Pairing based cooling of Fermi gases

We propose a pairing-based method for cooling an atomic Fermi gas. A three component (labels 1, 2, 3) mixture of Fermions is considered where the components 1 and 2 interact and, for instance, form pairs whereas the component 3 is in the normal state. For cooling, the components 2 and 3 are coupled by an electromagnetic field. Since the quasiparticle distributions in the paired and in the normal states are different, the coupling leads to cooling of the normal state even when initially $T_{paired}\geq T_{normal}$ (notation $T_S\geq T_N$). The cooling efficiency is given by the pairing energy and by the linewidth of the coupling field. No superfluidity is required: any type of pairing, or other phenomenon that produces a suitable spectral density, is sufficient. In principle, the paired state could be cooled as well but this requires $T_N<T_S$. The method has a conceptual analogy to cooling based on superconductor -- normal metal (SN) tunneling junctions. Main differences arise from the exact momentum conservation in the case of the field-matter coupling vs. non-conservation of momentum in the solid state tunneling process. Moreover, the role of processes that relax the energy conservation requirement in the tunneling, e.g. thermal fluctuations of an external reservoir, is now played by the linewidth of the field. The proposed method should be experimentally feasible due to its close connection to RF-spectroscopy of ultracold gases which is already in use.Comment: Journal version 4 pages, 4 figure

Cannon-Thurston maps for pared manifolds of bounded geometry

Let Nh ∈, H(M, P) be a hyperbolic structure of bounded geometry on a pared manifold such that each component of ∂0M = ∂M - P is incompressible. We show that the limit set of Nh is locally connected by constructing a natural Cannon-Thurston map. This provides a unified treatment, an alternate proof and a generalization of results due to Cannon and Thurston, Minsky, Bowditch, Klarreich and the author

Signatures of superfluidity for Feshbach-resonant Fermi gases

We consider atomic Fermi gases where Feshbach resonances can be used to continuously tune the system from weak to strong interaction regime, allowing to scan the whole BCS-BEC crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-$T_c$ and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap includes also a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. Incoherent nature of the non-condensed pairs leads to broadening of the peak. The pseudogap and therefore the broadening decay below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition.Comment: Revised version, accepted to Phys. Rev. Letters. Figures changed, explanations adde

On discreteness of commensurators

We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a (virtual) simple factor. In particular for rank one or simple Lie groups, Zariski dense subgroups with non-empty domain of discontinuity have discrete commensurators. This generalizes a Theorem of Greenberg for Kleinian groups. We then prove that for all finitely generated, Zariski dense, infinite covolume discrete subgroups of Isom(H3), commensurators are discrete. Together these prove discreteness of commensurators for all known examples of finitely presented, Zariski dense, infinite covolume discrete subgroups of Isom(X) for X an irreducible symmetric space of non-compact type

Mapping class groups and interpolating complexes: rank

Abstract. A family of interpolating graphs C(S, ξ) of complexity ξ is constructed for a surface S and -2 ≤ ξ ≤ ξ(S). For ξ = -2,-1, ξ (S) -1 these specialize to graphs quasi-isometric to the marking graph, the pants graph and the curve graph respectively. We generalize the notion of a hierarchy and Theorems of Brock-Farb and Behrstock-Minsky to show that the rank of C(S, ξ) is rξ, the largest number of disjoint copies of subsurfaces of complexity greater than ξ that may be embedded in S. The interpolating graphs C(S, ξ) interpolate between the pants graph and the curve graph

Polarons and Molecules in a Two-Dimensional Fermi Gas

We study an impurity atom in a two-dimensional Fermi gas using variational wave functions for (i) an impurity dressed by particle-hole excitations (polaron) and (ii) a dimer consisting of the impurity and a majority atom. In contrast to three dimensions, where similar calculations predict a sharp transition to a dimer state with increasing interspecies attraction, we show that the polaron ansatz always gives a lower energy. However, the exact solution for a heavy impurity reveals that both a two-body bound state and distortions of the Fermi sea are crucial. This reflects the importance of particle-hole pairs in lower dimensions and makes simple variational calculations unreliable. We show that the energy of an impurity gives important information about its dressing cloud, for which both ans\"atze give inaccurate results.Comment: 5 pages, 2 figures, minor change

Dielectric function of the semiconductor hole liquid: Full frequency and wave vector dependence

We study the dielectric function of the homogeneous semiconductor hole liquid of p-doped bulk III-V zinc-blende semiconductors within random phase approximation. The single-particle physics of the hole system is modeled by Luttinger's four-band Hamiltonian in its spherical approximation. Regarding the Coulomb-interacting hole liquid, the full dependence of the zero-temperature dielectric function on wave vector and frequency is explored. The imaginary part of the dielectric function is analytically obtained in terms of complicated but fully elementary expressions, while in the result for the real part nonelementary one-dimensional integrations remain to be performed. The correctness of these two independent calculations is checked via Kramers-Kronig relations. The mass difference between heavy and light holes, along with variations in the background dielectric constant, leads to dramatic alternations in the plasmon excitation pattern, and generically, two plasmon branches can be identified. These findings are the result of the evaluation of the full dielectric function and are not accessible via a high-frequency expansion. In the static limit a beating of Friedel oscillations between the Fermi wave numbers of heavy and light holes occurs.Comment: 16 pages, 11 figures included. Update: Minor additions and adjustments, published versio

Multilayer Thermionic Refrigerator and Generator

A new method of refrigeration is proposed. Cooling is obtained by thermionic emission of electrons over periodic barriers in a multilayer geometry. These could be either Schottky barriers between metals and semiconductors or else barriers in a semiconductor superlattice. The same device is an efficient power generator. A complete theory is provided.Comment: 17 pages with 5 postscript figures, submitted to J. Appl. Phy

Dielectric function of the semiconductor hole gas

We study the dielectric function of the homogeneous hole gas in p-doped zinc-blende III-V bulk semiconductors within random phase approximation with the valence band being modeled by Luttinger's Hamiltonian in the spherical approximation. In the static limit we find a beating of Friedel oscillations between the two Fermi momenta for heavy and light holes, while at large frequencies dramatic corrections to the plasmon dispersion occur.Comment: 4 pages, 1 figure included. Version to appear in Europhys. Let

Canted Magnetization Texture in Ferromagnetic Tunnel Junctions

We study the formation of inhomogeneous magnetization texture in the vicinity of a tunnel junction between two ferromagnetic wires nominally in the antiparallel configuration and its influence on the magnetoresistance of such a device. The texture, dependent on magnetization rigidity and crystalline anisotropy energy in the ferromagnet, appears upon an increase of ferromagnetic inter-wire coupling above a critical value and it varies with an external magnetic field.Comment: 5 pages, 4 figure