We investigate the factors that influence the usefulness of supersonic collisions of Bose-Einstein condensates as a potential source of entangled atomic pairs by analyzing the reduction of the number difference fluctuations between regions of opposit
e momenta. We show that non-monochromaticity of the mother clouds is typically the leading limitation on number squeezing, and that the squeezing becomes less robust to this effect as the density of pairs grows. We develop a simple model that explains the relationship between density correlations and the number squeezing, allows one to estimate the squeezing from properties of the correlation peaks, and shows how the multi-mode nature of the scattering must be taken into account to understand the behavior of the pairing. We analyze the impact of the Bose enhancement on the number squeezing, by introducing a simplified low-gain model. We conclude that as far as squeezing is concerned the preferable configuration occurs when atoms are scattered not uniformly but rather into two well separated regions.
Solitons, or non-destructible local disturbances, are important features of many one-dimensional (1D) nonlinear wave phenomena, from water waves in narrow canals to light pulses in optical fibers. In ultra-cold gases, they have long been sought, and
were first observed to be generated by phase-imprinting. More recently, their spontaneous formation in 1D gases was predicted as a result of the Kibble-Zurek mechanism, rapid evaporative cooling, and dynamical processes after a quantum quench. Here we show that they actually occur generically in the thermal equilibrium state of a weakly-interacting elongated Bose gas, without the need for external forcing or perturbations. This reveals a major new quality to the experimentally widespread quasicondensate state. It can be understood via thermal occupation of the famous and somewhat elusive Type II excitations in the Lieb-Liniger model of a uniform 1D gas.
The behavior of the spatial two-particle correlation function is surveyed in detail for a uniform 1D Bose gas with repulsive contact interactions at finite temperatures. Both long-, medium-, and short-range effects are investigated. The results span
the entire range of physical regimes, from ideal gas, to strongly interacting, and from zero temperature to high temperature. We present perturbative analytic methods, available at strong and weak coupling, and first-principle numerical results using imaginary time simulations with the gauge-P representation in regimes where perturbative methods are invalid. Nontrivial effects are observed from the interplay of thermally induced bunching behavior versus interaction induced antibunching.
