Observations of Density Fluctuations in an Elongated Bose Gas: Ideal Gas and Quasicondensate Regimes

We report in situ measurements of density fluctuations in a quasi-one-dimensional ${}^{87}\mathrm{Rb}$ Bose gas at thermal equilibrium in an elongated harmonic trap. We observe an excess of fluctuations compared to the shot-noise level expected for uncorrelated atoms. At low atomic density, the measured excess is in good agreement with the expected “bunching” for an ideal Bose gas. At high density, the measured fluctuations are strongly reduced compared to the ideal gas case. We attribute this reduction to repulsive interatomic interactions. The data are compared with a calculation for an interacting Bose gas in the quasicondensate regime.

Figure 1

Schematic of the experimental setup. Left: drawing of the wires constituting the atom chip. We keep $I_1+I_2=3\mathrm{A}$ and adjust $I_1-I_2$ between 0.3 and 1 A to vary the confinement along $z$. The uniform field $B_0$ is approximately 40 G, we also add a small field ($\lesssim 1\mathrm{G}$) along $z$. Right: optical imaging system. We image the cloud and its reflection on the atom chip onto a CCD camera. In the radial direction, the unresolved cloud images cover approximately five pixels whose size in the object plane is $\Delta =6\mu \mathrm{m}$.

Figure 2

Atom number variance as a function of the mean atom number per pixel. Open circles correspond to a hot cloud ($k_{B}T\simeq 10\hslash {\omega }_{\perp }$, ${\omega }_{\perp }=2\pi \times 2.85\mathrm{kHz}$) for which fluctuations are given by the shot noise (black line). The solid circles correspond to cold clouds. Error bars show the standard deviation of the mean of $⟨\delta N^2⟩$. The fluctuations in excess of shot noise are due to bosonic bunching. The dot-dashed line is the prediction for an ideal Bose gas while the dotted line uses the Maxwell-Boltzmann approximation [see Eq. (3)]. The insets show the longitudinal profile of the two cold clouds from which we deduce the temperature and the chemical potential used for the calculations.

Figure 3

We plot the same quantities as in Fig. 2. Dot-dashed lines are the predictions for an ideal Bose gas [deduced from Eq. (2)], whereas the dashed lines show the results of Eq. (6). The temperature of the sample is deduced by fitting the wings of the longitudinal profile to an ideal Bose gas profile as shown in the insets. The solid lines gives the atomic shot-noise level.