A single impurity in an ideal atomic Fermi gas: current understanding and some open problems

We briefly review some current theoretical and experimental aspects of the problem of a single spinless impurity in a 3D polarised atomic Fermi gas at zero temperature where the interactions can be tuned using a wide Feshbach resonance. We show that various few-body states in vacuum composed of the impurity and background gas atoms (single impurity, dimer, trimer, tetramer) give rise to corresponding dressed states ({\em polaron}, {\em dimeron}, {\em trimeron}, {\em tetrameron}) in the gas and inherit many of their characteristics. We study the ground state focussing on the choice of wave function and its properties. We raise a few unsolved problems: whether the polaron and dimeron are really separate branches, what other few-body states might exist, the nature of the groundstate for large numbers of particle-hole pairs and why is the polaron ansatz so good. We then turn to the excited states, and to the calculation of the effective mass. We examine the bounds on the effective mass and raise a conjecture about that of composite quasiparticle states.Comment: Review asked by Journal of the Indian Institute of Science, to appear in Vol. 94 No. 2 (Apr. - Jun. 2014) Cold Atom Quantum Emulators: From Condensed Matter to Filed Theory to Optical Clock

Optical lattices with large scattering length: Using few-body physics to simulate an electron-phonon system

We propose to go beyond the usual Hubbard model description of atoms in optical lattices and show how few-body physics can be used to simulate many-body phenomena, e.g., an electron-phonon system. We take one atomic species to be trapped in a deep optical lattice at full filling and another to be untrapped spin-polarized fermions (which do not see the optical lattice) but has an s-wave contact interaction with the first species. For large positive scattering length on the order of lattice spacing, the usual two-body bound (dimer) states overlap forming giant orbitals extending over the entire lattice, which can be viewed as an "electronic" band for the untrapped species while the trapped atoms become the "ions" with their own on-site dynamics, thereby simulating an electron-phonon system with renormalization of the phonon frequencies and Peierls transitions. This setup requires large scattering lengths but minimises losses, does not need higher bands and adds new degrees of freedom which cannot easily be described in terms of lattice variables, thus opening up intriguing possibilities to explore interesting physics at the interface between few-body and many-body systems.Comment: published version; title change

Excitonic states of an impurity in a Fermi gas

We study excitonic states of an atomic impurity in a Fermi gas, i.e., bound states consisting of the impurity and a hole. Previous studies considered bound states of the impurity with particles from the Fermi sea where the holes only formed part of the particle-hole dressing. Within a two-channel model, we find that, for a wide range of parameters, excitonic states are not ground but metastable states. We further calculate the decay rates of the excitonic states to polaronic and dimeronic states and find they are long lived, scaling as $\Gamma^{\rm{Exc}}_ {\rm{Pol}} \propto ( \Delta\omega)^{5.5}$ and $\Gamma^{\rm{Exc}}_ {\rm{Dim}} \propto (\Delta\omega)^{4}$. We also find that a new continuum of exciton-particle states should be considered alongside the previously known dimeron-hole continuum in spectroscopic measurements. Excitons must therefore be considered as a new ingredient in the study of metastable physics currently being explored experimentally.Comment: published versio

Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model

Many-body localization is a unique physical phenomenon driven by interactions and disorder for which a quantum system can evade thermalization. While the existence of a many-body localized phase is now well-established in one-dimensional systems, its fate in higher dimension is an open question. We present evidence for the occurrence of a transition to a many-body localized regime in a two-dimensional quantum dimer model with interactions and disorder. Our analysis is based on the results of large-scale simulations for static and dynamical properties of a consequent number of observables. Our results pave the way for a generic understanding of occurrence of a many-body localization transition in dimension larger than one, and highlight the unusual quantum dynamics that can be present in constrained systems.Comment: 15 pages, 14 figures, published versio

Eigenstate thermalization hypothesis in quantum dimer models

We use exact diagonalization to study the eigenstate thermalization hypothesis (ETH) in the quantum dimer model on the square and triangular lattices. Due to the nonergodicity of the local plaquette-ip dynamics, the Hilbert space, which consists of highly constrained close-packed dimer configurations, splits into sectors characterized by topological invariants. We show that this has important consequences for ETH: We find that ETH is clearly satisfied only when each topological sector is treated separately, and only for moderate ratios of the potential and kinetic terms in the Hamiltonian. By contrast, when the spectrum is treated as a whole, ETH breaks down on the square lattice, and apparently also on the triangular lattice. These results demonstrate that quantum dimer models have interesting thermalization dynamics that has not previously been studied

Quantum melting of two-component Rydberg crystals

We investigate the quantum melting of one-dimensional crystals that are realized in an atomic lattice in which ground state atoms are laser excited to two Rydberg states. We focus on a regime where both, intra- and interstate density-density interactions as well as coherent exchange interactions contribute. We determine stable crystalline phases in the classical limit and explore their melting under quantum fluctuations introduced by the excitation laser as well as two-body exchange. We find that within a specific parameter range quantum fluctuations introduced by the laser can give rise to a devil’s staircase structure which one might associate with transitions in the classical limit. The melting through exchange interactions is shown to also proceed in a steplike fashion, in the case of small crystals, due to the proliferation of Rydberg spin waves

Coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice

We investigate the properties of an edge-centered honeycomb lattice, and show that this lattice features both spin-1/2 and spin-1 Dirac-Weyl fermions at different filling fractions f (f=1/5,4/5 for spin-1/2 and f=1/2 for spin-1). This five-band system is the simplest lattice that can support simultaneously the two different paradigmatic Dirac-Weyl fermions with half-integer spin and integer spin. We demonstrate that these pseudo-relativistic structures, including a flat band at half-filling, can be deduced from the underlying Kagome sublattice. We further show that the signatures of the two kinds of relativistic fermions can be clearly revealed by several perturbations, such as a uniform magnetic field, a Haldane-type spin-orbit term, and charge density waves. We comment on the possibility to probe the similarities and differences between the two kinds of relativistic fermions, or even to isolate them individually. We present a realistic scheme to realize such a system using cold atoms.Comment: published versio