technique of stimulated Raman adiabatic passage (STIRAP) we have coherently transferred ultracold (87)Rb(2) Feshbach molecules into a more deeply bound vibrational quantum level. Our measurements indicate a high transfer efficiency of up to 87%. Because the molecules are held in an optical lattice with not more than a single molecule per lattice site, inelastic collisions between the molecules are suppressed and we observe long molecular lifetimes of about 1 s. Using STIRAP we have created quantum superpositions of the two molecular states and tested their coherence interferometrically. These results represent an important step towards Bose-Einstein condensation of molecules in the vibrational ground state.

Time crystals are a phase of matter, for which the discrete time symmetry of the driving Hamiltonian is spontaneously broken. The breaking of discrete time symmetry has been observed in several experiments in driven spin systems. Here, we show the observation of a space-time crystal using ultra-cold atoms, where the periodic structure in both space and time are directly visible in the experimental images. The underlying physics in our superfluid can be described ab initio and allows for a clear identification of the mechanism that causes the spontaneous symmetry breaking. Our results pave the way for the usage of space-time crystals for the discovery of novel nonequilibrium phases of matter. arXiv:1807.05904v2 [cond-mat.quant-gas]

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