Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate

The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics. However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized. Here, we use radio frequency spectroscopy of ultracold bosonic ${}^{39}\mathrm{K}$ atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC. We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, both in the weak-coupling limits and across unitarity. The spectral response consists of a well-defined quasiparticle peak at weak coupling, while for increasing interaction strength, the spectrum is strongly broadened and becomes dominated by the many-body continuum of excited states. Crucially, no significant effects of three-body decay are observed. Our results open up exciting prospects for studying mobile impurities in a bosonic environment and strongly interacting Bose systems in general.

Figure 1

Sketch of the spectroscopic method and the impurity energy spectrum. A radio frequency pulse transfers atoms from the $|1⟩$ to the $|2⟩$ state. Only a small fraction is transferred, corresponding to a rotation by a small angle on the Bloch sphere (inset) in a noninteracting system. The solid lines show the energies of the zero-momentum attractive ($E_a$) and repulsive ($E_r$) polaron states in a uniform BEC as a function of the interaction parameter $1/k_{n}a$ (see text). The dashed line shows the molecular binding energy $E_m$ on the repulsive side of the Feshbach resonance, and the gray shading denotes a continuum of many-body states. The bottom cartoon shows impurity atoms (orange) in a BEC (blue); the intensity of the background color indicates the change in the BEC density due to the presence of impurity atoms.

Figure 2

Spectral response of the impurity in the BEC. The false color plots show the experimentally measured spectroscopic signal (a) and the calculated spectrum (b), for different values of detuning $\mathrm{\Delta }$ and the interaction parameter $1/k_{n}a$. The experimental spectrum is recorded such that its peak amplitude is constant for all values of $1/k_{n}a$. Accordingly, the theoretical spectrum is normalized such that its frequency integrated weight is the same as the experimental spectrum. In addition, the independently measured molecular binding energy (white dots) and a fit to it (dashed line) are shown [37]. Negative values of the experimental signal are due to shot-to-shot atom number fluctuations. Panels (c)–(g) show the signal as a function of $\mathrm{\Delta }$ for various values of $1/k_{n}a$ (see panel). The solid lines show the calculated signal, which is in excellent agreement with the experiment, except for $1/k_{n}a=1.6$ where the agreement is qualitative. The dashed lines, obtained excluding three-body correlations, only agree with the experiment for weak interactions.

Figure 3

The average energy $\overline{E}$ of the impurity spectrum is shown as a function of the interaction parameter. The energy was obtained from Gaussian fits to the spectroscopic signal (blue dots) and to the full TBM spectrum (blue line). For comparison, we display the results for a TBM spectrum without three-body correlations (red line) and from perturbation theory (dashed line) [37].

Figure 4

The width $\sigma$ of the impurity spectrum is shown as a function of the interaction parameter. The widths were obtained from Gaussian fits to the spectroscopic signal (blue dots), the full TBM spectrum (blue line), and the TBM without three-body correlations (red line). The green dashed line was obtained from a spatial average and Fourier width convolution of the result from perturbation theory excluding the many-body continuum [37]. The inset shows the width for the entire experimental data set compared with the full TBM spectrum.