Yang-Yang Thermodynamics on an Atom Chip

We investigate the behavior of a weakly interacting nearly one-dimensional trapped Bose gas at finite temperature. We perform in situ measurements of spatial density profiles and show that they are very well described by a model based on exact solutions obtained using the Yang-Yang thermodynamic formalism, in a regime where other, approximate theoretical approaches fail. We use Bose-gas focusing [I. Shvarchuck et al., Phys. Rev. Lett. 89, 270404 (2002)] to probe the axial momentum distribution of the gas and find good agreement with the in situ results.

Figure 1

Linear atomic density from absorption images obtained in situ (a)–(d) and in focus (e)–(h) by lowering (from top to bottom as indicated) the final rf evaporation frequency. In situ: solid lines are fits using Yang-Yang thermodynamic equations (see text). The values of $\mu$ and $T$ resulting from the fits are shown in the figure. Dotted line: ideal Bose-gas profile showing divergence for $\mu (x)=0$. Dashed line in (d): quasicondensate profile with the same peak density as the experimental data. In focus: solid lines are the sum of two independent Gaussian fits—one to the wings (dotted lines) and one to the central part of the density profile.

Figure 2

Characterization of the atomic clouds as a function of the final rf frequency, as determined from fits of the Yang-Yang model to the in situ data and Gaussian fits to the in focus data. (a) Temperature from the in situ data (■) and from the radial (□) and axial (○) size of the broad Gaussian fit to the in focus data. The dash-dotted line is to guide the eye and indicates a ratio of 11 of the trap depth and the cloud temperature; dashed line corresponds to $\hslash {\omega }_{\perp }/k_B$. (b) Chemical potential from the Yang-Yang fit; dashed line indicates $\hslash {\omega }_{\perp }/k_B$. (c) Atom number from the in focus data: wide distribution (○) and central peak (▵); from the Yang-Yang model fit to the in situ data: atoms in the radial ground state (■), in radially excited states ($•$), and atoms in the radial ground state experiencing $\mu (x)>0$ (▴).