Repulsive polarons in two-dimensional Fermi gases

Abstract

Path-integral analyses originally pioneered in the study of the complex-phase problem afflicting lattice calculations of finite-density quantum chromodynamics are generalized to non-relativistic Fermi gases with repulsive interactions. Using arguments similar to those previously applied to relativistic theories, we show that the analogous problem in nonrelativistic systems manifests itself naturally in Tan's contact as a nontrivial cancellation between terms with varied dependence on extensive thermodynamic quantities. We analyze that case under the assumption of gaussian phase distribution, which is supported by our Monte Carlo calculations and perturbative considerations. We further generalize these results to observables other than the contact, as well as to polarized systems and systems with fixed particle number. Our results are quite general in that they apply to repulsive multi-component fermions, are independent of dimensionality or trapping potential, and hold in the ground state as well as at finite temperature. Introduction.-Cold-atom experimentalists continue to engineer astonishing techniques to probe fundamental properties of quantum mechanics by means of multi-component gases [1-9]. Access to the properties of these remarkable systems has expanded from the simplest ther-modynamic quantities to observables characterizing nu-anced dynamical and information-theoretic properties (see e.g. [10, 11]). Bridging a broad range of interactions, compositions, and dimensions, this ever-expanding repertoire of techniques is both celebrated and envied by the-orists, as attempting to answer similar questions about low-temperature, strongly correlated fermions is accompanied by a long list of nontrivial complications [12, 13]. Of these impediments, one which is not only particularly formidable but is also shared with lattice studies of quantum chromodynamics (QCD) is the complex phase problem associated on the one hand with non-relativistic, repulsive or imbalanced Fermi systems and on the other with QCD at finite quark density [14, 15]. In the QCD case, the problem can be traced back to the breaking of time-reversal invariance at finite chemical potential (which also appears in quasi-relativistic systems like low-energy graphene away from the Dirac point) [16, 17], which bears a strong resemblance to the (mass-or spin-) imbalanced non-relativistic Fermi gas [18]. Repulsive interactions, on the other hand, do not break time-reversal invariance per se, however that symmetry is lost upon decoupling via a Hubbard-Stratonovich transformation [19, 20]. As explained below, the partition function for N f identical fermion species then takes the path integral form

High-polarization limit of the quasi-two-dimensional Fermi gas

“…As opposed to the attractive polaron, our calculation demonstrates that the energy of the repulsive polaron depends solely on the interaction parameter k F a 2D . This is to be expected as | P | ω z and thus the energy should match previous studies of the repulsive polaron in 2D [13,14]. Furthermore, Fig.…”

“…The energy of a quasi-2D impurity is shown for F /ω z = 0.1 (solid line). Additionally we show the 2D results of Ref [14]. using the often used assumption a 2D = 1/ √ m B (dotted), and also using Eq.…”

Three-body bound states of two bosonic impurities immersed in a Fermi sea in 2D

“…However, as explained above, since our model captures the correct behavior of the two-body system, this small quantitative difference is not a problem. As an extra argument for using the self-consistent method in our analysis, notice that our three-body results when particle-hole fluctuations are taken into account lie mostly in h > -0.54 (see figures 8 and 10), from where the energy of the polaron is always lower than the molecular one and it is the same as calculated with nonself-consistent methods [34,36,39,42,43].…”

“…The problem of one single impurity on top of a Fermi sea has been successfully solved with non-selfconsistent methods (see, e.g. [34,36,39,42,43]). However, we found the self-consistent one more suitable to handle in the investigation of the three-body problem of two impurities immersed in a Fermi sea, whose results are presented in the following sections.…”

Magnetism in Strongly Interacting One-Dimensional Quantum Mixtures

“…In the hatched region all interactions are repulsive, and the spin-chain ground state is the actual ground state of the system. should be stable, unlike in higher dimensions [12][13][14].Experimentally, 1D quantum gases have been successfully realized with strongly interacting bosons [15,16], two species of fermions [17][18][19][20], and, more recently, fermions with SU (n) symmetry, where the number of spin components can be tuned from n = 2 to 6 [21]. All these 1D experiments feature an underlying harmonic trapping potential, which has enabled the study of the evolution from few to many particles [18,20,22].…”