Observation of spin-spin fermion-mediated interactions between ultracold bosons

TL;DR

This study demonstrates the first clear evidence of spin-spin interactions between ultracold bosons mediated by a fermionic gas, using Ramsey spectroscopy to measure the interaction enhancement and frequency shifts in a controlled mixture.

Contribution

It provides experimental evidence of fermion-mediated spin-spin interactions in a boson-fermion mixture, including quantification and analysis of the effects on boson spin coherence.

Findings

Measured a 45% increase in boson spin-spin interaction due to fermion mediation.

Observed a significant inhomogeneous density shift indicating mediated interactions.

Determined a boson-fermion scattering length difference beyond elastic approximation.

Abstract

Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a $^{87}$Rb BEC to measure the interaction mediated by a $^{40}$K DFG. By controlling the bosons density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of $\eta=1.45\pm 0.05^{stat} \pm 0.13^{sys}$ in the presence of the DFG, providing a clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of $a_{bf_2}-a_{bf_1}=-5.36 \pm 0.44^{stat} \pm 1.43^{sys}~a_0$ between the clock-transition states, a first measurement beyond the low-energy elastic approximation in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance. Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.