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arXiv:hep-ph/0312368

Entanglement in condensates involving strong interactions

Miller, David E., Abdel Nasser Tawfik

Published Dec 29, 2003• 5 citations
arXivHTMLPDF

Abstract

We look at two well known examples of interacting systems relating to condensed matter in which we put the strong interacting parameters. At high quark chemical potentials and low temperatures we study the entropy arising from the excitation in the BCS model of superconductivity and the Bose-Einstein condensation (BEC) of colored quark pairs. We compare it with the ground state entropy for a system consisting of two colored quarks. In the BCS model we found that the entropy strongly depends on the energy gap. Both for the very small values of the momenta as well as those much greater than the characterizing Fermi momentum $p_f$, the ground state entropy is dominant. For the BEC case we suggest a phenomenological model to build up colored bosonic quark pairs. Here the entropy entirely depends upon the short ranged repulsive interactions between the quark pairs and vanishes for large momenta.

DOI
10.48550/arxiv.hep-ph/0312368

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We look at two well known examples of interacting systems relating to condensed matter in which we put the strong interacting parameters. At high quark chemical potentials and low temperatures we study the entropy arising from the excitation in the BCS model of superconductivity and the Bose-Einstein condensation (BEC) of colored quark pairs. We compare it with the ground state entropy for a system consisting of two colored quarks. In the BCS model we found that the entropy strongly depends on the energy gap. Both for the very small values of the momenta as well as those much greater than the characterizing Fermi momentum pfp_fpf​, the ground state entropy is dominant. For the BEC case we suggest a phenomenological model to build up colored bosonic quark pairs. Here the entropy entirely depends upon the short ranged repulsive interactions between the quark pairs and vanishes for large momenta.
We relate short-range correlations in ultracold-atom Fermi gases to the entropy of the system over the entire temperature, TTT, vs coupling strength, $\ensuremath{-}1/{k}_{F}a$, plane. In the low-temperature limit the entropy is dominated by phonon excitations and the correlations increase as T4{T}^{4}T4. In the Bose-Einstein condensate (BEC) limit, we calculate a boson model within the Bogoliubov approximation to show explicitly how phonons enhance the fermion correlations. In the high-temperature limit, we show from the virial expansion that the correlations decrease as 1/T1/T1/T. The correlations therefore reach a maximum at a finite-temperature. We infer the general structure of the isentropes of the Fermi gas in the $(T,\ensuremath{-}1/{k}_{F}a)$ plane, and the temperature dependence of the correlations in the unitary, BEC, and BCS limits. Our results compare well with measurements of the correlations via photoassociation experiments at higher temperatures.
The two-particle spectrum in a dense Fermion system is treated using a thermodynamic Green function approach. A self-consistent description of possible bound states and a superfluid condensate in a correlated medium is given. A detailed understanding of superfluidity and superconductivity in correlated Fermion systems, especially the transition from the Cooper-paired state (weak-coupling limit) to the Bose condensed state of tightly bound pairs of Fermions (strong coupling limit) [1], is of great interest for very different physical systems. The problem of a unified treatment of Bose–Einstein condensation (BEC) and the Bardeen–Cooper–Schrieffer (BCS) phase arises not only in describing the electron structure of strongly correlated electron superfluids such as superconductors [2], the electronhole system in semiconductors [3], spin-polarized hydrogen and liquid He [4], but also in the theory of nuclear matter [5] and quark–gluon systems [6]. Recently, there have been several new approaches to this stimulating problem. A Monte-Carlo simulation of a finite He system at zero temperature has been performed in Ref. [7]. The microscopic theory of strongly coupled quantum fluids has been treated within the Jastrow approximation (cf. Ref. [8]) to obtain the ground state and low-lying excited states of strongly correlated boson quantum fluids. The crossover from weak to strong coupling superconductivity has been considered using a functional integral representation [2] (see also Ref. [7]).
The (mean field based) BCS theory is considered one of the most successful theories in condensed matter physics. It is justified in ordinary metal superconductors the coherence length ξξξ is large, with two important features: the order parameter (OP) and excitation gap (EG) are identical, and the pair formation and their Bose condensation take place at the same temperature Tc. It fails to explain the underdoped cuprate superconductivity: EG is finite at Tc and thus distinct from OP. Since these superconductors belong to a large class of small ξξξ materials, this failure has the potential for widespread impact. Here we have extended BCS theory in a natural way to short ξξξ superconductors, based on a BCS--BEC crossover scenario, and arrived at a simple physical picture in which incoherent, finite momentum pairs become progressively more important as the pairing interaction becomes stronger, leading to the distinction between EG and OP. The superconductivity from the fermionic perspective and BEC from the bosonic perspective are just two sides of the same coin. Our theory is capable of making verifiable quantitative predictions. We obtain a cuprate phase diagram (with one free parameter) , in (semi-)quantitative agreement with experiment. The mutually compensating contributions from fermionic quasiparticles and bosonic pair excitations provides a natural explanation for the quasi-universal behavior of the in-plane superfluid density versus T. Our bosonic pair excitations also provide an intrinsic mechanism for the long mysterious linear T terms in the specific heat. Incoherent pair contributions lead to new low T power laws, consistent with existing experiments. Finally, we demonstrated that the onset of superconducting long range order leads to sharp features in the specific heat at Tc, consistent with experiment.
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) in a relativistic superfluid within a boson-fermion model. The model includes, besides the fermions, separate bosonic degrees of freedom, accounting for the bosonic nature of the Cooper pairs. The crossover is realized by tuning the difference between the boson mass and boson chemical potential as a free parameter. The model yields populations of condensed and uncondensed bosons as well as gapped and ungapped fermions throughout the crossover region for arbitrary temperatures. Moreover, we observe the appearance of antiparticles for sufficiently large values of the crossover parameter. As an application, we study pairing of fermions with imbalanced populations. The model can potentially be applied to color superconductivity in dense quark matter at strong couplings.
Abstract From the viewpoint of the Bose–Einstein condensation (BEC) of the fermion system, the maximum geminal of the second-order reduced density matrix of the superconducting state exactly corresponds to the Cooper pair. In this paper the entanglement entropy (EE) for the maximum geminal of the BCS ground state is evaluated. The EE behaves logarithmically with respect to the number of the maximum geminal. Furthermore, the disappearance point of superconductivity is defined on the basis of the fermion BEC. In the superconducting ground state, almost all electrons in the energy width of the gap parameter near the Fermi level are condensed as a maximum geminal. They suddenly change to normal electrons with a finite gap of the EE at the disappearance point like a first-order phase transition.
The role of repulsive interactions in statistical systems of Bose particles is investigated. Three different phenomenological frameworks are considered: a mean-field model, an excluded volume model, and a model with a medium-dependent effective mass. All three models are tuned to yield similar equations of state, with only minor deviations from the ideal Bose gas at small chemical potentials. Our analysis indicates, however, that these models lead to qualitatively different results for the Bose-Einstein condensation phenomenon. We discuss the different aspects of this phenomenon, namely, an onset of the Bose-Einstein condensation, particle number fluctuations, and a behavior of the Bose condensate. The obtained results can be helpful for interpreting the lattice QCD data at small temperature and large isospin chemical potential and the data on multiple pion production in high-energy nuclear collisions.