Interacting mixtures of bosons and fermions are prevalent in various natural phenomena, including the Standard Model of physics, quantum materials, and helium dilution refrigerators. Understanding their coupled thermodynamics and collective behavior is a significant challenge. Ultracold atomic gases provide an ideal platform for studying Bose-Fermi mixtures due to their highly controllable environment where parameters such as species concentration and interaction strength can be precisely tuned. This research focuses on characterizing the collective oscillations of spin-polarized fermionic impurities embedded in a BEC, investigating the influence of interaction strength and temperature on these oscillations. The collective excitations are exceptionally sensitive probes of interparticle scattering and interactions, and this study delves into a novel regime – a dilute gas of spin-polarized fermions immersed in a BEC – relevant to Bose polaron physics and unconventional superconductors with low carrier densities. Understanding the dynamics of fermions interacting with a partially condensed Bose gas at finite temperature is complex because interactions occur in two ways: incoherent scattering with thermal bosons leading to momentum changes, and momentum-preserving interactions with the BEC via an effective potential. The interplay between these interactions dictates the overall system dynamics, particularly in the strongly interacting regime where the non-superfluid system transitions from collisionless to collisionally hydrodynamic behavior, as seen in electron-phonon mixtures related to high-temperature superconductivity. This research directly addresses the questions of superfluidity maintenance with strong interactions and the impact of thermal bosonic excitations on fermion transport properties.

The study draws parallels to various systems exhibiting Bose-Fermi interactions. The paradigmatic example is the movement of electrons through an ionic crystal, forming polarons. Other examples include dilute solutions of ³He in ⁴He, quark-meson models in high-energy physics, and 2D electronic materials with controllable exciton-electron interactions. Ultracold atomic gases offer arguably the purest realization of Bose-Fermi mixtures, permitting direct comparisons to theoretical models. Previous research on atomic Bose-Fermi mixtures has explored dual superfluids, phase separation and mean-field collapse, and the observation of strong-coupling Bose polarons. Collective excitations have been used to demonstrate superfluid hydrodynamic flow in BECs and collisional hydrodynamics in interacting Fermi gases. Studies have also examined collective oscillations in coupled Bose-Fermi superfluids and mixtures, revealing phenomena like collisional hydrodynamics, collisionless dipole oscillations, and sound propagation. However, this research explores the novel regime of a dilute gas of spin-polarized fermions immersed in a BEC, a previously less-explored area relevant to several research fields.

The experiment uses a mixture of ⁴⁰K fermions and a ²³Na BEC, held in a crossed optical dipole trap with near-cylindrical symmetry. The mixture is cooled evaporatively to temperatures around 30 nK. Interspecies interactions are controlled by adjusting the magnetic field near Feshbach resonances, allowing continuous tuning of the s-wave scattering length. The typical peak boson density is 7 × 10¹³ cm⁻³, and the impurity concentration varies. Collective excitations are probed by modulating the radial trapping potential depth at a variable frequency for 10 cycles. The in-situ width of the clouds is measured to determine the spectral response. When a resonant mode is excited, the cloud width expands radially. The experiment characterizes low-energy radial excitations at different interaction strengths. The BEC's response is well-described by a hydrodynamic scaling ansatz. The fermions' response is initially described by their collisionless mode in a harmonic trap. The experiment varies the interspecies coupling strength, observing a strong dependence of the fermionic response. At weak couplings, the collisionless mode shifts linearly. At stronger interactions, additional modes appear, coinciding with the BEC's superfluid hydrodynamic modes. The absence of significant spectral broadening is notable. To analyze the dynamics across various interaction strengths, the researchers compare experimental data to numerical models. A mean-field description qualitatively matches the weak interaction regime, where the fermionic collisionless mode shifts linearly with the scattering length. A Boltzmann-Vlasov equation is employed to model the fermions' full dynamics, initially neglecting collisions. A scaling ansatz is derived, which captures the fermionic response to the BEC's superfluid mode on the attractive side. A full numerical simulation of the collisionless Boltzmann-Vlasov equation is used to accurately capture all observed modes across interaction strengths. The impact of collisions with thermal bosons is measured by varying the temperature at a fixed scattering length. The study also investigates the appearance of high-order excitations – Faraday waves – observing their emergence in both the BEC and the fermionic gas.

The study's key findings are: 1. At strong interactions, the fermionic impurities closely mimic the BEC's superfluid hydrodynamic modes, exhibiting both quadrupole and breathing modes. 2. Increasing temperature leads to a crossover from collisionless to collisionally hydrodynamic flow, akin to 2D electron gases. 3. The fermions' collective modes exhibit a strong dependence on interspecies interaction strength. At weak interactions, a mean-field-like shift is observed, while at stronger interactions, the fermionic response becomes locked to the BEC's hydrodynamic modes, even exhibiting Faraday waves, similar to the synchronized flow of dye particles in water. 4. A collisionless Boltzmann-Vlasov model accurately captures the observed fermionic modes across all interaction strengths, validating the assumption of negligible collisions between fermions interacting solely with the BEC at low temperatures. 5. Increasing temperature introduces collisions with thermal bosons, resulting in the appearance of new modes in the fermionic response, indicative of a crossover to the hydrodynamic regime. Above the BEC critical temperature, the mixture reverts to collisionless flow for both species. 6. The observation of Faraday waves in both the BEC and the fermionic gas at strong interspecies interactions provides striking visual evidence of synchronized flow, suggesting a significant transfer of energy and momentum between the two components. The speed of sound, inferred from the observed Faraday wave period, matches theoretical predictions, validating the experimental findings.

The findings demonstrate a novel regime of collective motion for fermions, mirroring the superfluid hydrodynamic flow of a BEC. The observed crossover from collisionless to collisionally dominated hydrodynamic flow with increasing temperature parallels behavior in 2D electron gases, establishing a significant connection between these disparate systems. The accurate modeling of the fermionic response using a collisionless Boltzmann-Vlasov equation, even at strong interactions, provides valuable insight into the underlying dynamics and interaction mechanisms. The appearance of Faraday waves in both components strongly suggests a synchronized and coherent flow between the fermions and the BEC, providing visual confirmation of the theoretical models. This research opens new avenues for exploring strongly interacting Bose-Fermi mixtures and understanding phenomena in condensed matter physics where such interactions are crucial.

This study reveals a novel regime of collective motion in a Bose-Fermi mixture, where fermionic impurities mimic the BEC's superfluid hydrodynamic modes. The temperature-dependent crossover to a collisionally hydrodynamic regime highlights the importance of thermal excitations. The excellent agreement between the collisionless Boltzmann-Vlasov model and experimental results validates the theoretical framework. Future research could explore the impact of induced fermion-fermion interactions at lower temperatures, potentially revealing insights into p-wave superfluidity mediated by bosons.

The study primarily focuses on a specific range of interaction strengths and temperatures. Extrapolating the findings to other parameter regimes requires further investigation. The numerical simulations rely on certain approximations, such as the use of the Boltzmann-Vlasov equation and specific model assumptions, which might affect the accuracy of the results. Although the experimental setup minimizes power broadening, some level of power broadening might still be present. Future studies could improve accuracy and extend the study to a wider parameter space.