Abstract:
We demonstrate that the Bell test cannot be realized at finite temperatures in the vast majority of electronic setups proposed previously for quantum entanglement generation. This fundamental difficulty is shown to originate in a finite probability of quasiparticle emission from Fermi-sea detectors. In order to overcome the feedback problem, we suggest a detection strategy, which takes advantage of a resonant coupling to the quasiparticle drains. Unlike other proposals, the designed Bell test provides a possibility to determine the critical temperature for entanglement production in the solid state.

Abstract:
We study stimulated light scattering off a superfluid Fermi gas of atoms at finite temperature. We derive response function that takes into account vertex correction due to final state interactions; and analyze finite temperature effects on collective and quasiparticle excitations of a uniform superfluid Fermi gas. Light polarization is shown to play an important role in excitations. Our results suggest that it is possible to excite Bogoliubov-Anderson phonon at a large scattering length by light scattering.

Abstract:
We study the entanglement in various fully-gapped complex paired states of fermions in two dimensions, focusing on the entanglement spectrum (ES), and using the BCS form of the ground state wavefunction on a cylinder. Certain forms of the pairing functions allow a simple and explicit exact solution for the ES. In the weak-pairing phase of l-wave paired spinless fermions (l odd), the universal low-lying part of the ES consists of |l| chiral Majorana fermion modes [or 2|l| (l even) for spin-singlet states]. For |l|>1, the pseudo-energies of the modes are split in general, but for all l there is a zero--pseudo-energy mode at zero wavevector if the number of modes is odd. This ES agrees with the perturbed conformal field theory of the edge excitations. For more general BCS states, we show how the entanglement gap diverges as a model pairing function is approached.

Abstract:
Free fermions with a finite Fermi surface are known to exhibit an anomalously large entanglement entropy. The leading contribution to the entanglement entropy of a region of linear size $L$ in $d$ spatial dimensions is $S\sim L^{d-1} \log{L}$, a result that should be contrasted with the usual boundary law $S \sim L^{d-1}$. This term depends only on the geometry of the Fermi surface and on the boundary of the region in question. I give an intuitive account of this anomalous scaling based on a low energy description of the Fermi surface as a collection of one dimensional gapless modes. Using this picture, I predict a violation of the boundary law in a number of other strongly correlated systems.

Abstract:
The leading asymptotic large-scale behavior of the spatially bipartite entanglement entropy (EE) of the free Fermi gas infinitely extended in multidimensionsal Euclidean space at zero absolute temperature, T=0, is by now well understood. Here, we announce and discuss the first rigorous results for the corresponding EE of thermal equilibrium states at T>0. The leading large-scale term of this thermal EE turns out to be twice the leading finite-size correction to the infinite-volume thermal entropy (density). Not surprisingly, this correction is just the thermal entropy on the boundary surface of the bipartition. However, it is given by a rather complicated analytical expression derived from semiclassical functional calculus and differs, at least at high temperature, from simpler expressions previously obtained by arguments based on conformal field theory. In the zero-temperature limit, the leading large-scale term of the thermal EE considerably simplifies and displays a ln(1/T)-singularity which one may identify with the known logarithmic correction at T=0 to the so-called area-law scaling. Our results extend to the whole one-parameter family of (quantum) R\'enyi entropies.

Abstract:
We present calculations of the tunneling density of states in an anisotropically paired superconductor for two different sample geometries: a semi-infinite system with a single specular wall, and a slab of finite thickness and infinite lateral extent. In both cases we are interested in the effects of surface pair breaking on the tunneling spectrum. We take the stable bulk phase to be of $d_{x^2-y^2}$ symmetry. Our calculations are performed within two different band structure environments: an isotropic cylindrical Fermi surface with a bulk order parameter of the form $\Delta\sim k_x^2-k_y^2$, and a nontrivial tight-binding Fermi surface with the order parameter structure coming from an anti-ferromagnetic spin-fluctuation model. In each case we find additional structures in the energy spectrum coming from the surface layer. These structures are sensitive to the orientation of the surface with respect to the crystal lattice, and have their origins in the detailed form of the momentum and spatial dependence of the order parameter. By means of tunneling spectroscopy, one can obtain information on both the anisotropy of the energy gap, $|\Delta(\p)|$, as well as on the phase of the order parameter, $\Delta(\p) = |\Delta(\p)|e^{i\varphi(\p)}$.

Abstract:
In this paper we present the quantity, which is an entanglement parameter. Its origin is very intriguing, because its construction is motivated by separability criteria based on uncertainty relation. We show that this quantity is asymptotically continuous. We also find the lower and upper bounds for it. Our entanglement parameter has the same feature as the coherent information: both can be negative. There are also some classes of states for which these quantities coincide with each other.

Abstract:
We investigate the entanglement between individual field theory modes in finite-density systems of interacting relativistic and non-relativistic fermions in one spatial dimension. We calculate the entanglement entropy for a single field theory mode and the mutual information between any two modes. The calculation is perturbative in the four-fermion (two-body) coupling, with the leading contribution at order lambda^2 log(lambda^2). At this leading order, the perturbative expression for the entanglement entropy of a mode diverges logarithmically as the momentum of the mode approaches the Fermi surface from above or below. The mutual information between modes is largest for pairs of modes just above and below the Fermi momentum. The entanglement properties of modes near the Fermi surface are qualitatively the same if the field theory is cut off to eliminate modes away from the Fermi surface.

Abstract:
We argue that Landau-Fermi liquids do not have any gravity duals in the purely classical limit. We employ the logarithmic behavior of entanglement entropy to characterize the existence of Fermi surfaces. By imposing the null energy condition, we show that the specific heat always behaves anomalously. We also present a classical gravity dual which has the expected behavior of the entanglement entropy and specific heat for non-Fermi liquids.

Abstract:
We propose a model for realizing exotic paired states in cold atomic Fermi gases. By using a {\it spin dependent} optical lattice it is possible to engineer spatially anisotropic Fermi surfaces for each hyperfine species, that are rotated 90 degrees with respect to one another. We consider a balanced population of the fermions with an attractive interaction. We explore the BCS mean field phase diagram as a function of the anisotropy, density, and interaction strength, and find the existence of an unusual paired superfluid state with coexisting pockets of momentum space with gapless unpaired carriers. This state is a relative of the Sarma or breached pair states in polarized mixtures, but in our case the Fermi gas is unpolarized. We also propose the possible existence of an exotic paired "Cooper-pair Bose-Metal" (CPBM) phase, which has a gap for single fermion excitations but gapless and uncondensed "Cooper pair" excitations residing on a "Bose-surface" in momentum space.