Quantum dynamics of impurities in a one-dimensional Bose gas

Using a species-selective dipole potential, we create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration during expansion. We find an interaction-dependent amplitude reduction of the oscillation of the impurities' size with no measurable frequency shift, and study it as a function of the interaction strength. We discuss possible theoretical interpretations of the data. We compare, in particular, with a polaronic mass shift model derived following Feynman variational approach.

Figure 1

Ultracold Rb atoms with K impurities are loaded into an array of 1D systems, “tubes” (left). The SSDP light blade spatially localizes the impurities into the center of the Rb tubes (right).

Figure 2

Time sequence of the experimental procedure used to prepare the K impurities in the middle of 1D tubes filled with Rb atoms.

Figure 3

Upper panel: oscillations of the K impurities axial width $\sigma =\sqrt{\langle x^2\rangle }$ after extinction of the confining SSDP, for different interaction strengths with the surrounding Rb bulk, $\eta =g_1\mathrm{D},\mathrm{KRb}/g_1\mathrm{D},\mathrm{Rb}$. Solid lines represent a fit to data, and triangles the Rb axial size. Inset images show the observed in situ density distributions of Rb (red, left) and K (blue, right) within a window of $200\times 150\mu$m. Lower panel: values of the fit parameters $\omega /2\pi$, $\gamma$, and $\beta$ (left to right, see text for definition).

Figure 4

Experiment: impurities' axial size at the first oscillation maximum ${\sigma }_p$, normalized so that ${\sigma }_p=1$ for $\eta =0$, versus the coupling strength parameter $\eta =g_1\mathrm{D},\mathrm{KRb}/g_1\mathrm{D},\mathrm{Rb}$, for attractive (left, $\eta <0$) and repulsive (right, $\eta >0$) interactions (circles). Theory: $\sqrt{m_K/m_K^{*}}$ calculated with impurity-bath coupling $g_1\mathrm{D},\mathrm{KRb}$ derived from two-body scattering [24] (solid line) and with $g_1\mathrm{D},\mathrm{KRb}$ multiplied by a fit parameter (dashed line). Both curves are computed for a Rb density of 7 atoms/$\mu$m and $\tilde{\gamma }=0$.

Figure 5

Amplitude of the first oscillation of the axial size of K impurities (right) following different preparation sequences (left): (a) $\eta$ always negligible; (b) $\eta$ large while K in the SSDP light blade and negligible during expansion at $t>0$; and (c) $\eta$ always large.

Figure 6

Square root of the inverse impurities' renormalized mass versus interspecies interaction strength $\eta$, calculated for different values of Rb density. This quantity directly compares with the measured K width ${\sigma }_p$.