Effective size of a trapped atomic Bose gas

We investigate the temperature-dependent effective size of a trapped interacting atomic Bose gas within a mean field theory approximation. The sudden shrinking of the average length, as observed in an earlier experiment by Wang {\it et al.} [Chin. Phys. Lett. {\bf 20}, 799 (2003)], is shown to be a good indication for Bose-Einstein condensation (BEC). Our study also supports the use of the average width of a trapped Bose gas for a nondestructive calibration of its temperature.Comment: RevTex4, 6 pages, 4 eps figures, to appear in Phys. Rev.

Emergent patterns in a spin-orbit coupled spin-2 Bose-Einstein condensate

The ground-state phases of a spin-orbit (SO) coupled atomic spin-2 Bose-Einstein condensate (BEC) are studied. Interesting density patterns spontaneously formed are widespread due to the competition between SO coupling and spin-dependent interactions like in a SO coupled spin-1 condensate. Unlike the case of spin-1 condensates, which are characterized by either ferromagnetic or polar phase in the absence of SO, spin-2 condensates can take a cyclic phase, where we find the patterns formed due to SO are square or triangular in their spin component densities for axial symmetric SO interaction. Both patterns are found to continuously evolve into striped forms with increased asymmetry of the SO coupling.Comment: 5 pages, 5 figure

Quantum-limited metrology in the presence of collisional dephasing

Including collisional decoherence explicitly, phase sensitivity for estimating effective scattering strength $\chi$ of a two-component Bose-Einstein condensate is derived analytically. With a measurement of spin operator $\hat{J}_{x}$, we find that the optimal sensitivity depends on initial coherent spin state. It degrades by a factor of $(2\gamma)^{1/3}$ below super-Heisenberg limit $\propto 1/N^{3/2}$ for particle number $N$ and the dephasing rate $1<\!<\gamma<N^{3/4}$. With a $\hat{J}_y$ measurement, our analytical results confirm that the phase $\phi=\chi t\sim 0$ can be detected at the limit even in the presence of the dephasing.Comment: 3.2 pages, 3 figure