Bogoliubov Approach Research Articles

Tensor Force Effect on Shape Coexistence of N = 28 Neutron-Rich Isotones

The tensor force effect on potential energy surfaces of the N = 28 neutron-rich isotones is investigated by using the deformed Skyrme—Hartree—Fock—Bogoliubov approach with the T22 interaction. It is found that, without the tensor force, 40Mg and 46Ar have prolate and spherical ground states, respectively. The ground states of 42Si and 44S are oblate. The shape coexistence in 40Mg, 42Si and 44S is evident. However, the ground state deformations of these isotones are not changed and the shape coexistence in 42Si and 44S vanishes when the tensor force is switched on. Taking 42Si as an example, the disappearance of the shape coexistence is understood by analyzing the tensor force effect on the shell correction energies.

Excitation picture of an interacting Bose gas

Atomic Bose–Einstein condensates (BECs) can be viewed as macroscopic objects where atoms form correlated atom clusters to all orders. Therefore, the presence of a BEC makes the direct use of the cluster-expansion approach–lucrative e.g. in semiconductor quantum optics–inefficient when solving the many-body kinetics of a strongly interacting Bose. An excitation picture is introduced with a nonunitary transformation that describes the system in terms of atom clusters within the normal component alone. The nontrivial properties of this transformation are systematically studied, which yields a cluster-expansion friendly formalism for a strongly interacting Bose gas. Its connections and corrections to the standard Hartree–Fock–Bogoliubov approach are discussed and the role of the order parameter and the Bogoliubov excitations are identified. The resulting interaction effects are shown to visibly modify number fluctuations of the BEC. Even when the BEC has a nearly perfect second-order coherence, the BEC number fluctuations can still resolve interaction-generated non-Poissonian fluctuations.

Superheavy magic structures in the relativistic Hartree–Fock–Bogoliubov approach

We have explored the occurrence of the spherical shell closures for superheavy nuclei in the framework of the relativistic Hartree–Fock–Bogoliubov (RHFB) theory. Shell effects are characterized in terms of two-nucleon gaps δ2n(p). Although the results depend slightly on the effective Lagrangians used, the general set of magic numbers beyond 208Pb are predicted to be Z=120, 138 for protons and N=172, 184, 228 and 258 for neutrons, respectively. Specifically the RHFB calculations favor the nuclide 120304 as the next spherical doubly magic one beyond 208Pb. Shell effects are sensitive to various terms of the mean-field, such as the spin-orbit coupling, the scalar and effective masses.

Finite-resolution fluctuation measurements of a trapped Bose-Einstein condensate

We consider the fluctuations in atom number that occur within finite-sized measurement cells in a trapped Bose-Einstein condensate (BEC). This approximates the fluctuation measurements made in current experiments with finite resolution in situ imaging. A numerical scheme is developed to calculate these fluctuations using the quasiparticle modes of a cylindrically symmetric three-dimensionally trapped condensate with either contact or dipole-dipole interactions (DDIs). We use this scheme to study the properties of a pancake shaped condensate using cylindrical cells. The extension of the theory to washer shaped cells with azimuthal weighting is made and used to discriminate between the low energy roton modes in a dipolar condensate according to their pro- jection of angular momentum. Our results are based on the Bogoliubov approach valid for zero and small finite temperatures.

Dynamic effects of a Feshbach resonance on Bragg scattering from a Bose-Einstein condensate

We present a theoretical model for Bragg scattering from a Bose-Einstein condensate (BEC) in the vicinity of a magnetic Feshbach resonance, using a two-$c$-field formalism, one $c$ field for the atom and the other for a molecule formed of two atoms. We use this model to numerically simulate an experiment [Papp et al., Phys. Rev. Lett. 101, 135301 (2008)] investigating the effects of strong interactions on the Bragg spectrum from a ${}^{85}$Rb BEC. Results from these simulations and from our previous calculations using an atom-molecule Bogoliubov approach are in very good quantitative agreement with the experimental results, confirming the importance of the resonance bound state in the dynamics of the condensate for fast experiments like Bragg scattering.

Time-of-flight patterns of ultracold bosons in optical lattices in various Abelian artificial magnetic field gauges

We calculate the time-of-flight patterns of strongly interacting bosons confined in a two-dimensional square lattice in the presence of an artificial magnetic field, using a quantum rotor model that is inherently combined with the Bogoliubov approach. We consider various geometries of the magnetic flux, which are expected to be realizable, or have already been implemented in experimental settings. The flexibility of the method allowed us to study cases where the artificial magnetic field is uniform or staggered or forms a checkerboard configuration. The effects of additional temporal modulation of the optical potential that results from application of Raman lasers driving particle transitions between lattice sites are also included. The time-of-flight patterns presented may serve as a verification of the chosen gauge in experiments, but also provide important hints on unconventional, nonzero-momentum condensates, or the possibility of observing graphenelike physics resulting from the occurrence of Dirac cones in artificial magnetic fields in systems of ultracold bosons in optical lattices. Also, we elucidate the differences between the effects of magnetic fields in solids and of artificial magnetic fields in optical lattices, which can be controlled on a much higher level, leading to effects not possible in condensed matter physics.

Systematic study of tensor force effect on pseudospin orbital splittings in Sn isotopes

The tensor force effect on the proton pseudospin orbital splittings of the 1 and 1 states in Sn isotopes is systematically analyzed with 36 sets of the TIJ interactions in the framework of the Hartree–Fock–Bogoliubov approach. It is shown that not all tensor parametrizations preserve the pseudospin symmetry.

Efimov states of heavy impurities in a Bose-Einstein condensate

We consider the problem of two heavy impurity particles embedded in a gas of weakly interacting light mass bosonic particles in the condensed state. Using the Bogoliubov approach to describe the bosonic gas and the Born-Oppenheimer approximation for the three-body dynamics, we calculate the modification to the heavy-heavy two-body potential due to the presence of the condensate. For the case of resonant interaction between the light bosons and the impurities, we present (semi)-analytical results for the potential in the limit of a large condensate coherence length. In particular, we find a formula for the modification of the Efimov scaling factor due to the presence of a degenerate bosonic gas background.

Two-dimensional dipolar Bose gas with the roton-maxon excitation spectrum

We discuss fluctuations in a dilute two-dimensional Bose-condensed dipolar gas, which has a roton-maxon character of the excitation spectrum. We calculate the density-density correlation function, fluctuation corrections to the chemical potential, compressibility, and the normal (superfluid) fraction. It is shown that the presence of the roton strongly enhances fluctuations of the density, and we establish the validity criterion of the Bogoliubov approach. At T=0 the condensate depletion becomes significant if the roton minimum is sufficiently close to zero. At finite temperatures exceeding the roton energy, the effect of thermal fluctuations is stronger and it may lead to a large normal fraction of the gas and compressibility.

BCS ansatz for superconductivity in the light of the Bogoliubov approach and the Richardson–Gaudin exact wave function

The Bogoliubov approach to superconductivity provides a strong mathematical support to the wave function ansatz proposed by Bardeen, Cooper and Schrieffer (BCS). Indeed, this ansatz — with all pairs condensed into the same state — corresponds to the ground state of the Bogoliubov Hamiltonian. Yet, this Hamiltonian only is part of the BCS Hamiltonian. As a result, the BCS ansatz definitely differs from the BCS Hamiltonian ground state. This can be directly shown either through a perturbative approach starting from the Bogoliubov Hamiltonian, or better by analytically solving the BCS Schrödinger equation along Richardson–Gaudin exact procedure. Still, the BCS ansatz leads not only to the correct extensive part of the ground state energy for an arbitrary number of pairs in the energy layer where the potential acts — as recently obtained by solving Richardson–Gaudin equations analytically — but also to a few other physical quantities such as the electron distribution, as here shown. The present work also considers arbitrary filling of the potential layer and evidences the existence of a super dilute and a super dense regime of pairs, with a gap different from the usual gap. These regimes constitute the lower and upper limits of density-induced BEC–BCS cross-over in Cooper pair systems.

Measurement of Giant Monopole Resonance in unstable nuclei and the determination of the nuclear matter incompressibility

The role of superfluidity in incompressibility is studied in nuclear matter and finite nuclei. Pairing has a weak effect on nuclear matter incompressibility at saturation density, but the effects are strong at lower densities. The pairing effect on the centroid energy of the isoscalar Giant Monopole Resonance (GMR) is also evaluated by using a microscopic constrained-Hartree–Fock Bogoliubov approach. The measurement of the GMR in isotopic chains including unstable nuclei is useful for the determination of nuclear incompressibility.

Matrix Elements for Neutrinoless Double Beta Decay

The status of calculation of the neutrinoless double beta decay (0νββ-decay) nuclear matrix elements (NMEs) is reviewed. The 0νββ-decay NMEs obtained in the framework of the Quasiparticle Random Phase Approximation (QRPA), Large Scale Shell Model (LSSM), Interacting Boson Model (IBM), Projected Hartree-Fock Bogoliubov approach (P-HFB) and Energy Density Functional Method (EDF) are presented and discussed. The problem of reliable determination of the 0νββ-decay NMEs is addressed. It is manifested that the uncertainty associated with the calculation of the 0νββ-decay NMEs can be diminished by suitable chosen nuclear probes. Further, the recent development in the field of double beta decay showed that the search for the neutrinoless double electron capture process (0νECEC) may establish the Majorana nature of neutrinos. This possibility should be considered as alternative and complementary to searches for the 0νββ-decay.

Dark soliton in a disorder potential

We consider a dark soliton in a Bose-Einstein condensate in the presence of a weak disorder potential. Deformation of the soliton shape is analyzed within the Bogoliubov approach and by employing an expansion in eigenstates of the P\"oschl-Teller Hamiltonian. Comparison of the results with the numerical simulations indicates that the linear response analysis reveals a good agreement even if the strength of disorder is of the order of the chemical potential of the system. In the second part of the paper we concentrate on the quantum nature of the dark soliton and demonstrate that the soliton may reveal Anderson localization in the presence of disorder. The Anderson-localized soliton may decay due to quasiparticle excitations induced by the disorder. However, we show that the corresponding lifetime is much longer than the condensate lifetime in a typical experiment.

Tensor Effect on Bubble Nuclei

In the framework of the Hartree—Fock—Bogoliubov (HFB) approach with Skyrme interactions SLy5+T, SLy5+Tw and several sets of TIJ parametrizations, i.e. the Skyrme interaction parametrizations including the tensor terms, the proton density distribution in 34Si and 46Ar nuclei is calculated with and without the tensor force. It is shown that the bubble effect in 34Si does not depend a great deal on the Skyrme parametrization and the proton density distribution in 34Si is hardly influenced by the tensor force. As to 46Ar, the SLy5+Tw parametrization favors the formation of the bubble structure due to the inversion between the 2s1/2 and 1d3/2 orbits (2s1/2−1d3/2 inversion). The inversion mechanism induced by the SLy5+Tw interaction is analyzed based on the proton single-particle spectra obtained from the SLy5 and SLy5+Tw interactions as well as the wave functions of the 2s1/2 and 1d3/2 states.

NUCLEAR MATTER SUPERFLUIDITY IN AN EFFECTIVE HADRONIC FIELD MODEL WITH EXCLUDED VOLUME CORRECTIONS

Properties of the 1S0 superfluid phase are studied for symmetric nuclear matter at finite temperature. It is described within a covariant hadronic field model, of the σ–ω type, with addition of density dependent correlations simulating effects due to finite extension of nucleons. The model is solved in a self-consistent Hartree–Bogoliubov approach, assuming instantaneous interactions in the superfluid phase. A comparison with the results obtained from several hadronic field models is made. Main characteristics of our description of the superfluid gap are in qualitative agreement with some studies using microscopic potentials, although further refinements could improve its performance.

Comparison between microscopic methods for finite-temperature Bose gases

We analyze the equilibrium properties of a weakly interacting, trapped quasi-one-dimensional Bose gas at finite temperatures and compare different theoretical approaches. We focus in particular on two stochastic theories: a number-conserving Bogoliubov (ncB) approach and a stochastic Gross-Pitaevskii equation (sGPe) that have been extensively used in numerical simulations. Equilibrium properties like density profiles, correlation functions, and the condensate statistics are compared to predictions based upon a number of alternative theories. We find that due to thermal phase fluctuations, and the corresponding condensate depletion, the ncB approach loses its validity at relatively low temperatures. This can be attributed to the change in the Bogoliubov spectrum, as the condensate gets thermally depleted, and to large fluctuations beyond perturbation theory. Although the two stochastic theories are built on different thermodynamic ensembles (ncB: canonical, sGPe: grand-canonical), they yield the correct condensate statistics in a large BEC (strong enough particle interactions). For smaller systems, the sGPe results are prone to anomalously large number fluctuations, well-known for the grand-canonical, ideal Bose gas. Based on the comparison of the above theories to the modified Popov approach, we propose a simple procedure for approximately extracting the Penrose-Onsager condensate from first- and second-order correlation functions that is computationally convenient. This also clarifies the link between condensate and quasi-condensate in the Popov theory of low-dimensional systems.

Polaronic slowing of fermionic impurities in lattice Bose-Fermi mixtures

We generalize the application of small polaron theory to ultracold gases [M. Bruderer, A. Klein, S. R. Clark, and D. Jaksch, New J. Phys. 10, 033015 (2008)] to the case of Bose-Fermi mixtures, where both components are loaded into an optical lattice. In a suitable range of parameters, the mixture can be described within a Bogoliubov approach in the presence of fermionic (dynamic) impurities; an effective description in terms of polarons applies. In the dilute limit of the slow-impurity regime, the hopping of fermionic particles is exponentially renormalized due to polaron formation, regardless of the sign of the Bose-Fermi interaction. This should lead to clear experimental signatures of polaronic effects, once the regime of interest is reached. The validity of our approach is analyzed in the light of currently available experiments. We provide results for the hopping renormalization factor for different values of temperature, density, and Bose-Fermi interaction for three-dimensional $^{87}\mathrm{Rb}$-$^{40}\mathrm{K}$ mixtures in an optical lattice.

Contributions of different neutron pairs in different approaches for neutrinoless double-beta decay

The methods used till now to calculate the neutrinoless double-beta decay (0νββ decay) matrix elements are the quasiparticle random phase approximation (QRPA), the shell model (SM), the angular momentum projected Hartee–Fock–Bogoliubov approach (HFB) and the interacting boson model (IBM). The different approaches are compared specifically concerning the angular momenta and parities of the neutron pairs, which are changed into two protons by the 0νββ decay. The QRPA and SM involve about the same angular momentum and parity neutron pairs, while the HFB is restricted to 0+, 2+, 4+, … and the IBM to 0+ and 2+ nucleon pairs.

Double-slit experiment and Bogoliubov’s causality principle

In the Bogoliubov approach the causality principle is the basic constructive element of quantum field theory. At the same time, this principle has obvious classical interpretation. On the other hand, it is well-known Feynman statement that the double-slit experiment is “impossible, absolutely impossible to explain in classical way, and has in it the heart of quantum mechanics. We describe how taking into account of infrared singularities allows to give quite evident interpretation to double-slit experiment. And this interpretation agrees with the Bogoliubov’s causality principle.

Generation of directional, coherent matter beams through dynamical instabilities in Bose-Einstein condensates

We present a theoretical analysis of a coupled, two-state Bose-Einstein condensate with nonequal scattering lengths and show that dynamical instabilities can be excited. We demonstrate that these instabilities are exponentially amplified, resulting in highly directional, oppositely propagating, coherent matter beams at specific momenta. To accomplish this we prove that the mean field of our system is periodic and extend the standard Bogoliubov approach to consider a time-dependent, but cyclic, background. This allows us to use Floquet's theorem to gain analytic insight into such systems, rather than employing the usual Bogoliubov--de Gennes approach, which is usually limited to numerical solutions. We apply our theory to the metastable helium atom laser experiment by Dall et al. [Phys. Rev. A 79, 011601(R) (2009)] and show that it explains the anomalous beam profiles they observed. Finally, we demonstrate that the paired particle beams will be Einstein-Podolsky-Rosen entangled on formation.