Empirical Manifestations of Integrability in Cold Quantum Gases

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Integrable quantum many-body systems traditionally belong to the domainof mathematical physics, with little or no connection to experiments. However, the experiments on confined quantum-degenerate gases has recently yielded faithful AMO realizations of a number of integrable systems. The new phenomenological relevance of integrable models, unique to atomic, molecular, and optical physics, opens up the possibility of a new research direction that is the focus of this proposal: the experimental manifestations of integrability in cold dilute quantum gases.It is shown that the presence of nontrivial conserved quantities in a quantum system leads to dramatic, initial-state-dependent discrepancy between the equilibrium state of the system and the predictions of thermodynamics. A new thermodynamic ensemble is suggested and successfully numerically tested: there all integrals of motion participate on an equal footing.Furthermore, the relaxation dynamics in an integrable system is conjectured to be very different from generic: it cannot be reduced to the analysis of few-body collisions, but is rather a substantially many-body effect. Overall, it is argued that the kinetic and thermodynamic properties of integrable quantum gases are so different from the usual, that they well-qualify for a new state of quantum matter.The objects of study chosen include bosons in one-dimensional optical lattices in the deep Mott regime, spin-0 Bose and spin-1/2 Fermi gases confined to waveguides, and two-dimensional harmonically trapped Bose condensates, all of which have been experimentally realized already.Momentum distribution and chemical composition are suggested as the simplest experimental observables sensitive to the effects of integrability.