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Recently Javanainen and Wilkens [Phys. Rev. Lett. 78, 4675 (1997)] have analysed an experiment in which an interacting Bose condensate, after being allowed to form in a single potential well, is cut by splitting the well adiabatically with a very high potential barrier, and estimate the rate at which, following the cut, the two halves of the condensate lose the memory of their relative phase. We argue that, by neglecting the effect of interactions in the initial state before the separation, they have overestimated the rate of phase randomization by a numerical factor which grows with the interaction strength and with the slowness of the separation process.
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With exciton lifetime much extended in semiconductor quantum-well structures, their transport and Bose-Einstein condensation become a focus of research in recent years. We reveal a momentum-space gauge field in the exciton center-of-mass dynamics due to Berry phase effects. We predict spin-dependent topological transport of the excitons analogous to the anomalous Hall and Nernst effects for electrons. We also predict spin-dependent circulation of a trapped exciton gas and instability in an exciton condensate in favor of vortex formation.
We theoretically study the structure of a stationary soliton in the polar phase of spin-1 Bose--Einstein condensate in the presence of quadratic Zeeman effect at zero temperature. The phase diagram of such solitons is mapped out by finding the states of minimal soliton energy in the defining range of polar phase. The states are assorted into normal, anti-ferromagnetic, broken-axisymmetry, and ferromagnetic phases according to the number and spin densities in the core. The order of phase transitions between different solitons and the critical behaviour of relevant continuous transitions are proved within the mean-field theory.
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We demonstrate a spatially resolved autocorrelation measurement with a Bose-Einstein condensate (BEC) and measure the evolution of the spatial profile of its quantum mechanical phase. Upon release of the BEC from the magnetic trap, its phase develops a form that we measure to be quadratic in the spatial coordinate. Our experiments also reveal the effects of the repulsive interaction between two overlapping BEC wavepackets and we measure the small momentum they impart to each other.
We point out that the widely accepted condition g11g22<g122 for phase separation of a two-component Bose-Einstein condensate is insufficient if kinetic energy is taken into account, which competes against the intercomponent interaction and favors phase mixing. Here g11, g22, and g12 are the intra- and intercomponent interaction strengths, respectively. Taking a d-dimensional infinitely deep square well potential of width L as an example, a simple scaling analysis shows that if d=1 (d=3), phase separation will be suppressed as Lrightarrow0 (Lrightarrowinfty) whether the condition g11g22<g122 is satisfied or not. In the intermediate case of d=2, the width L is irrelevant but again phase separation can be partially or even completely suppressed even if g11g22<g122. Moreover, the miscibility-immiscibility transition is turned from a first-order one into a second-order one by the kinetic energy. All these results carry over to d-dimensional harmonic potentials, where the harmonic oscillator length {xi}ho plays the role of L. Our finding provides a scenario of controlling the miscibility-immiscibility transition of a two-component condensate by changing the confinement, instead of the conventional approach of changing the values of the gs.
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