We study the general-setting quantum geometric phase acquired by a particle in a vibrating cavity. Solving the two-level theory with the rotating-wave approximation and the SU (2) method, we obtain analytic formulae that give excellent descriptions of the geometric phase, energy and wavefunction of the resonating system. In particular, we observe a sudden π-jump in the geometric phase when the system is in resonance. Similar behaviour is found in the geometric phase of a spin- particle in a rotating magnetic field. Our result suggests that the π-jump is a general feature for two-level systems, for which we developed a geometrical model to help visualize its evolution.We study the general-setting quantum geometric phase acquired by a particle in a vibrating cavity. Solving the two-level theory with the rotating-wave approximation and the SU (2) method, we obtain analytic formulae that give excellent descriptions of the geometric phase, energy and wavefunction of the resonating system. In particular, we observe a sudden π-jump in the geometric phase when the system is in resonance. Similar behaviour is found in the geometric phase of a spin- particle in a rotating magnetic field. Our result suggests that the π-jump is a general feature for two-level systems, for which we developed a geometrical model to help visualize its evolution.

arXiv:quant-ph/0210182Journal of Physics A Mathematical and GeneralOct 22, 20034 citations

Observing SU(2) phases with neutrons

Veer Chand Rakhecha, Apoorva G. Wagh

PramanaFeb 1, 20014 citations

Berry phases in superconducting transitions

Armando A. Aligia

I generalize the concept of Berry's geometrical phase for quasicyclic Hamiltonians to the case in which the ground state evolves adiabatically to an excited state after one cycle, but returns to the ground state after an integer number of cycles. This allows to extend the charge Berry phase γ c related to the macroscopic polarization, to many-body systems with fractional number of particles per site. Under certain conditions, γ c and the spin Berry phase γ s jump in π at the boundary of superconducting phases. In the extended Hubbard chain with on-site attraction U and nearest-neighbor interaction V at quarter filling, the transitions detected agree very well with exact results in two limits solved by the Bethe ansatz, and with previous numerical studies. In chains with spin SU (2) symmetry, γ s jumps when a spin gap opens.I generalize the concept of Berry's geometrical phase for quasicyclic Hamiltonians to the case in which the ground state evolves adiabatically to an excited state after one cycle, but returns to the ground state after an integer number of cycles. This allows to extend the charge Berry phase γ c related to the macroscopic polarization, to many-body systems with fractional number of particles per site. Under certain conditions, γ c and the spin Berry phase γ s jump in π at the boundary of superconducting phases. In the extended Hubbard chain with on-site attraction U and nearest-neighbor interaction V at quarter filling, the transitions detected agree very well with exact results in two limits solved by the Bethe ansatz, and with previous numerical studies. In chains with spin SU (2) symmetry, γ s jumps when a spin gap opens.

arXiv:cond-mat/9810170Europhysics Letters (EPL)Feb 15, 199925 citations

Mixed-state geometric phases of coherent and squeezed spin states

Xin Wang, Jia-Chen Tang, Xu-Yang Hou +2 more

Two mixed-state geometric phases, known as the Uhlmann phase and interferometric geometric phase (IGP), of spin coherent states (CSSs) and spin squeezed states (SSSs) are analyzed. Exact solutions and numerical results of selected examples are presented. For the $j=3/2$ CSS, the Uhlmann phase exhibits finite-temperature topological phase transitions characterized by abrupt jumps. The IGP for the same state similarly shows discontinuous jumps as the temperature varies. In the case of the $j=1$ one-axis SSS, both the Uhlmann phase and IGP display discrete finite-temperature jumps. By contrast, the $j=1$ two-axis SSS shows no such transitions because the Uhlmann phase and IGP both vary smoothly with temperature. We also briefly discuss potential realizations and simulations related to these phenomena in spin systems.Two mixed-state geometric phases, known as the Uhlmann phase and interferometric geometric phase (IGP), of spin coherent states (CSSs) and spin squeezed states (SSSs) are analyzed. Exact solutions and numerical results of selected examples are presented. For the $j=3/2$ CSS, the Uhlmann phase exhibits finite-temperature topological phase transitions characterized by abrupt jumps. The IGP for the same state similarly shows discontinuous jumps as the temperature varies. In the case of the $j=1$ one-axis SSS, both the Uhlmann phase and IGP display discrete finite-temperature jumps. By contrast, the $j=1$ two-axis SSS shows no such transitions because the Uhlmann phase and IGP both vary smoothly with temperature. We also briefly discuss potential realizations and simulations related to these phenomena in spin systems.

arXiv:2502.07268Physical review. B./Physical review. BJun 27, 20252 citations

Representations of SU(3) and geometric phases for three- state systems

Mark Byrd

Jan 1, 19990 citations

j=3/2

CSS, the Uhlmann phase exhibits finite-temperature topological phase transitions characterized by abrupt jumps. The IGP for the same state similarly shows discontinuous jumps as the temperature varies. In the case of the

j=1

one-axis SSS, both the Uhlmann phase and IGP display discrete finite-temperature jumps. By contrast, the

j=1

two-axis SSS shows no such transitions because the Uhlmann phase and IGP both vary smoothly with temperature. We also briefly discuss potential realizations and simulations related to these phenomena in spin systems.