Magicity of neutron-rich isotopes within relativistic self-consistent approaches

The formation of new shell gaps in intermediate mass neutron-rich nuclei is investigated within the relativistic Hartree-Fock-Bogoliubov theory, and the role of the Lorentz pseudo-vector and tensor interactions is analyzed. Based on the Foldy-Wouthuysen transformation, we discuss in detail the role played by the different terms of the Lorentz pseudo-vector and tensor interactions in the appearing of the $N=16$, 32 and 34 shell gaps. The nuclei $^{24}$O, $^{48}$Si and $^{52,54}$Ca are predicted with a large shell gap and zero ($^{24}$O, $^{52}$Ca) or almost zero ($^{48}$Si, $^{54}$Ca) pairing gap, making them candidates for new magic numbers in exotic nuclei. We find from our analysis that the Lorentz pseudo-vector and tensor interactions induce very specific evolutions of single-particle energies, which could clearly sign their presence and reveal the need for relativistic approaches with exchange interactions.

Pairing phase transition: A Finite-Temperature Relativistic Hartree-Fock-Bogoliubov study

Background: The relativistic Hartree-Fock-Bogoliubov (RHFB) theory has recently been developed and it provides a unified and highly predictive description of both nuclear mean field and pairing correlations. Ground state properties of finite nuclei can accurately be reproduced without neglecting exchange (Fock) contributions. Purpose: Finite-temperature RHFB (FT-RHFB) theory has not yet been developed, leaving yet unknown its predictions for phase transitions and thermal excitations in both stable and weakly bound nuclei. Method: FT-RHFB equations are solved in a Dirac Woods-Saxon (DWS) basis considering two kinds of pairing interactions: finite or zero range. Such a model is appropriate for describing stable as well as loosely bound nuclei since the basis states have correct asymptotic behaviour for large spatial distributions. Results: Systematic FT-RH(F)B calculations are performed for several semi-magic isotopic/isotonic chains comparing the predictions of a large number of Lagrangians, among which are PKA1, PKO1 and DD-ME2. It is found that the critical temperature for a pairing transition generally follows the rule $T_c = 0.60Delta(0)$ for a finite-range pairing force and $T_c = 0.57Delta(0)$ for a contact pairing force, where $Delta(0)$ is the pairing gap at zero temperature. Two types of pairing persistence are analysed: type I pairing persistence occurs in closed subshell nuclei while type II pairing persistence can occur in loosely bound nuclei strongly coupled to the continuum states. Conclusions: This first FT-RHFB calculation shows very interesting features of the pairing correlations at finite temperature and in finite systems such as pairing re-entrance and pairing persistence.

Generation and detection of large and robust entanglement between two different mechanical resonators in cavity optomechanics

We investigate a general scheme for generating, either dynamically or in the steady state, continuous variable entanglement between two mechanical resonators with different frequencies. We employ an optomechanical system in which a single optical cavity mode driven by a suitably chosen two-tone field is coupled to the two resonators. Significantly large mechanical entanglement can be achieved, which is extremely robust with respect to temperature.

Transferring entanglement to the steady-state of flying qubits

The transfer of entanglement from optical fields to qubits provides a viable approach to entangling remote qubits in a quantum network. In cavity quantum electrodynamics, the scheme relies on the interaction between a photonic resource and two stationary intracavity atomic qubits. However, it might be hard in practice to trap two atoms simultaneously and synchronize their coupling to the cavities. To address this point, we propose and study entanglement transfer from cavities driven by an entangled external field to controlled flying qubits. We consider two exemplary non-Gaussian driving fields: NOON and entangled coherent states. We show that in the limit of long coherence time of the cavity fields, when the dynamics is approximately unitary, entanglement is transferred from the driving field to two atomic qubits that cross the cavities. On the other hand, a dissipation-dominated dynamics leads to very weakly quantum-correlated atomic systems, as witnessed by vanishing quantum discord.