Fermion Exchange Research Articles

Composite boson signature in the interference pattern of atomic dimer condensates

We predict the existence of high frequency modes in the interference pattern of two condensates made of fermionic-atom dimers. These modes, which result from fermion exchanges between condensates, constitute a striking signature of the dimer composite nature. From the 2-coboson spatial correlation function, that we derive analytically, and the Shiva diagrams that visualize many-body effects specific to composite bosons, we identify the physical origin of these high frequency modes and determine the conditions to see them experimentally by using bound fermionic-atom pairs trapped on optical lattice sites. The dimer granularity which appears in these modes comes from Pauli blocking that prevents two dimers to be located at the same lattice site.

Electronic spectra and chemical potential of 2-D multi-electron quantum dots in magnetic field: exact multi-pole expansion of coulomb correlation

Two-dimensional superlattices, TMDCs and graphene family exhibit strong coulomb correlations among e–e, e–h, electron-phonon and etc. As the number of electron increases, confining gate voltage and transverse magnetic field are superseded by increasing coulomb interactions (N(N−1)/2 factors) that composes non-trivial Schrödinger equations. Representing such equations in Whittaker-M functions yields a modest alternate formalism, that accommodates integrals of coulomb (exchange) correlations in single-summed, finite and exact Lauricella functions via Chu-Vandermonde identity. For higher carrier density (N = 3, 4, 5, 6, ..), the multipole expansion is incurred as exact and finite-summed coulomb, coulomb-type and dipole-type integrals. Although, fermionic exchange symmetry of many electron systems could be included in terms of various two-electron integrals, for the sake of brevity we have aimed to reproduce experimental results without spin. Signature of interplay among gate voltage, magnetic field, dielectric constant, mass and density of carriers is examined in electronic spectra, magnetization, chemical potential for the systems spanning over wide range of materials (He, BN, GaAs and etc.). Interestingly, chemical potential and addition energy as a function of magnetic field and number of carriers monitor the statistics between strongly degenerate to weakly degenerate composite fermions, coulomb blockade and shell structure of 2-D superlattices. At the most, quadrapole and octapole suffice the convergence.

Diverging Exchange Force and Form of the Exact Density Matrix Functional.

For translationally invariant one-band lattice models, we exploit the abinitio knowledge of the natural orbitals to simplify reduced density matrix functional theory (RDMFT). Striking underlying features are discovered. First, within each symmetry sector, the interaction functional F depends only on the natural occupation numbers n. The respective sets P_{N}^{1} and E_{N}^{1} of pure and ensemble N-representable one-matrices coincide. Second, and most importantly, the exact functional is strongly shaped by the geometry of the polytope E_{N}^{1}≡P_{N}^{1}, described by linear constraints D^{(j)}(n)≥0. For smaller systems, it follows as F[n]=[under ∑]i,i^{'}V[over ¯]_{i,i^{'}}sqrt[D^{(i)}(n)D^{(i^{'})}(n)]. This generalizes to systems of arbitrary size by replacing each D^{(i)} by a linear combination of {D^{(j)}(n)} and adding a nonanalytical term involving the interaction V[over ^]. Third, the gradient dF/dn is shown to diverge on the boundary ∂E_{N}^{1}, suggesting that the fermionic exchange symmetry manifests itself within RDMFT in the form of an "exchange force." All findings hold for systems with a nonfixed particle number as well and V[over ^] can be any p-particle interaction. As an illustration, we derive the exact functional for the Hubbard square.

Recent results for UPC at the LHC

Ultraperipheral heavy ion collisions are a source of photons which can collide with each other producing a pair of particles. This work will be focused on analysis of the light-by-light scattering. Here contribution from fermionic boxes, resonance scattering, VDM-Regge model, two-gluon exchange and pionic background will be compared. Each of these processes dominate at different ranges of two-photon invariant masses. Our calculated nuclear cross section is in good agreement with recently measured ATLAS and CMS data. Predictions including ALICE and LHCb experimental cuts for the next run at the LHC will be shown.

Isotropic Bipolaron–Fermion Exchange Theory and Unconventional Pairing in Cuprate Superconductors

AbstractThe appearance of unconventional pairing in superconducting cuprates is examined from a microscopic model, taking into account important properties of hole‐doped copper oxides. An exchange interaction between fermions and dominantly inter‐site bipolarons is considered to be the mechanism which leads to the pairing. Its momentum dependency is connected to the well‐established fermion–phonon anomalies in cuprate superconductors. Since charge carriers in these materials are strongly correlated, a screened Coulomb repulsion is added to this exchange term. Any ad hoc assumptions like anisotropy are avoided, but a microscopic explanation of unconventional pairing for coupling strengths that are in accordance with experimental facts is provided. One important outcome is a mathematically rigorous elucidation of the role of Coulomb repulsion in unconventional pairing, which is shown to be concomitant with a strong depletion of superconducting pairs. The theory, applied to the special case of LaSr 214, predicts at optimal doping i) a coherence length of , which is the same as that obtained from the Ginzburg–Landau critical magnetic field measured for this material, and ii) d‐wave pair formation in the pseudogap regime, that is, at temperatures much higher than the superconducting transition temperature.

Coboson many-body formalism for atom–dimer scattering length

We use the composite boson (coboson) many-body formalism to tackle scattering lengths for cold fermionic atoms. We show that bound dimers can be taken as elementary entities provided that fermion exchanges between them are treated exactly, as can be done through the coboson formalism. This alternative tool extended to cold atom physics not only makes transparent many-body processes through Shiva diagrams specific to cobosons, but also simplifies calculations. Indeed, the integral equation we derive for the atom–dimer scattering length and solve by restricting the dimer relative motion to the ground state, gives values in remarkable agreement with the exact scattering length values for all fermion mass ratios. This remarkable agreement also holds true for the dimer–dimer scattering length, except for equal fermion masses where our restricted procedure gives a value slightly larger than the accepted one (0.64ad instead of 0.60ad). All this proves that the scattering of a cold-atom dimer with an atom or another dimer is essentially controlled by the dimer relative-motion ground state, a physical result not obvious at first.

Shell structure and paramagnetism of 3-DN-eanisotropic (ellipsoidal) quantum dots: Exact multi-pole expansion of coulomb interaction under fermionic exchange symmetry

As the density of electrons (N=2, 3, 4, 5, 6, 7, 8,.) increases, complexity arises due to coulomb interactions, inclusion of fermionic exchange symmetry and anisotropy. Consequently, Schrodinger equations of anisotropic quantum dots become non-trivial. Recasting such non-relativistic quantum equations into Whittaker-M basis functions unifies coulomb (exchange) correlation and antisymmetric nature of electrons in two-centered integrals of exact, finite, single-summed, terminated and simplest Lauricella functions (F2) via multi-pole expansion and the subsequent Chu-Vandermonde identity. Coulomb correlations interplay with in-plane and out-of-plane electrical and magnetic confinements in their moderate fields. On the other hand, full-scale fermionic exchange symmetry is incorporated through multiple number of Slater determinants, unlike Hartree-Fock method. In this context, both open-shell and restricted closed-shell configurations are considered for trial Hartree-products which are composed of the basis set of oscillator spin-orbitals. Thus optimized bound states can easily capture large number of mixed term symbols. Consequently, level clustering/accidental degeneracies occur in energy level diagram due to competition among strength of anisotropy in electrical confinements, magnetic field, mass of the carrier and dielectric constant. It brings about orbital induced paramagnetism (T∼(0-1)K), signature of fractional quantum Hall effect (FQHE) in chemical potential cusps (μ) and formation of different ′shell structures′ in capacitive energy respectively, spanning over wide dielectric range of materials (atomic like quantum dot, ZnO, GaAs, CdSe (Cadmium Chalcogenide) and PbSe (Lead Chalcogenide) etc).As the density of electrons (N=2, 3, 4, 5, 6, 7, 8,.) increases, complexity arises due to coulomb interactions, inclusion of fermionic exchange symmetry and anisotropy. Consequently, Schrodinger equations of anisotropic quantum dots become non-trivial. Recasting such non-relativistic quantum equations into Whittaker-M basis functions unifies coulomb (exchange) correlation and antisymmetric nature of electrons in two-centered integrals of exact, finite, single-summed, terminated and simplest Lauricella functions (F2) via multi-pole expansion and the subsequent Chu-Vandermonde identity. Coulomb correlations interplay with in-plane and out-of-plane electrical and magnetic confinements in their moderate fields. On the other hand, full-scale fermionic exchange symmetry is incorporated through multiple number of Slater determinants, unlike Hartree-Fock method. In this context, both open-shell and restricted closed-shell configurations are considered for trial Hartree-products which are composed of the basis set...

Addition energy and magnetization of 3-D multicarrier anisotropic quantum dots in magnetic field by exact multi-pole expansion of coulomb correlations

Coulomb interactions replicates in N(N − 1)∕2 terms for interacting 3-D N − e confined quantum dots leading to non-trivial Schrödinger equations. For the systems having N > 3, e − e interaction reciprocating to both lateral (electrical) and transverse (magnetic) confinements in moderate fields causes acute interplay in anisotropic quantum dots. As DFT, Hartree-Fock and other perturbative methods have certain limitations, recasting Schrödinger equations into self-adjoint Whittaker-M functions addresses coulomb (exchange) integrals as simplest, finite and single-summed analytical Lauricella functions (F2) via Chu-Vandermonde identity. In case of higher ′N′, expansion of coulomb correlations in terms of multi-pole expansion facilitates the convergences for bound states upto quadrapole and octopole terms. Although, fermionic exchange symmetry of many electron systems could be included in terms of various two-electron integrals, for the sake of brevity we have aimed to reproduce experimental results without spin. Level clustering/accidential degeneracies manifest on energy level spectra due to competitive role among anisotropic confinement strength, magnetic field, mass of the carrier and dielectric constant of the medium. It triggers orbital induced paramagnetism (T ∼ (0 − 1)K), signature of fractional quantum Hall effect (FQHE) in chemical potential cusps (μ) and formation of different ′shell structures′ in capacitive energy respectively, spanning over wide dielectric range of materials (atomic like quantum dots, ZnO, GaAs and PbSe (Lead Chalcogenide) etc).

Fermions in geodesic Witten diagrams

We develop the embedding formalism for odd dimensional Dirac spinors in AdS and apply it to the (geodesic) Witten diagrams including fermionic degrees of freedom. We first show that the geodesic Witten diagram (GWD) with fermion exchange is equivalent to the conformal partial waves associated with the spin one-half primary field. Then, we explicitly demonstrate the GWD decomposition of the Witten diagram including the fermion exchange with the aid of the split representation. The geodesic representation of CPW indeed gives the useful basis for computing the Witten diagrams.

Static correlated functionals for reduced density matrix functional theory

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities stemming from the generalized Pauli principle, the many-body wave-function can be written explicitly in terms of the natural occupation numbers and natural orbitals. This leads to an expression for the two-particle density matrix and therefore for the correlation energy functional. This functional was then tested for a three-electron Hubbard model where it showed excellent performance both in the weak and strong correlation regimes.

Role of the pair potential for the saturation of generalized Pauli constraints

The dependence of the (quasi-)saturation of the generalized Pauli constraints on the pair potential is studied for ground states of few-fermion systems. For this, we consider spinless fermions in one dimension which are harmonically confined and interact by pair potentials of the form $|{x}_{i}\ensuremath{-}{x}_{j}{|}^{s}$ with $\ensuremath{-}1\ensuremath{\le}s\ensuremath{\le}5$. We use the density matrix renormalization group approach and large orbital basis to achieve the convergence on more than ten digits of both the variational energy and the natural occupation numbers. Our results confirm that the conflict between energy minimization and fermionic exchange symmetry results in a universal and nontrivial quasisaturation of the generalized Pauli constraints (quasipinning), implying tremendous structural simplifications of the fermionic ground state for all $s$. Those numerically exact results are complemented by an analytical study based on a self-consistent perturbation theory which we develop for this purpose. The respective results for the weak-coupling regime eventually elucidate the singular behavior found for the specific values $s=2,4,...,$ resulting in an extremely strong quasipinning.

Z Boson Decay into Light and Darkness.

We study the Z→γγ[over ¯] process in which the Z boson decays into a photon γ and a massless dark photon γ[over ¯], when the latter couples to standard-model fermions via dipole moments. This is a simple yet nontrivial example of how the Landau-Yang theorem-ruling out the decay of a massive spin-1 particle into two photons-is evaded if the final particles can be distinguished. The striking signature of this process is a resonant monochromatic single photon in the Z-boson center of mass together with missing momentum. LEP experimental bounds allow a branching ratio up to about 10^{-6} for such a decay. In a simplified model of the dark sector, the dark-photon dipole moments arise from one-loop exchange of heavy dark fermions and scalar messengers. The corresponding prediction for the rare Z→γγ[over ¯] decay width can be explored with the large samples of Z bosons foreseen at future colliders.

Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics.

When two identical fermions exchange their positions, their wave function gains a phase factor of -1. We show that this distance-independent effect can induce nonlocal entanglement in one-dimensional (1D) electron systems having Majorana fermions at the ends. It occurs in the system bulk and has a nontrivial temperature dependence. In a system having a single Majorana fermion at each end, the nonlocal entanglement has a Bell-state form at zero temperature and decays as the temperature increases, vanishing suddenly at a certain finite temperature. In a system having two Majorana fermions at each end, it is in a cluster-state form and its nonlocality is more noticeable at a finite temperature. By contrast, the thermal states of corresponding 1D spins do not have nonlocal entanglement.

Scattering amplitudes for dark and bright excitons

Using the composite boson many-body formalism that takes single-exciton states rather than free carrier states as a basis, we derive the integral equation fulfilled by the exciton-exciton effective scattering from which the role of fermion exchanges can be unraveled. For excitons made of -spin electrons and -spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude Δ, despite differences in the carrier exchanges involved. A brightness-changing channel also exists when two opposite-spin excitons scatter: dark excitons can end either in the same dark states with an amplitude , or in opposite-spin bright states , with a different amplitude , the number of carrier exchanges involved in these scatterings being even or odd, respectively. Another major result is that these amplitudes are linked by a striking relation, , which has decisive consequence on exciton Bose-Einstein condensation. By using Born values, we show that the exciton condensate can be optically observed through a bright part when excitons have large dipole only, that is, when the electrons and holes are in two well-separated layers, as in current experiments.

Influence of the fermionic exchange symmetry beyond Pauli's exclusion principle

Pauli's exclusion principle has a strong impact on the properties of most fermionic quantum systems. Remarkably, the fermionic exchange symmetry implies further constraints on the one-particle picture. By exploiting those generalized Pauli constraints we derive a measure which quantifies the influence of the exchange symmetry beyond Pauli's exclusion principle. It is based on a geometric hierarchy induced by the exclusion principle constraints. We provide a proof of principle by applying our measure to a simple model. In that way, we conclusively confirm the physical relevance of the generalized Pauli constraints and show that the fermionic exchange symmetry can have an influence on the one-particle picture beyond Pauli's exclusion principle. Our findings provide a new perspective on fermionic multipartite correlation since our measure allows one to distinguish between static and dynamic correlations.

Correlated-pair approach to composite-boson scattering lengths

We derive the scattering length of composite bosons (cobosons) within the framework of the composite boson many-body formalism that uses correlated-pair states as a basis, instead of free fermion states. The integral equation constructed from this physically relevant basis makes transparent the role of fermion exchange in the coboson-coboson effective scattering. Three potentials used for Cooper pairs, fermionic-atom dimers, and semiconductor excitons are considered. While the s-wave scattering length for the BCS-like potential is just equal to its Born value, the other two are substantially smaller. For fermionic-atom dimers and semiconductor excitons, our results, calculated within a restricted correlated-pair basis, are in good agreement with those obtained from procedures numerically more demanding. We also propose model coboson-coboson scatterings that are separable and thus easily workable, and that produce scattering lengths which match quantitatively well with the numerically-obtained values for all fermion mass ratios. These separable model scatterings can facilitate future works on many-body effects in coboson gases.

Pinning of fermionic occupation numbers: Higher spatial dimensions and spin

The role of the generalized Pauli constraints (GPCs) in higher spatial dimensions and by incorporating spin degrees of freedom is systematically explored for a system of interacting fermions confined by a harmonic trap. Physical relevance of the GPCs is confirmed by analytical means for the ground state in the regime of weak couplings by finding its vector of natural occupation numbers close to the boundary of the allowed region. Such quasipinning is found to become weaker in the intermediate and strong coupling regime. The study of crossovers between different spatial dimensions by detuning the harmonic trap frequencies suggests that quasipinning is essentially an effect for systems with reduced spatial dimensionality. In addition, we find that quasipinning becomes stronger by increasing the degree of spin-polarization. Consequently, the number of states available around the Fermi level plays a key role for the occurrence of quasipinning. This suggests that quasipinning emerges from the conflict between energy minimization and fermionic exchange symmetry.

Number-parity effect for confined fermions in one dimension

For $N$ spin-polarized fermions with harmonic pair interactions in a $1$-dimensional trap an odd-even effect is found. The spectrum of the $1$-particle reduced density matrix of the system's ground state differs qualitatively for $N$ odd and $N$ even. This effect does only occur for strong attractive and repulsive interactions. Since it does not exists for bosons, it must originate from the repulsive nature implied by the fermionic exchange statistics. In contrast to the spectrum, the $1$-particle density and correlation function for strong attractive interactions do not show any sensitivity on the number parity. This also suggests that reduced-density-matrix-functional theory has a more subtle $N$-dependency than density functional theory.

Coboson many-body formalism for cold-atom dimers with attraction between different fermion species only

Unlike the Coulomb potential that acts between all semiconductor carriers, the potential commonly used for BCS superconductors and cold-atom gases acts between different fermion species only, these species differing by their spin or hyperfine index. The coboson formalism we develop here evidences that such composite bosons interact through fermion exchange only, thus rendering the structure of the Shiva diagrams that visualize their many-body effects far simpler. A separable potential is used to obtain analytical results for the $N$-coboson normalization factor and the $N$-coboson ground-state energy within the Born approximation, in terms of the Born dimer-dimer scattering length. This formalism opens the route toward approaching complex many-body effects, such as Bose-Einstein condensation, through a different perspective.

Dephasing effects on coherent exciton-polaritons and the breakdown of the strong coupling regime

Using femtosecond pump-probe spectroscopy, we identify excitation induced dephasing as a major mechanism responsible for the breaking of the strong-coupling between excitons and photons in a semiconductor microcavity. The effects of dephasing are observed on the transmitted probe pulse spectrum as a density dependent broadening of the exciton-polariton resonances and the emergence of a third resonance at high excitation density. A striking asymmetry in the energy shift between the upper and the lower polaritons is also evidenced. Using the excitonic Bloch equations, we quantify the respective contributions to the energy shift of many-body effects associated with Fermion exchange and photon assisted exchange processes and the contribution to collisional broadening.