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arXiv:1110.1649 · Physical Review A

Fermi polarons in two dimensions

Richard Schmidt, Tilman Enss, Ville Pietilä, Eugene Demler

Published Feb 7, 2012• 157 citations
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Abstract

We theoretically analyze inverse radio-frequency (rf) spectroscopy experiments in two-component Fermi gases. We consider a small number of impurity atoms interacting strongly with a bath of majority atoms. In two-dimensional geometries we find that the main features of the rf spectrum correspond to an attractive polaron and a metastable repulsive polaron. Our results suggest that the attractive polaron has been observed in a recent experiment [B. Fr\"ohlich et al., Phys. Rev. Lett. 106, 105301 (2011)].

DOI
10.1103/physreva.85.021602

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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 a single spin-down impurity atom interacting via an attractive, short-range potential with a spin-up Fermi sea in two dimensions (2D). Similarly to 3D, we show how the impurity can form a metastable state (the "repulsive polaron") with energy greater than that of the non-interacting impurity. Moreover, we find that the repulsive polaron can acquire a finite momentum for sufficiently weak attractive interactions. Even though the energy of the repulsive polaron can become sizeable, we argue that saturated ferromagnetism is unfavorable in 2D because of the polaron's finite lifetime and small quasiparticle weight.
We study the repulsive Fermi polaron in a two-component, two-dimensional system of fermionic atoms inspired by the results of a recent experiment with 173Yb^{173}\mathrm{Yb}173Yb atoms [N. Darkwah Oppong et al., Phys. Rev. Lett. 122, 193604 (2019)]. We use the diffusion Monte Carlo method to report properties such as the polaron energy and the quasiparticle residue that have been measured in that experiment. To provide insight into the quasiparticle character of the problem, we also report results for the effective mass. We show that the effective range, together with the scattering length, is needed in order to reproduce the experimental results. Using different model potentials for the interaction between the Fermi sea and the impurity, we show that it is possible to establish a regime of universality, in terms of these two parameters, that includes the whole experimental regime. This illustrates the relevance of quantum fluctuations and beyond mean-field effects to correctly describe the Fermi polaron problem.
We examine pairing and molecule formation in strongly interacting Fermi gases, and we discuss how radio-frequency (rf) spectroscopy can reveal these features. For the balanced case, the emergence of stable molecules in the Bose-Einstein condensation regime results in a two-peak structure in the rf spectrum with clearly visible medium effects on the low-energy part of the molecular wave function. For the highly imbalanced case, we show the existence of a well-defined quasiparticle (a spin polaron) on both sides of the Feshbach resonance, we evaluate its lifetime, and we illustrate how its energy may be measured by rf spectroscopy.
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 TTT-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 TTT-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.
Mobile impurity atoms immersed in Bose–Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one-dimensional systems of ultracold atoms. By combining a non-perturbative renormalization group approach with numerically exact diffusion Monte Carlo calculations we obtain not only detailed numerical results over a broad range of parameters but also qualitative understanding of different regimes of the system. We find that an accurate description of Bose polarons requires the inclusion of two-phonon scattering terms which go beyond the commonly used Fröhlich model. Furthermore we show that when the Bose gas is in the strongly interacting regime, one needs to include interactions between the phonon modes. We use several theoretical approaches to calculate the polaron energy and its effective mass. The former can be measured using radio-frequency spectroscopy and the latter can be studied experimentally using impurity oscillations in a harmonic trapping potential. We compare our theoretical results for the effective mass to the experiments by Catani et al (2012 Phys. Rev. A 85 023623). In the weak-to-intermediate coupling regimes we obtain excellent quantitative agreement between theory and experiment, without any free fitting parameter. We supplement our analysis by full dynamical simulations of polaron oscillations in a shallow trapping potential. We also use our renormalization group approach to analyze the full phase diagram and identify regions that support repulsive and attractive polarons, as well as multi-particle bound states.