Quantum gases in optical boxes

Quantum atomic and molecular gases are flexible systems for studies of fundamental many-body physics. They have traditionally been produced in harmonic electromagnetic traps and thus had inhomogeneous densities, but recent advances in light shaping for optical trapping of neutral particles have led to the development of flat-bottomed optical box traps, allowing the creation of homogeneous samples. Box trapping simplifies the interpretation of experimental results, provides more direct connections with theory and, in some cases, allows qualitatively new, hitherto impossible experiments. It has now been achieved for both Bose and Fermi atomic gases in various dimensionalities, and also for gases of heteronuclear molecules. Here we review these developments and the consequent breakthroughs in the study of both equilibrium and non-equilibrium phenomena such as superfluidity, turbulence and the dynamics of phase transitions. Optical box traps create a potential landscape for quantum gases that is close to the homogeneous theoretical ideal. This Review of box trapping methods highlights the breakthroughs in experimental many-body physics that have followed their development.