Quantum dynamics in phase space: From coherent states to the Gaussian representation

We give an outlook on the future of coherence theory and manybody quantum dynamics as experiments develop in the arena of ultra-cold atoms. Novel results on quantum heating of center-of-mass temperature in evaporative cooling and simulation methods for long-range interactions are obtained, using positive-P phase-space techniques. 1 Coherence theory in the 21st century One recognition of important developments in coherence theory was the 2005 Nobel award in Physics, one half to Roy J. Glauber, ‘for his contribution to the quantum theory of optical coherence’ , and one half to Ted Haensch and Jan Hall ‘for their contributions to the development of laser-based precision spectroscopy’ . This richly deserved award recognizes crucial developments in quantum optics and laser science in the second half of the twentieth century. One may ask now: What is the future of coherence theory? One answer to this question lies in the groundbreaking work of experimentalists working with ultra-cold atoms. Perhaps the ideal quantum system for experimental investigation, ultracold atoms display many useful properties under active investigation, including: • Ultra-low temperatures to below 1nK • Bose-Einstein condensates (BEC): atom ‘photons’ • Quantum superfluid degenerate Fermi gases (DFG): atom ‘electrons’