Two-Boson Correlations in Various One-Dimensional Traps

T. Jacqmin

In this manuscript, we present spatial one and two-body correlation measurements performed on a one-dimensional gas of ultra-cold bosons trapped at the surface of a microstructure. Two body correlations are highlighted by measurements of in situ density fluctuations and one-body correlations are probed through measurements of momentum distributions.We observed sub-Poissonian density fluctuations in the regime of weak interactions, thus demonstrating for the first time the regime of quasi-condensate in which the two-body correlation function is dominated by quantum fluctuations. We also observed sub-Poissonian fluctuations regardless of the density in the regime of strong interactions. Our measurement is the first observation of a single one-dimensional gas of bosons in this regime.The magnetic trap that we used is a modulated trap that has the remarkable property of decoupling between transverse and longitudinal confinements. This specificity has enabled us to engineer at will the shape of the longitudinal confinement. In particular, we were able to obtain harmonic and quartic traps.

Han Guangze

Tarun Kanti Ghosh

We present a quantized hydrodynamic theory and its applications of one-dimensional hard-core bosons in a harmonic trap. Quantizing the Hamiltonian of a trapped hard-core bosons and diagonalize it in terms of the phase and density fluctuations associated with the Bose field operator. As an applications, we calculate discrete energy spectrum, dynamic structure factor, momentum transferred by a two-photon Bragg pulse, single-particle density matrix, momentum distribution, and two-particle correlation function. The dynamic structure factor has multiple peaks due to the discrete nature of the energy spectrum which can be observed by a two-photon Bragg pulse with long duration. The coherence length at zero temperature is very small due to the "fermionization" of the system. We also compute the momentum distributions which has oscillatory behavior at large momentum. The pair distribution function shows that there are many deep valleys at various relative separations which implies shell structure due to the Pauli blocking in real space.

Michele Pizzardo, G. Mazzarella, Luca Salasnich

Przemysław Kościk

We study two one-dimensional atomic models composed of identical bosons trapped in a harmonic trap: one model with a short-range interaction potential and another model with a long-range one, and compare their entanglement features. Properties of the ground-states of two-, three-, and four-particle systems are explored.

James G. Glimm, Arthur M. Jaffe