Energy-Dependent Three-Body Loss in 1D Bose Gases

We study the loss of atoms in quantum Newton’s cradles with a range of average energies and transverse confinements. We find that the three-body collision rate in one-dimension is strongly energy dependent, as predicted by a strictly 1D theory. We adapt the theory to atoms in waveguides, then, using detailed momentum measurements to infer all the collisions that occur, we compare the observed loss to the adapted theory and find that they agree well.

Figure 1

Axial trap sequence used to change the average energy of the atoms. At $t=0\mathrm{ms}$ most of the atoms are diffracted and the axial trap depth is immediately increased from $U_o$ to $U_i$. When the atoms reach their turning point a quarter cycle later the axial trap is decreased to $U_{\text{final}}=\{9.3,10,11,12\}{E}_R$ for $V_{\mathrm{latt}}=\{36,40,45,50\}{E}_R$, respectively. The atoms then evolve for 200 ms, by which time the distributions are fully dephased.

Figure 2

Normalized 1D trap distributions, for various QNC energies and a $45E_R$ lattice confinement. (a) $f(p)$. (b) $f(p_o)$. (c) $f(z)$. (d) $f(z_o)$. The curves for $f(p)$ and $f(z)$ are normalized to 0.5, while the $f(p_o)$ and $f(z_o)$ distributions are normalized to 1. In (c) and (d) $w_0=42.6\mu \mathrm{m}$ is the beam waist of the axial dipole trap.

Figure 3

Total atom number as a function of holding time in a (a) lower and (b) higher density QNC distribution with ${\overline{E}}_o=3.05E_R$ in a $50E_R$ lattice depth. Black circles are the average of six data points; the standard deviation of these points are smaller than the marker size. The red dashed lines are the fits of the experimental data curves to Eq. (1). The insets show the direct comparison between the experimental data curves and the theoretical curves (open blue circles) derived from the global fit of the loss model [Eq. (3)] to the data. In order to make many such comparisons on the same plot (see Fig. 4), we fit the theoretical curves to Eq. (1) (solid green lines in the main figures). To make solid green curves and blue circles more visible, they have been offset by a factor of 0.8. As is clear from the insets, without the offset they would be nearly overlapped.

Figure 4

Experimental and theoretical $K_{3_{\mathrm{eff}}}^{1\mathrm{D}}$. The experimental points are the solid symbols (larger for higher density and smaller for lower density) shown as red diamonds, black circles, green squares, and blue triangles for 36, 40, 45, and $50E_R$ lattice depths, respectively. We obtain the experimental points by fitting the experimental loss curves to Eq. (1). $K_{3_{\mathrm{eff}}}^{1\mathrm{D}}$ increases with energy at all lattice depths, but does not depend on the lattice depth. We obtain the theoretical points (hollow symbols) by fitting the decay curves derived from our detailed loss model [Eq. (3)] to Eq. (1).

Figure 5

(a) Plot of $K_3^{1\mathrm{D}}$ as a function of the center of mass collision energy for atoms in a 36, 40, 45, and $50E_R$ lattice. Note that, although $K_3$ is constant, deeper lattices have higher $K_{3_{\max }}^{1\mathrm{D}}$. (b) Plot of the distribution of collisions in the $40E_R$ lattice as a function of the collision energy for different $\overline{E_o}$.