Exciting Collective Oscillations in a Trapped 1D Gas

We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be $({\omega }_B/{\omega }_D{)}^2\simeq 3.1$, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure $({\omega }_B/{\omega }_D{)}^2\simeq 4$. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.

Figure 1

The geometry and size of trapped 1D gases in a two-dimensional optical lattice. The spacing between the 1D tubes in the horizontal and vertical direction is 413 nm.

Figure 2

Dipole oscillation (a) and breathing mode (b) of a quantum degenerate one-dimensional Bose gas. For this data set an almost pure Bose-Einstein condensate with $N=(9.8\pm 0.8)\times {10}^4$ atoms was loaded into the optical lattice and imaged after 15 ms of ballistic expansion. From the fits we obtain ${\omega }_D=2\pi \times (84.6\pm 0.4)\mathrm{H}\mathrm{z}$ and ${\omega }_B=2\pi \times (152.6\pm 2.0)\mathrm{H}\mathrm{z}$.

Figure 3

The measured frequency ratio $({\omega }_B/{\omega }_D{)}^2$ for a Bose condensed 1D gas (solid symbols). The solid curve is the theoretical prediction from 9 using the measured dipole frequency along the 1D tubes ${\omega }_z=2\pi \times 84\mathrm{H}\mathrm{z}$ and the frequency $\omega$ of the slowly varying confining potential in the transverse direction with $\sqrt{m/m^{*}}\omega =2\pi \times 4\mathrm{H}\mathrm{z}$. Averaging all measurements, independent of the atom number, we obtain a frequency ratio of $({\omega }_B/{\omega }_D{)}^2=3.15\pm 0.22$. For a 1D gas of thermal atoms we find $({\omega }_B/{\omega }_D{)}^2=4.10\pm 0.08$ (open circles). The depth of the optical lattice is $30E_{\mathrm{r}\mathrm{e}\mathrm{c}}$. The error bars reflect only the statistical uncertainties on the total atom number and fit errors on the frequencies.

Figure 4

The measured frequency ratio $({\omega }_B/{\omega }_D{)}^2$ for a Bose gas with $7\times {10}^4$ atoms after heating in the optical lattice. The rms axial width is given after 15 ms of time of flight. The inset shows the evolution of the axial width vs hold time in the optical lattice prior to excitation of the collective modes.