Uncertainty product of an out-of-equilibrium Bose-Einstein condensate

The variance and uncertainty product of the position and momentum many-particle operators of structureless bosons interacting by a long-range inter-particle interaction and trapped in a single-well potential are investigated. In the first example, of an out-of-equilibrium interaction-quench scenario, it is found that, despite the system being fully condensed, already when a fraction of a particle is depleted differences with respect to the mean-field quantities emerge. In the second example, of the pathway from condensation to fragmentation of the ground state, we find out that, although the cloud's density broadens while the system's fragments, the position variance actually decreases, the momentum variance increases, and the uncertainty product is not a monotonous function but has a maximum. Implication are briefly discussed.Comment: 14 pages, 3 figure

The uncertainty product of an out-of-equilibrium many-particle system

In the present work we show, analytically and numerically, that the variance of many-particle operators and their uncertainty product for an out-of-equilibrium Bose-Einstein condensate (BEC) can deviate from the outcome of the time-dependent Gross-Pitaevskii dynamics, even in the limit of infinite number of particles and at constant interaction parameter when the system becomes 100% condensed. We demonstrate our finding on the dynamics of the center-of-mass position--momentum uncertainty product of a freely expanding as well as of a trapped BEC. This time-dependent many-body phenomenon is explained by the existence of time-dependent correlations which manifest themselves in the system's reduced two-body density matrix used to evaluate the uncertainty product. Our work demonstrates that one has to use a many-body propagation theory to describe an out-of-equilibrium BEC, even in the infinite particle limit.Comment: 26 pages, 5 figure

Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices

Quantum phases and phase transitions of weakly- to strongly-interacting bosonic atoms in deep to shallow optical lattices are described by a {\it single multi-orbital mean-field approach in real space}. For weakly-interacting bosons in 1D, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with {\it many-body} treatments of the Bose-Hubbard model. For strongly-interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in {\it each site} undergo a Tonks-Girardeau-like transition and localize and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.Comment: 12 pages, 3 figure

Quantum dynamics of attractive versus repulsive bosonic Josephson junctions: Bose-Hubbard and full-Hamiltonian results

The quantum dynamics of one-dimensional bosonic Josephson junctions with attractive and repulsive interparticle interactions is studied using the Bose-Hubbard model and by numerically-exact computations of the full many-body Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an equivalence between the evolution in time of attractive and repulsive Josephson junctions with attractive and repulsive interactions of equal magnitude. The full many-body Hamiltonian does not possess this symmetry and consequently the dynamics of the attractive and repulsive junctions are different.Comment: 9 pages, 2 figure

Formation of dynamical Schr\"odinger cats in low-dimensional ultracold attractive Bose gases

Dynamical Schr\"odinger cats can be formed when a one-dimensional attractive Bose-gas cloud is scattered off a potential barrier. Once formed, these objects are stable in time. The phenomenon and its mechanism -- transformation of kinetic energy to internal energy of the scattered atomic cloud -- are obtained by solving the time-dependent many-boson Schr\"odinger equation. Implications are discussed.Comment: 11 pages, 3 figure