Strongly interacting Bose gas: Nozières and Schmitt-Rink theory and beyond

We calculate the critical temperature for Bose-Einstein condensation in a gas of bosonic atoms across a Feshbach resonance and show how medium effects at negative scattering lengths give rise to pairs reminiscent of the ones responsible for fermionic superfluidity. We find that the formation of pairs leads to a large suppression of the critical temperature. Within the formalism developed by Nozi\`eres and Schmitt-Rink, the gas appears mechanically stable throughout the entire crossover region, but when interactions between pairs are taken into account we show that the gas becomes unstable close to the critical temperature. We discuss prospects of observing these effects in a gas of ultracold ¹³³Cs atoms where recent measurements indicate that the gas may be sufficiently long lived to explore the many-body physics around a Feshbach resonance.