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arXiv:1604.06249 · Physical review. B./Physical review. B

Tunable breakdown of the polaron picture for mobile impurities in a topological semimetal

M. A. Caracanhas, Rodrigo G. Pereira

Published Dec 9, 2016• 2 citations
arXivHTMLPDF

Abstract

Mobile impurities in cold atomic gases constitute a new platform for investigating polaron physics. Here we show that when impurity atoms interact with a two-dimensional Fermi gas with quadratic band touching, the polaron picture may either hold or break down depending on the particle-hole asymmetry of the band structure. If the hole band has a smaller effective mass than the particle band, the quasiparticle is stable and its diffusion coefficient varies with temperature as $D(T)\ensuremath{\propto}{ln}^{2}T$. If the hole band has larger mass, the quasiparticle weight vanishes at low energies due to an emergent orthogonality catastrophe. In this case we map the problem onto a set of one-dimensional channels and use conformal field theory techniques to obtain $D(T)\ensuremath{\propto}{T}^{\ensuremath{\nu}}$ with an interaction-dependent exponent $\ensuremath{\nu}$. The different regimes can be detected in the nonequilibrium expansion dynamics of an initially confined impurity.

DOI
10.1103/physrevb.94.220302

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Abstract We study the polaron problem of an impurity immersed in the background of a Fermi sea confined in one-dimensional or two-dimensional isotropic traps. By changing the trapping potential from loose to tight, a dimensional crossover from anisotropically trapped three-dimensional to quasi-two-dimensional (quasi-2D) or quasi-one-dimensional (quasi-1D) configurations is investigated by calculating the ground-state energy in a wide range of interaction strength. We adopt a low-dimensional effective Hamiltonian in the form of a two-channel model, where the excited levels in the confined directions are described phenomenologically by a dressed molecule, and use the variational approach up to one pair of particle-hole fluctuations to calculate the energies of polaron and molecule states. We map out the phase diagrams for both quasi-1D and quasi-2D configurations and different mass ratios, and conclude that the polaron phase is preferable with tighter confinement and lighter impurity mass in lower dimensions. We also find that owing to the significant population of excited levels by strong interaction, a strictly low-dimensional system with all particles residing in the ground state of the trap can never work when study polaron-molecule transition, even in the tightly confined limit. This discrepancy has been observed in an experiment of quasi-2D gases of 40 K atoms and is well explained by our calculation.

Europhysics Letters (EPL)•Mar 31, 2023•1 citation
Mobile impurities in cold atomic gases constitute a new platform for investigating polaron physics. Here we show that when impurity atoms interact with a two-dimensional Fermi gas with quadratic band touching, the polaron picture may either hold or break down depending on the particle-hole asymmetry of the band structure. If the hole band has a smaller effective mass than the particle band, the quasiparticle is stable and its diffusion coefficient varies with temperature as D(T)\ensuremath∝ln2TD(T)\ensuremath{\propto}{ln}^{2}TD(T)\ensuremath∝ln2T. If the hole band has larger mass, the quasiparticle weight vanishes at low energies due to an emergent orthogonality catastrophe. In this case we map the problem onto a set of one-dimensional channels and use conformal field theory techniques to obtain D(T)\ensuremath∝T\ensuremathνD(T)\ensuremath{\propto}{T}^{\ensuremath{\nu}}D(T)\ensuremath∝T\ensuremathν with an interaction-dependent exponent \ensuremathν\ensuremath{\nu}\ensuremathν. The different regimes can be detected in the nonequilibrium expansion dynamics of an initially confined impurity.
Recently, a mass-gap description of mobile impurities in a Fermi gas was introduced, which connects Anderson's orthogonality catastrophe for static impurities to the quasiparticle picture of Fermi polarons through a recoil-induced energy gap in the fermionic dispersion. That description, however, was restricted to zero temperature and did not address dynamics. Here we generalize the mass-gap model to finite temperature by combining the Lee--Low--Pines transformation with a self-consistent Hartree--Fock decoupling of the recoil-induced interaction, and we study the quench dynamics within this framework using the functional-determinant approach. At finite temperature the effective mass gap obeys the self-consistency equation Δ(T)=2UFtanh⁡[Δ(T)/4kBT]Δ(T)=2U_F\tanh[Δ(T)/4k_B T]Δ(T)=2UF​tanh[Δ(T)/4kB​T], with UF=kF2/2MU_F=k_F^2/2MUF​=kF2​/2M and MMM the impurity mass. This equation admits a nonzero solution below the characteristic temperature T∗=UF/(2kB)T^*=U_F/(2k_B)T∗=UF​/(2kB​) and closes as (T∗−T)1/2(T^*-T)^{1/2}(T∗−T)1/2. We identify this closing as the mean-field signature of the thermal melting of the polaron and molecule quasiparticles. Computing the Ramsey response S(t)S(t)S(t) after a sudden quench of the impurity--fermion interaction, we find that its long-time oscillations---quantum beats between the bound and in-gap states---disappear precisely above T∗T^*T∗. Our work ties the thermodynamic and dynamical fingerprints of polaron formation to a single temperature-dependent mean-field parameter.
We study the problem of a mobile impurity of mass MMM interacting {\sl via} a s-wave broad or narrow Feshbach resonance with a Fermi sea of particles of mass mmm. Truncating the Hilbert space to at most one pair of particle-hole excitations of the Fermi sea, we determine ground state properties of the polaronic branch other than its energy, namely the polaron quasiparticle residue ZZZ, and the impurity-to-fermion pair correlation function G(x)G(x)G(x). We show that G(x)G(x)G(x) deviates from unity at large distances as −(A_4+B_4cos⁡2k_Fx)/(k_Fx)4-(A\_4+B\_4 \cos 2 k\_F x)/(k\_F x)^4−(A_4+B_4cos2k_Fx)/(k_Fx)4, where k_Fk\_Fk_F is the Fermi momentum; since A_4>0A\_4>0A_4>0 and B_4>0B\_4>0B_4>0, the polaron has a diverging rms radius and exhibits Friedel-like oscillations. In the weakly attractive limit, we obtain analytical results, that in particular detect the failure of the Hilbert space truncation for a diverging mass impurity, as expected from Anderson orthogonality catastrophe; at distances between ∼1/k_F\sim 1/k\_F∼1/k_F and the asymptotic distance where the 1/x41/x^41/x4 law applies, they reveal that G(x)G(x)G(x) exhibits an intriguing multiscale structure.
We present a unified theory that connects the quasiparticle picture of Fermi polarons for mobile impurities to the Anderson orthogonality catastrophe for static impurities. By operator reordering of the underlying many-body Hamiltonian, we obtain a modified fermionic dispersion relation that features a recoil-induced energy gap, which we call the "mass gap." We show that the resulting mean-field Hamiltonian exhibits an in-gap state for finite impurity mass, which takes a key role in Fermi polaron and molecule formation. We identify the mass gap as the microscopic origin of the quasiparticle weight of Fermi polarons and derive a power-law scaling of the weight with the impurity-to-fermion mass ratio. The associated in-gap state is shown to give rise to the emergence of the polaron-to-molecule transition away from the limiting case of the Anderson orthogonality catastrophe in which the transition is absent.
The Fermi polaron, formed by an impurity interacting with a surrounding Fermi sea, exemplifies the canonical quasiparticle concept as a cornerstone in our description of quantum many-body systems across a wide range of energy scales. Experiments on atomic quantum gases have provided profound insights into the universal nature of the Fermi polaron. While most previous studies have focused on the case of zero impurity momentum, finite-momentum properties have remained largely uncharted. Here, we investigate the moving Fermi polaron by combining a novel Raman acceleration scheme with high-precision radio-frequency spectroscopy, exploring the quasiparticle dispersion relation over a wide range of momenta. We compare our measurements of energy shifts and spectral linewidths with a microscopic theory and reach quantitative agreement for all momenta. For low momenta, we find the energy of the moving polaron to be fully consistent with the Fermi liquid picture of a dressed particle with a constant effective mass. At high momenta, the polaron approaches the behavior of a weakly interacting bare particle, featuring small energy shifts and weak broadening. For intermediate momenta, broadening is generally larger and, most strikingly, the behavior differs for attractive and repulsive polarons. While the repulsive polaron exhibits a smooth connection between both regimes along with a monotonic change of the energy shift, the attractive case shows a peculiar non-monotonic behavior. With increasing momentum, the attractive polaron enters a regime where its energy deviates from the constant effective mass expression and broadening suddenly increases. By comparing this observation with theory, we show that this abrupt behavior coincides with the attractive polaron entering a molecule-hole continuum, where it is no longer the ground state. We interpret this as a motion-induced polaron-molecule transition.
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.
Abstract We study the polaron problem of an impurity immersed in the background of a Fermi sea confined in one-dimensional or two-dimensional isotropic traps. By changing the trapping potential from loose to tight, a dimensional crossover from anisotropically trapped three-dimensional to quasi-two-dimensional (quasi-2D) or quasi-one-dimensional (quasi-1D) configurations is investigated by calculating the ground-state energy in a wide range of interaction strength. We adopt a low-dimensional effective Hamiltonian in the form of a two-channel model, where the excited levels in the confined directions are described phenomenologically by a dressed molecule, and use the variational approach up to one pair of particle-hole fluctuations to calculate the energies of polaron and molecule states. We map out the phase diagrams for both quasi-1D and quasi-2D configurations and different mass ratios, and conclude that the polaron phase is preferable with tighter confinement and lighter impurity mass in lower dimensions. We also find that owing to the significant population of excited levels by strong interaction, a strictly low-dimensional system with all particles residing in the ground state of the trap can never work when study polaron-molecule transition, even in the tightly confined limit. This discrepancy has been observed in an experiment of quasi-2D gases of 40 K atoms and is well explained by our calculation.