BCS-like Modewise Entanglement of Fermion Gaussian States

选定二叉树态中的纠缠：Dicke/总自旋态、粒子数投影BCS态

Entanglement in selected Binary Tree States: Dicke/Total spin states, particle number projected BCS states

本文研究二叉树态（BTS）中任意k个量子比特子系统的纠缠熵，提出实用计算方法，并分析其标度性质、上界及与涨落的关系，以Dicke态和投影BCS态为例进行说明。

Fermionic Entanglement in Superconducting Systems

We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single particle states $k$ of positive quasimomenta and their time reversed partners $\bar{k}$. In cont…

Entanglement spectra of complex paired superfluids

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 …

Fermionic entanglement in itinerant systems

We study pairwise quantum entanglement in systems of fermions itinerant in a lattice from a second-quantized perspective. Entanglement in the grand-canonical ensemble is studied, both for energy eigenstates and for the thermal state. Relations between entanglement and superconducting correlations are discussed in a BCS-like model and for $η$-pair superconductivity.

Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states

The quantum states built with the eta paring mechanism i.e., eta pairing states, were first introduced in the context of high temperature superconductivity where they were recognized as important example of states allowing for off-diagonal long-range order (ODLRO). In this paper we describe the structure of the correlations present in these states when considered in their momentum representation and we explore the relations between the quantum bipartite/multipartite correlations exhibited in k space and the direct lattice superconducting correlations. In particular, we show how the negativity …

Momentum space entanglement of interacting fermions

Momentum space entanglement entropy probes quantum correlations in interacting fermionic phases. It is very sensitive to interactions, obeying volume-law scaling in general, while vanishing in the Fermi gas. We show that the Rényi entropy in momentum space has a systematic expansion in terms of the phase space volume of the partition, which holds at all orders in perturbation theory. This permits, for example, the controlled computation of the entropy of thin shells near the Fermi wavevector in isotropic Fermi liquids and BCS superconductors. In the Fermi liquid, the thin shell entropy is a un…

Entanglement between two fermionic atoms inside a cylindrical harmonic trap

We investigate quantum entanglement between two (spin-1/2) fermions inside a cylindrical harmonic trap, making use of the von Neumann entropy for the reduced single particle density matrix as the pure state entanglement measure. We explore the dependence of pair entanglement on the geometry and strength of the trap and on the strength of the pairing interaction over the complete range of the effective BCS to BEC crossover. Our result elucidates an interesting connection between our model system of two fermions and that of two interacting bosons.

Entanglement of Fermi gases in a harmonic trap

For both cases with and without interactions, bipartite entanglement of two-fermions from a Fermi gas in a trap is investigated. We show how the entanglement depends on the locations of the two fermions and the total number of particles. Fermions at the verge of trap have longer entanglement distance (beyond it, the entanglement disappears) than those in the center. We derive a lower limitation to the average overlapping for two entangled fermions in the BCS ground state, it is shown to be $\sqrt{Q/2M}$, a function of Cooper pair number $Q$ and total number of occupied energy levels $M$.

Entanglement in condensates involving strong interactions

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 …

监控超导链中的测量增强纠缠

Measurement-enhanced entanglement in a monitored superconducting chain

研究发现，在一维费米子链中，配对抑制纠缠增长，而测量抑制配对，二者竞争导致测量增强纠缠，纠缠随测量率增加而增强，但热力学极限下不持续。

Composite-boson approach to molecular Bose-Einstein condensates in mixtures of ultracold Fermi gases

We show that an ansatz based on independent composite bosons [Phys. Rep. 463, 215 (2008)] accurately describes the condensate fraction of molecular Bose-Einstein condensates in ultracold Fermi gases. The entanglement between the fermionic constituents of a single Feshbach molecule then governs the many-particle statistics of the condensate, from the limit of strong interaction to close to unitarity. This result strengthens the role of entanglement as the indispensable driver of composite-boson behavior. The condensate fraction of fermion pairs at zero temperature that we compute matches excell…