Scattering in Mixed Dimensions with Ultracold Gases

We experimentally investigate the mix-dimensional scattering occurring when the collisional partners live in different dimensions. We employ a binary mixture of ultracold atoms and exploit a species-selective 1D optical lattice to confine only one atomic species in 2D. By applying an external magnetic field in proximity of a Feshbach resonance, we adjust the free-space scattering length to observe a series of resonances in mixed dimensions. By monitoring 3-body inelastic losses, we measure the magnetic field values corresponding to the mix-dimensional scattering resonances and find a good agreement with the theoretical predictions based on simple energy considerations.

Figure 1

(top) Sketch of the experimental configuration: 3D(Rb)-2D(K) mix-dimensional system obtained using a SSDP lattice. (bottom) Energy diagram of the open and closed channel as a function of the Feshbach field $B$: due to the external potential, both channels are uplifted and split into many levels, separated by the relevant harmonic oscillator quanta $\hslash {\omega }_i$ ($i=\mathrm{K},\mathrm{KRb}$). MDR may occur when closed-channel levels ($n^{\prime }$, sloping lines) intercept populated open-channel levels (horizontal lines). The shift $b$ due to the channel coupling is assumed equal to that in free space for $n^{\prime }=0$, and is neglected for $n^{\prime }>0$.

Figure 2

(a) Calculated $a_{\mathrm{eff}}$ as a function of $1/a$ for the masses of our mixture and $s=20$. The dashed line corresponds to $a_{\mathrm{eff}}=a$. Only even $n^{\prime }$ resonances are allowed (see text). (b) Calculated $a_{\mathrm{eff}}$ as a function of the magnetic field, for several lattice strengths $s$. The dotted lines show the resonance positions calculated from Eq. (1) for $n^{\prime }=2$, 4 and $s=20$.

Figure 3

Recorded atom number $N_{\mathrm{K}}+N_{\mathrm{Rb}}$, versus the Feshbach magnetic field without lattice (top), with a SSDP lattice strength $s=10$ (middle) and $s=23$ (bottom). Solid lines are a guide to the eye. Predictions based on the harmonic oscillator analysis, Eq. (1) (dashed) and on band structure, Eq. (2) (shaded areas) are shown.

Figure 4

Summary of observed loss peak centers as a function of the lattice strength $s$. Resonance positions are extracted from magnetic field scans (see Fig. 2), by fitting the bottom of the loss peaks with a Gaussian. Error bars are dominated by the width of the loss peaks (vertical) and by the systematic uncertainty in the lattice calibration (horizontal). Predictions based on the harmonic oscillator analysis, Eq. (1) (dashed) and on band structure, Eq. (2) (shaded areas) are shown.