We investigate the thermal evolution of radio-frequency (RF) spectra of a spin-imbalanced Fermi gas near a Feshbach resonance in which degenerate Fermi-polaron and classical Boltzmann-gas regimes emerge in the low-temperature and high-temperature limits, respectively. By using self-consistent frameworks of strong-coupling diagrammatic approaches, both the ejection and the reserve RF spectra available in cold-atom experiments are analyzed. We find a variety of transfers from Fermi polarons to the Boltzmann gas such that a thermal crossover expected in the weak-coupling regime is shifted to a sharp transition near unitarity and to double-peak coexistence of attractive and repulsive branches in the strong-coupling regime. Our theory provides semiquantitative descriptions for a recent experiment on the ejection RF spectroscopy at unitarity [Z. Yan, P. B. Patel, B. Mukherjee, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Phys. Rev. Lett. 122, 093401 (2019)] and suggests the importance of beyond-two-body correlations in the high-temperature regime due to the absence of Pauli-blocking effects.
We investigate the thermal evolution of radio-frequency (RF) spectra of a spin-imbalanced Fermi gas near a Feshbach resonance in which degenerate Fermi-polaron and classical Boltzmann-gas regimes emerge in the low-temperature and high-temperature limits, respectively. By using self-consistent frameworks of strong-coupling diagrammatic approaches, both the ejection and the reserve RF spectra available in cold-atom experiments are analyzed. We find a variety of transfers from Fermi polarons to the Boltzmann gas such that a thermal crossover expected in the weak-coupling regime is shifted to a sharp transition near unitarity and to double-peak coexistence of attractive and repulsive branches in the strong-coupling regime. Our theory provides semiquantitative descriptions for a recent experiment on the ejection RF spectroscopy at unitarity [Z. Yan, P. B. Patel, B. Mukherjee, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Phys. Rev. Lett. 122, 093401 (2019)] and suggests the importance of beyond-two-body correlations in the high-temperature regime due to the absence of Pauli-blocking effects.
We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures T. In this regime, we observe a characteristic T^{2} dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high T, the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, ∝T^{-1/2}. In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons.
We theoretically study the normal phase properties of strongly interacting two-component Fermi gases in two spatial dimensions. In the limit of weak attraction, we find that the gas can be described in terms of effective polarons. As the attraction between fermions increases, we find a crossover from a gas of noninteracting polarons to a pseudogap regime. We investigate how this crossover is manifested in the radio-frequency (rf) spectroscopy. Our findings qualitatively explain the differences in the recent rf spectroscopy measurements of two-dimensional Fermi gases [Sommer et al., Phys. Rev. Lett. 108, 045302 (2012) and Zhang et al., Phys. Rev. Lett. 108, 235302 (2012)].
We consider the highly spin-imbalanced limit of a two-component Fermi gas, where there is a small density of $\ensuremath{\downarrow}$ impurities attractively interacting with a sea of $\ensuremath{\uparrow}$ fermions. In the single-impurity limit at zero temperature, there exists the so-called polaron-molecule transition, where the impurity sharply changes its character by binding a $\ensuremath{\uparrow}$ fermion at sufficiently strong attraction. Using a recently developed variational approach, we calculate the thermodynamic properties of the impurity, and we show that the transition becomes a smooth crossover at finite temperature due to the thermal occupation of excited states in the impurity spectral function. However, remnants of the single-impurity transition are apparent in the momentum-resolved spectral function, which can in principle be probed with Raman spectroscopy. We furthermore show that the Tan contact exhibits a characteristic nonmonotonic dependence on temperature that provides a signature of the zero-temperature polaron-molecule transition. For a finite impurity density, we argue that descriptions purely based on the behavior of the Fermi polaron are invalid near the polaron-molecule transition, since correlations between impurities cannot be ignored. In particular, we show that the spin-imbalanced system undergoes phase separation at low temperatures due to the strong attraction between $\ensuremath{\uparrow}\ensuremath{\downarrow}$ molecules induced by the Fermi sea. Thus, we find that the impurity spectrum and the induced impurity-impurity interactions are key to understanding the phase diagram of the spin-imbalanced Fermi gas.
Understanding the behavior of an impurity strongly interacting with a Fermi sea is a long-standing challenge in many-body physics. When the interactions are short-ranged, two vastly different ground states exist: a polaron quasiparticle and a molecule dressed by the majority atoms. In the single-impurity limit, it is predicted that at a critical interaction strength, a first-order transition occurs between these two states. Experiments, however, are always conducted in the finite temperature and impurity density regime. The fate of the polaron-to-molecule transition under these conditions, where the statistics of quantum impurities and thermal effects become relevant, is still unknown. Here, we address this question experimentally and theoretically. Our experiments are performed with a spin-imbalanced ultracold Fermi gas with tunable interactions. Utilizing a novel Raman spectroscopy combined with a high-sensitivity fluorescence detection technique, we isolate the quasiparticle contribution and extract the polaron energy, spectral weight, and the contact parameter. As the interaction strength is increased, we observe a continuous variation of all observables, in particular a smooth reduction of the quasiparticle weight as it goes to zero beyond the transition point. Our observation is in good agreement with a theoretical model where polaron and molecule quasiparticle states are thermally occupied according to their quantum statistics. At the experimental conditions, polaron states are hence populated even at interactions where the molecule is the ground state and vice versa. The emerging physical picture is thus that of a smooth transition between polarons and molecules and a coexistence of both in the region around the expected transition.
We present a systematic study of a mobile impurity immersed in a three-dimensional Fermi sea of fermions at finite temperature, by using the standard non-self-consistent many-body T-matrix theory that is equivalent to a finite-temperature variational approach with the inclusion of one-particle-hole excitation. The impurity spectral function is determined in the real-frequency domain, avoiding any potential errors due to the numerical analytic continuation in previous T-matrix calculations and the small spectral broadening parameter used in variational calculations. In the weak-coupling limit, we find that the quasiparticle decay rate of both attractive and repulsive polarons does not increase significantly with increasing temperature, and therefore Fermi polarons may remain well defined far above Fermi degeneracy. In contrast, near the unitary limit with strong coupling, the decay rate of Fermi polarons rapidly increases and the quasiparticle picture breaks down close to the Fermi temperature. We analyze in detail the recent ejection and injection radio-frequency (rf) spectroscopy measurements, performed at Massachusetts Institute of Technology (MIT) and at the European Laboratory for Non-Linear Spectroscopy (LENS), respectively. We show that the momentum average of the spectral function, which is necessary to account for the observed rf spectroscopy, has a sizable contribution to the width of the quasiparticle peak in spectroscopy. As a result, the measured decay rate of Fermi polarons could be significantly larger than the calculated quasiparticle decay rate at zero momentum. By taking this crucial contribution into account, we find that there is a reasonable agreement between theory and experiment for the lifetime of Fermi polarons in the strong-coupling regime, as long as they remain well defined.
A single down-spin fermion with an attractive zero-range interaction with a Fermi sea of up-spin fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wave function in the molecular limit, we determine the critical value for the polaron-to-molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirotzek et al. [Phys. Rev. Lett. 102, 230402 (2009)]. In addition, we calculate the contact coefficient of the strongly imbalanced gas, using the adiabatic theorem of Tan and discuss the implications of the polaron-to-molecule transition for the phase diagram of the attractive Fermi gas at finite imbalance.