We study entanglement between the spin components of the Bardeen-Cooper-Schrieffer (BCS) ground state by calculating the full entanglement spectrum and the corresponding von Neumann entanglement entropy. The entanglement spectrum is effectively modeled by a generalized Gibbs ensemble (GGE) of non-interacting electrons, which may be approximated by a canonical ensemble at the BCS critical temperature. We further demonstrate that the entanglement entropy is jointly proportional to the pairing energy and to the number of electrons about the Fermi surface (an area law). Furthermore, the entanglement entropy is also proportional to the number fluctuations of either spin component in the BCS state.PACS numbers: 74.20.Fg, 03.65.Ud Bipartite entanglement in a pure state, say ρ AB = |ψ ψ|, arises from quantum correlations between subsystem partitions A and B. Due to these correlations measurements performed on one partition, say A, exhibits fluctuations of purely quantum character. Complete information on these subsystem fluctuations is contained in the reduced density operator ρ A = tr B ρ AB , which is obtained by averaging over a complete set of states belonging to B. Quantifying entanglement in ρ AB involves measuring the degree of uncertainty of the underlying probability distribution over projections onto the Schmidt states of ρ A (that is, the eigenvalues and eigenvectors of the reduced density operator). A popular scalar measure used for this purpose is the von Neumann entanglement entropywhich is identical to the Gibbs entropy associated with the probability distribution {p i } = spec ρ A . Alternatively, the full eigenvalue spectrum of ρ A may be used as a measure of entanglement in pure states, because comparisons with effective thermal distributions can sometimes provide additional physical insight. 1-3Many recent studies of entanglement entropy in manyparticle systems focus on correlations between spatial partitions.4 This emphasis may be based on some current designs of quantum computers that manipulate entangled qubits that are separated in space. 5,6 However, the more general idea of entanglement as a manifestation of quantum correlations makes studies of entanglement under other partitioning schemes valuable in the understanding of interacting systems. For instance, a general scheme for the computation of modewise entanglement entropy that is relevant to the system discussed here has been derived for bosonic 7-10 and fermionic 11,12 Gaussian states. One of the main conclusions in these papers is that the analysis of mode entanglement in such Gaussian states can be reduced to an analysis of two-mode (pair-wise) entanglement, which greatly simplifies the theoretical study of entanglement in these many-body systems. Also, mode entanglement has been studied previously in the context of examining single-particle nonlocal quantum effects (Bell inequalities)13-17 and extractable entanglement from assemblies of identical particles for quantum information processing tasks (entanglement of particles). 18-23In t...
We report on a novel mechanism of BCS-like superconductivity, mediated by a pair of Bogoliubov quasiparticles (bogolons). It takes place in hybrid systems consisting of a two-dimensional electron gas in a transition metal dichalcogenide monolayer in the vicinity of a Bose–Einstein condensate. Taking a system of two-dimensional indirect excitons as a testing ground of Bose-Einstein condensate we show, that the bogolon-pair-mediated electron pairing mechanism is stronger than phonon-mediated and single bogolon-mediated ones. We develop a microscopic theory of bogolon-pair-mediated superconductivity, based on the Schrieffer–Wolff transformation and the Gor’kov’s equations, study the temperature dependence of the superconducting gap and estimate the critical temperature of superconducting transition for various electron concentrations in the electron gas and the condensate densities.
We propose an optical approach to monitor superconductors in conjunction with a normal metal layer. Effectively such a hybrid system represents a resonator, where electrons are strongly coupled with light. We show that the interaction of light with the superconductor turns out strongly boosted in the presence of the neighboring metal and as a result, the electromagnetic power absorption of the system is dramatically enhanced. It manifests itself in a giant Fanolike resonance which can uniquely characterize the elementary excitations of the system. Our approach is especially promising for topological superconductors, where the Majorana fermions can be revealed and controlled by light.
We report on an unconventional mechanism of electron scattering in graphene in hybrid Bose-Fermi systems. We study energy-dependent electron relaxation time, accounting for the processes of emission and absorption of a Bogoliubov excitation (a bogolon). Then using the Bloch-Grüneisen approach, we find the finite-temperature resistivity of graphene and show that its principal behavior is ∼ T 4 in the limit of low temperatures and linear at high temperatures. We show that bogolonmediated scattering can surpass the acoustic phonon-assisted relaxation. It can be controlled by the distance between the layers and the condensate density, giving us additional degrees of freedom and a useful tool to render electron mobility by the sample design and external pump.
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