Nodes and Spin Windings for Topological Transitions in Light-Matter Interactions: \\ Anisotropic Quantum Rabi Model as a Born Abstract Artist

By extracting different levels of topological information a new light is shed on the energy spectrum of the anisotropic quantum Rabi model (QRM) which is the fundamental model of light-matter interactions with indispensable counter-rotating terms in ultra-strong couplings. Besides conventional topological transitions (TTs) at gap closing, abundant unconventional TTs including a particular one universal for different energy levels are unveiled underlying level anticrossings without gap closing by tracking the wave-function nodes. On the other hand, it is found that the nodes have a correspondence to spin windings, which not only endows the nodes a more explicit topological character in supporting single-qubit TTs but also turns the topological information physically detectable. Furthermore, hidden small-spin-knot transitions are exposed for the ground state, while more kinds of spin-knot transitions emerge in excited states including unmatched node numbers and spin winding numbers. As a surprise, frequently the spin windings produce portraits in high spiritual similarity with abstract artistic works, which demonstrates that the anisotropic QRM may be the Picasso of physical models. This signifies that art is joining the dialogue between mathematics and physics which was triggered by the milestone work of revealing integrability of the QRM.Comment: 17 pages, 12 figure

Thermodynamics of SU(2) bosons in one dimension

On the basis of Bethe ansatz solution of two-component bosons with SU(2) symmetry and $\delta$-function interaction in one dimension, we study the thermodynamics of the system at finite temperature by using the strategy of thermodynamic Bethe ansatz (TBA). It is shown that the ground state is an isospin "ferromagnetic" state by the method of TBA, and at high temperature the magnetic property is dominated by Curie's law. We obtain the exact result of specific heat and entropy in strong coupling limit which scales like $T$ at low temperature. While in weak coupling limit, it is found there is still no Bose-Einstein Condensation (BEC) in such 1D system.Comment: 7 page

Designing Electron Spin Textures and Spin Interferometers by Shape Deformations

We demonstrate that the spin orientation of an electron propagating in a one-dimensional nanostructure with Rashba spin-orbit (SO) coupling can be manipulated on demand by changing the geometry of the nanosystem. Shape deformations that result in a non-uniform curvature give rise to complex three-dimensional spin textures in space. We employ the paradigmatic example of an elliptically deformed quantum ring to unveil the way to get an all-geometrical and all-electrical control of the spin orientation. The resulting spin textures exhibit a tunable topological character with windings around the radial and the out-of-plane directions. We show that these topologically non trivial spin patterns affect the spin interference effect in the deformed ring, thereby resulting in different geometry-driven ballistic electronic transport behaviors. Our results establish a deep connection between electronic spin textures, spin transport and the nanoscale shape of the system.Comment: 8 pages, 4 figure

Exact solution and magnetic properties of an anisotropic spin ladder

We study an integrable two-leg spin-1/2 ladder with an XYZ-type rung interaction. Exact rung states and rung energies are obtained for the anisotropic rung coupling in the presence of a magnetic field. Magnetic properties are analyzed at both zero and finite temperatures via the thermodynamic Bethe ansatz and the high-temperature expansion. According to different couplings in the anisotropic rung interaction, there are two cases in which a gap opens, with the ground state involving one or two components in the absence of a magnetic field. We obtain the analytic expressions of all critical fields for the field-induced quantum phase transitions (QPT). Anisotropic rung interaction leads to such effects as separated magnetizations and susceptibilities in different directions, lowered inflection points and remnant weak variation of the magnetization after the last QPT.Comment: 9 pages, 8 figures; a typo in C_2(below eq.7) correcte

Switchable Superradiant Phase Transition with Kerr Magnons

The superradiant phase transition (SPT) has been widely studied in cavity quantum electrodynamics (CQED). However, this SPT is still subject of ongoing debates due to the no-go theorem induced by the so-called ${\bf A}^2$ term (AT). We propose a hybrid quantum system, consisting of a single-mode cavity simultaneously coupled to both a two-level system and yttrium-iron-garnet sphere supporting magnons with Kerr nonlinearity, to restore the SPT against the AT. The Kerr magnons here can effectively introduce an additional strong and tunable AT to counteract the intrinsic AT, via adiabatically eliminating the degrees of freedom of the magnons. We show that the Kerr magnons induced SPT can exist in both cases of ignoring and including the intrinsic AT. Without the intrinsic AT, the critical coupling strength can be dramatically reduced by introducing the Kerr magnons, which greatly relaxes the experimental conditions for observing the SPT. With the intrinsic AT, the forbidden SPT can be recovered with the Kerr magnons in a reversed way. Our work paves a potential way to manipulate the SPT against the AT in hybrid systems combining CQED and nonlinear magnonics