The nucleus is one of the most multifaceted many-body systems in the Universe. It exhibits a multitude of responses depending on the way one ''probes'' it. With increasing technical advancements of beams at the various accelerators and of detection systems the nucleus has, over and over again, surprised us by expressing always new ways of ''organized'' structures and layers of complexity. Nuclear magnetism is one of those fascinating faces of the atomic nucleus discussed in the present review. We shall not just limit ourselves to presenting the by now large data set that has been obtained in the past two decades using various probes, electromagnetic and hadronic alike and that presents ample evidence for a low-lying orbital scissors mode around 3 MeV, albeit fragmented over an energy interval of the order of 1.5 MeV, and higher-lying spin-flip strength in the energy region 5-9 MeV in deformed nuclei nor to the presently discovered evidence for low-lying proton-neutron isovector quadrupole excitations in spherical nuclei. To the contrary, the experimental evidence is put in the perspectives of understanding the atomic nucleus and its various structures of well-organized modes of motion and thus enlarges the discussion to more general fermion and bosonic many-body systems.

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Magnetic dipole excitations in nuclei: Elementary modes of nucleonic motion

Nuclear equation of state from ground and collective excited state properties of nuclei

This article reviews recent investigations on the phenomenon of Bose-Einstein condensation of dilute gases. Since the experimental observation of quantum degeneracy in atomic gases, the research activity in the field of coherent matter-waves literally exploded. The present topical review aims to give an introduction into the thermodynamics of Bose-Einstein condensation, a general overview over experimental techniques and investigations, and a theoretical foundation for the description of bosonic many-body quantum systems.

Bose-Einstein Condensation of Trapped Atomic Gases

Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977(1) and 0.977(9), respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamical gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.

Experimental Implementation of Universal Nonadiabatic Geometric Quantum Gates in a Superconducting Circuit

We review recent developments in the Skyrme–Hartree–Fock (SHF) approach for a self-consistent description of nuclear ground-state properties and dynamics. A brief summary of the Skyrme energy functional and additional ingredients (pairing, Coulomb, center-of-mass correction) is given. Strategies for phenomenological calibration of the SHF functional are discussed. Applications to a variety of observables are presented: the bulk properties of nuclei (energy, charge radius, surface thickness), the impact of information on neutron radii, extrapolation to super-heavy elements and fission stability thereof, isotopic shifts of radii, odd nuclei and associated single-nucleon spectra, low-lying surface vibrations together with the ground-state correlations associated with them, and giant resonances (electric as well as magnetic modes).

https://iopscience.iop.org/article/10.1088/0954-3899/38/3/033101/pdf

Self-consistent nuclear mean-field models: example Skyrme–Hartree–Fock

The $E1(T=1)$ isovector dipole giant resonance (GDR) in heavy and superheavy deformed nuclei is analyzed over a sample of 18 rare-earth nuclei, four actinides, and three chains of superheavy elements ($Z=102$, 114, and 120). The basis of the description is the self-consistent separable random-phase approximation (SRPA) using the Skyrme force SLy6. The model well reproduces the experimental data in the rare-earth and actinide regions. The trend of the resonance peak energies follows the estimates from collective models, showing a bias to the volume mode for the rare-earth isotopes and a mix of volume and surface modes for actinides and superheavy elements. The widths of the GDR are mainly determined by the Landau fragmentation, which in turn is found to be strongly influenced by deformation. A deformation splitting of the GDR can contribute to about one-third of the width, and about 1 MeV further broadening can be associated with mechanisms beyond the SRPA description (e.g., escape widths and coupling with complex configurations).

Description of the dipole giant resonance in heavy and superheavy nuclei within Skyrme random-phase approximation

We formulate the self-consistent separable random phase approximation (SRPA) method and specify it for Skyrme forces with pairing for the case of axially symmetric deformed nuclei. The factorization of the residual interaction allows diagonalization of high-ranking RPA matrices to be avoided, which dramatically reduces the computational expense. This advantage is crucial for the systems with a huge configuration space, first of all for deformed nuclei. SRPA self-consistently takes into account the contributions of both time-even and time-odd Skyrme terms as well as of the Coulomb force and pairing. The method is implemented to describe isovector E1 and isoscalar E2 giant resonances in a representative set of deformed nuclei: $^{154}\mathrm{Sm}$, $^{238}\mathrm{U}$, and $^{254}\mathrm{No}$. Four different Skyrme parameterizations (SkT6, SkM${}^{*}$, SLy6, and SkI3) are employed to explore the dependence of the strength distributions on some basic characteristics of the Skyrme functional and nuclear matter. In particular, we discuss the role of isoscalar and isovector effective masses and their relation to time-odd contributions. The high sensitivity of the right flank of E1 resonance to different Skyrme forces and the related artificial structure effects are analyzed.

Self-consistent separable random-phase approximation for Skyrme forces: Giant resonances in axial nuclei

A complete adiabatic transport of Bose–Einstein condensate (BEC) in a double-well trap is investigated within the mean field approximation. The transfer is driven by the time-dependent (Gaussian) coupling between the wells and their relative detuning. The protocol successfully works in a wide range of both repulsive and attractive BEC interaction. The nonlinear effects caused by the interaction can be turned from detrimental into favourable for the transport. The results are compared with familiar Landau–Zener scenarios using the constant coupling. It is shown that the pulsed Gaussian coupling provides a new transport regime where coupling edges are decisive and convenient switch of the transport is possible.

https://iopscience.iop.org/article/10.1088/0953-4075/42/23/235303/pdf

An adiabatic transport of Bose–Einstein condensates in double-well traps

The systematics of the plasmon response in spherical K, Na and Li clusters in a wide size region is studied. Two simplifying approximations whose validity has been established previously are considered: (a) a separable approach to the random-phase-approximation, involving an expansion of the residual interaction into a sum of separable terms, (b) the electron-ion interaction is modeled within the pseudo-Hamiltonian jellium model (PHJM) including nonlocal effects by means of realistic atomic pseudoHamiltonians. In cases where nonlocal effects turn out to be negligible, the Structure Averaged Jellium Model (SAJM) has been used. The leading role of Landau damping in forming the plasmon width in medium and large clusters is demonstrated. Good agreement with available experimental data is achieved for K, Na (using the SAJM) and small Li clusters (invoking the PHJM). The trends for peak position and width are generally well reproduced, even up to details of the Landau fragmentation in several clusters. Less good agreement, however, is found for large Li clusters. The possible reasons of the discrepancy are discussed.

Plasmon response in K, Na and Li clusters: systematics using the separable random-phase-approximation with pseudo-Hamiltonians

Two aspects of the transport of a repulsive Bose?Einstein condensate (BEC) in a double-well trap are inspected: The impact of the interatomic interaction and the analogy with the Josephson effect. The analysis employs a numerical solution of a 3D time-dependent Gross?Pitaevskii equation?for a total order parameter covering the whole trap. The population transfer is driven by a time-dependent shift of a barrier separating the left and right wells. The sharp and soft profiles of the barrier velocity are tested. The evolution of the relevant characteristics, involving phase differences and currents, is inspected. It is shown that the repulsive interaction substantially supports the transfer making it possible (i) in a wide velocity interval and (ii) three orders of magnitude faster than in the ideal BEC. The transport can be approximately treated as the dc Josephson effect. The dual origin of the critical barrier velocity (break of the adiabatic following and dc/ac transition) is discussed. Following the calculations, the robustness of the transport (dc) crucially depends on the interaction and barrier velocity profile. Only soft profiles which minimize undesirable dipole oscillations are acceptable.

https://iopscience.iop.org/article/10.1088/1054-660X/24/12/125501/pdf

V. O. Nesterenko

Papers

Description of the dipole giant resonance in heavy and superheavy nuclei within Skyrme random-phase approximation

Self-consistent separable random-phase approximation for Skyrme forces: Giant resonances in axial nuclei

An adiabatic transport of Bose–Einstein condensates in double-well traps

Plasmon response in K, Na and Li clusters: systematics using the separable random-phase-approximation with pseudo-Hamiltonians

Transport of the repulsive Bose-Einstein condensate in a double-well trap: interaction impact and relation to the Josephson effect