Confinement Induced Molecules in a 1D Fermi Gas

We have observed two-particle bound states of atoms confined in a one-dimensional matter waveguide. These bound states exist irrespective of the sign of the scattering length, contrary to the situation in free space. Using radio-frequency spectroscopy we have measured the binding energy of these dimers as a function of the scattering length and confinement and find good agreement with theory. The strongly interacting one-dimensional Fermi gas which we create in an optical lattice represents a realization of a tunable Luttinger liquid.

Figure 1

Radio-frequency (rf) spectroscopy of a one-dimensional gas at magnetic fields 201.5 G (a) and 203.1 G (b), (c) with respective scattering lengths $(2.5\times {10}^3)a_0$ (a) and $(-1.2\times {10}^3)a_0$ (b), (c), where $a_0$ is the Bohr radius. The atom number in the respective spin states is plotted vs the detuning of the applied rf pulse in (a) and (b). The solid lines are single or double Lorentzian fits. (c) Width of the $|-9/2⟩$ atom cloud along the 1D tube direction after 7 ms time of flight obtained from a fit [39] to the atomic density distribution. The horizontal line marks the average width for an off-resonant rf pulse; the increase at the molecule dissociation threshold is fitted using a linear function. The decrease in width at higher detunings is due to a diminishing dissociation efficiency.

Figure 2

1D and 3D molecules. Confinement induced molecules in the 1D geometry exist for arbitrary sign of the scattering length. The solid lines show the theoretical prediction of the binding energy with no free parameters (see text). In the 3D case, we observed no bound states at magnetic fields above the Feshbach resonance (vertical dashed line). The error bars reflect the uncertainty in determining the position of the dissociation threshold.

Figure 3

Changing the confinement. The spectra are taken very close to the Feshbach resonance at a magnetic field of $B=202.0\mathrm{G}$. The binding energy is measured by rf spectroscopy. For $V_0\ge 30E_r$ no increase in kinetic energy could be detected and we used the rising edge in the $|-5/2⟩$ atom number in the spectrum to determine the binding energy. The error bars reflect the uncertainty in determining the position of the dissociation threshold. The solid line shows the theoretically expected value.