The entanglement and coherence of the wobbling mode are studied in the framework of the particle plus triaxial-rotor model for the one-quasiparticle nucleus
135Pr and the two-quasiparticles nucleus
130Ba. The focus lies on the coupling between the total and the particle angular momenta. Using the Schmidt decomposing, it is quantified in terms of the von Neumann entropy of the respective subsystems, which measures their mutual entanglement. The entropy and the entanglement increase with spin
I and number of wobbling quanta
n. The coherence of the wobbling mode is studied by means of the eigenstate decomposition of its reduced density matrix. To a good approximation, the probability distributions of the total angular momentum can be interpreted as the incoherent combination of the coherent contributions from the first two pairs of eigenvectors with the largest weight of the reduced density matrix. Decoherence measures are defined, which, in accordance, scatter between 0.1 to 0.2 at low spin and between 0.1 and 0.3 at high spin. Entanglement in the framework of the adiabatic approximation is further analyzed. In general, the coherent eigenstates of the effective collective Hamiltonian approximate the reduced density matrix with the limited accuracy of its pair of eigenstates with the largest weight. As the adiabatic approximation becomes more accurate with decreasing excitation energy, the probability distribution of the angle of the total angular momentum around a principal axis approaches the one of the full reduced density matrix. The
E2 transition probabilities and spectroscopic quadrupole moments reflect this trend.
The entanglement and coherence of the wobbling mode are studied in the framework of the particle plus triaxial rotor model for the one-quasiparticle nucleus
135Pr and the two-quasiparticles nucleus
130Ba. The focus lies on the coupling between the total and the particle angular momenta. Using the Schmidt decomposing, it is quantified in terms of the von Neumann entropy of the respective sub-systems, which measures their mutual entanglement. The entropy and the entanglement increase with spin
I and number of wobbling quanta
n. The coherence of the wobbling mode is studied by means of the eigenstate decomposition of its reduced density matrix. To a good approximation, the probability distributions of the total angular momentum can be interpreted as the incoherent combination of the coherent contributions from the first two pairs of eigenvectors with the largest weight of the reduced density matrix. Decoherence measures are defined, which, in accordance, scatter between 0.1 to 0.2 at low spin and between 0.1 and 0.3 at high spin. Entanglement in the framework of the adiabatic approximation is further analyzed. In general, the coherent eigenstates of the effective collective Hamiltonian approximate the reduced density matrix with the limited accuracy of its pair of eigenstates with the largest weight. As the adiabatic approximation becomes more accurate with decreasing excitation energy, the probability distribution of the angle of the total angular momentum around a principal axis approaches the one of the full reduced density matrix. The
E2 transition probabilities and spectroscopic quadrupole moments reflect this trend.
We investigate the entanglement in two-quasiparticle plus triaxial-rotor (PTR) model for the particle-hole configuration
π(1h11/2)1⊗ν(1h11/2)−1, the particle-particle configuration
π(1h11/2)1⊗ν(1h11/2)1, and two-proton particles configuration
π(1h11/2)2 for different values of the triaxiality parameter. The entanglement between the angular momenta of the two quasiparticles and the total angular momentum is quantified by the three bipartite concurrences
C of one type of angular momentum with the other two angular momenta and the area
F of the triangle formed by the bipartite concurrences. Collective chiral and wobbling modes are identified for
γ>15∘ via spin coherent state (SCS) maps and spin squeezed state (SSS) plots. Their entanglement increases from moderate values at the band head to near-maximal values at
I=20. The area
F of the chiral partners changes order as function of
I which reflects the crossing of the partner bands as a signature of chirality. For the
π(1h11/2)2 configuration, the antisymmetrization required by the Pauli exclusion principle causes strong entanglement between the two protons, which significantly amplifies the area
F. For
γ<15∘, the lowest bands become various uniformly rotating quasiparticle configurations, which have large values of
F for all values
I.
The Nuclear Rotor Atlas reveals that coherence in matter is not a fragile quantum probability but a geometric property of curvature on S³. Within this framework, the wavefunction phase ψ corresponds to orientation of a four-dimensional curvature field whose stiffness κ and coherence Σ determine its stability. Quantum computing, viewed through this lens, becomes the art of maintaining and manipulating curvature continuity rather than superposition. Here we develop a unified geometric theory of qubit formation, entanglement, and logical operations based on curvature coherence. Curvature knots and 4-D rotor domains serve as robust topological qubits, ψ-aligned arrays form natural entanglement networks, and logical gates arise from holonomic rotations of curvature phase. Unlike conventional qubits that demand extreme isolation and cryogenic control, curvature-based qubits are predicted to retain coherence through geometric stiffness, allowing warm or condensedphase operation. Examples drawn from the Atlas-including isotope-linked ψ fields, nuclear-electron curvature ₙ coupling, and measurable curvature resonances-suggest experimental paths toward geometric qubit arrays and curvature-locked logic gates. The result is a radical reinterpretation of quantum computation as geometry processing within curvature space, offering a physical and scalable route to stable, energy-efficient quantum information systems. A website featuring The Nuclear Rotor Atlas as an interactive 3D chart.
We calculate the propagator and the transition probabilities for a coherently driven three-state quantum system. The energies of the three states change linearly in time, whereas the interactions between them are pulse shaped. We derive a highly accurate analytic approximation by assuming independent pairwise Landau-Zener transitions occurring instantly at the relevant avoided crossings, and adiabatic evolution elsewhere. Quantum interferences are identified, which occur due to different possible evolution paths in Hilbert space between an initial and a final state. A detailed comparison with numerical results for Gaussian-shaped pulses demonstrates a remarkable accuracy of the analytic approximation. We use the analytic results to derive estimates for the half-width of the excitation profile, and for the parameters required for creation of a maximally coherent superposition of the three states. These results are of potential interest in ladder climbing in alkali-metal atoms by chirped laser pulses, in quantum rotors, in transitions between Zeeman sublevels of a
J=1 level in a magnetic field, and in control of entanglement of a pair of spin-
1∕2 particles. The results for the three-state system can be generalized, without essential difficulties, to higher dimensions.