Spin-orbit gauge and quantum spin Hall effect

We have shown that the non-Abelian spin-orbit gauge field strength of the Rashba and Dresselhaus interactions, when split into two Abelian field strengths, the Hamiltonian of the system can be re-expressed as a Landau level problem with a particular relation between the two coupling parameters. The quantum levels are created with up and down spins with opposite chirality and leads to the quantum spin Hall effect.     

Non-Abelian gauge potentials driven localization transition in quasiperiodic optical lattices

Derived from quantum waves immersed in an Abelian gauge potential, the quasiperiodic Aubry-André-Harper (AAH) model is a simple yet powerful Hamiltonian to study the Anderson localization of ultracold atoms. Here, we investigate the localization properties of ultracold atoms in quasiperiodic optical lattices subject to a non-Abelian gauge potential, which are depicted by non-Abelian AAH models. We identify that the non-Abelian AAH models can bear the self-duality. We analyze the localization of such non-Abelian self-dual optical lattices, revealing a rich phase diagram driven by the non-Abelian gauge potential involved: a transition from a pure delocalization phase, then to coexistence phases, and finally to a pure localization phase. This is in stark contrast to the Abelian counterpart that does not support the coexistence phases. Our results establish the connection between localization and gauge symmetry, and thus comprise a new insight on the fundamental aspects of localization in quasiperiodic systems, from the perspective of non-Abelian gauge potential.     

Renormalization group and infrared behaviour in theories with coupled massless fields

The renormalization-group method is applied to investigate the infrared singularities in gauge theories with Abelian or non-Abelian symmetry, involving both massive and massless fermions. In the Abelian gauge model the infrared structures of massive and massless fermion propagators and of a massive fermion form factor are found. In the non-Abelian gauge model (quantum chromodynamics) the infrared behaviour of a massless gluon propagator and a massive quark form factor is considered in the logarithmic approximation.     

Vacuum-Induced Abelian and Non-Abelian Gauge Potentials in CavityQuantum Electrodynamics

Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems. In this paper, we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics. It is shown that a non-Abelian gauge potential is achieved only for a single atom, whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble. More importantly, two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted. The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes, which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.     

Exotic quantum holonomy in Hamiltonian systems

We consider evolution of quantum eigenstates in the presence of level crossing under slow cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.     

Quantization of non-abelian gauge theory. I. Gauge invariant Hamiltonian formulation

An essentially gauge invariant canonical Hamiltonian formulation is given for a non-Abelian Yang-Mills system coupled to a fermion field. The Hamiltonian contains only unconstrained dynamical variables, which in the quantum version satisfy canonical equal time commutation relations.     

Symmetries, Quantum Geometry, and the Fundamental Interactions

A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making these relations dynamical implies the nonlocal effect of the fundamental interactions on the wave function, as in the Aharonov–Bohm effect and its generalizations to non-Abelian gauge fields and gravity. The usual space–time geometry is obtained as the classical limit of this quantum geometry using the quantum-state space metric.     

Non-Abelian holonomies,charge pumping,and quantum computation with Josephson junctions

Non-Abelian holonomies can be generated and detected in certain superconducting nanocircuits. Here we consider an example where the non-Abelian operations are related to the adiabatic charge dynamics of the Josephson network. We demonstrate that such a device can be applied both for adiabatic charge pumping and as an implementation of a quantum computer.     

Quantal Conserved Charges in Gauge Theory

Starting from the configuration-space generating functional for gauge theory obtained by using the Faddeev-Popov method,the conservation laws at the quantum level for the gauge-invariant system are derived.Appling to non-Abel Chern-Simons(CS)theory,the quantum BRS conserved charge and quantuml conserved angular momentum for the non-Abelian CS fields coupled to Fermion field are deduced.The property of fractional spin in CS theory is discussed.     

Quantal symmetries in the non-linear σ model with Maxwell and non-Abelian Chern-Simons terms

The quantal symmetry property of the CP1 nonlinear σ model with Maxwell non-Abelian ChernSimons terms in(2+1) dimension is studied.In the Coulomb gauge,the system is quantized by using the Faddeev-Senjanovic(FS) path-integral formalism.Based on the quantaum Noether theorem,the quantal conserved angular momentum is derived and the fractional spin at the quantum level in this system is presented.     

Selected topics of quantum computing for nuclear physics

Nuclear physics,whose underling theory is described by quantum gauge field coupled with matter,is fundamentally important and yet is formidably challenge for simulation with classical computers.Quantum computing provides a perhaps transformative approach for studying and understanding nuclear physics.With rapid scaling-up of quantum processors as well as advances on quantum algorithms,the digital quantum simulation approach for simulating quantum gauge fields and nuclear physics has gained lots of attention.In this review,we aim to summarize recent efforts on solving nuclear physics with quantum computers.We first discuss a formulation of nuclear physics in the language of quantum computing.In particular,we review how quantum gauge fields(both Abelian and non-Abelian)and their coupling to matter field can be mapped and studied on a quantum computer.We then introduce related quantum algorithms for solving static properties and real-time evolution for quantum systems,and show their applications for a broad range of problems in nuclear physics,including simulation of lattice gauge field,solving nucleon and nuclear structures,quantum advantage for simulating scattering in quantum field theory,non-equilibrium dynamics,and so on.Finally,a short outlook on future work is given.     

Metal-insulator transition revisited for cold atoms in non-Abelian gauge potentials

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.     

Magnetic symmetry and dyons

A self-consistent theory of dyons in Abelian and non-Abelian limits has been formulated in terms of an extra magnetic symmetry and topological magnetic charge. It has been shown that the restricted gauge potential describes the fields of dyons in terms of two regular (time-like) potentials only when recourse is made to the duality of topological (magnetic) and isocolour (electric) charges. Choosing a suitable Lagrangian density for the system of dyons in non-Abelian gauge theory, the field equations, energy-momentum tensor, Hamiltonian and momentum densities have also been derived and the conservation of the four-linear momentum and the total angular momentum has been demonstrated.     

Observing Zitterbewegung with ultracold atoms

We propose an optical lattice scheme which would permit the experimental observation of Zitterbewegung (ZB) with ultracold, neutral atoms. A four-level tripod variant of the setup for stimulated Raman adiabatic passage (STIRAP) has previously been proposed for generating non-Abelian gauge fields. Dirac-like Hamiltonians, which exhibit ZB, are simple examples of such non-Abelian gauge fields; we show how a variety of them can arise, and how ZB can be observed, in a tripod system. We predict that the ZB should occur at experimentally accessible frequencies and amplitudes.     

Chaotic Quantization of Classical Gauge Fields

We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges, and calculate Planck's constant from quantities defined in the underlying classical gauge theory.     

Topological quantum liquids with quaternion non-Abelian statistics

Noncollinear magnetic order is typically characterized by a tetrad ground state manifold (GSM) of three perpendicular vectors or nematic directors. We study three types of tetrad orders in two spatial dimensions, whose GSMs are SO(3) = S(3)/Z(2), S(3)/Z(4), and S(3)/Q(8), respectively. Q(8) denotes the non-Abelian quaternion group with eight elements. We demonstrate that after quantum disordering these three types of tetrad orders, the systems enter fully gapped liquid phases described by Z(2), Z(4), and non-Abelian quaternion gauge field theories, respectively. The latter case realizes Kitaev's non-Abelian toric code in terms of a rather simple spin-1 SU(2) quantum magnet. This non-Abelian topological phase possesses a 22-fold ground state degeneracy on the torus arising from the 22 representations of the Drinfeld double of Q(8).     

Non-Abelian Geometric Manipulation of a Crystal of Molecular NanomagnetMn12

Based on the strong magnetic anisotropy along the symmetry of the crystal, we construct a U(2) non-Abelian gauge potential for the molecular nanomagnet Mn₁₂ by varying the external magnetic field adiabatically. Moreover, the non-Abelian geometric phase and the unitary matrix operation, which are the key steps to realize the universal holonomic quantum computing in the degenerate subspace, are also obtained by means of choosing an evolution path properly.     

Exact solutions of a spin-orbit coupling model in two-dimensional central-potentials and quantum-classical correspondence

In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition, which leads to an effective non-Abelian gauge field generated by the spin-orbit coupling. Coherent superposition of orbital angular-eigenfunctions obtained explicitly under the condition of zero-energy exhibits the quantum-classical correspondence in the meaning of exact coincidence between classical orbits and spatial patterns of quantum wave-functions, which as a consequence results in the fractional quantization of orbital angular-momentum by the requirement of the same rotational symmetry of quantum and classical orbits. A non-Abelian anyon-model emerges in a natural way.     

Bound States of Monopoles and Dyons with Spin-1/2 Particles in SU(2) Gauge Theory Under Moduli Space Approximation

Energy spectrum and degeneracy associated with bound states of monopoles and dyons in non-Abelian gauge theory has been investigated and it is shown that energy levels expand due to the presence of additional degeneracies. Splitting of energy level of dyonium in presence of external magnetic and electric field has also been analyzed confirming the presence of additional degeneracy levels of the system. In addition, the study of behaviour of a fermion moving in the field of non-Abelian dyon in moduli space under SU(2) gauge potential has been undertaken and energy eigen values for the system are carried out. Detailed analysis of relativistic correction in fermion-dyon system in moduli space is presented and angular momentum operators of the system are derived, which demonstrates that besides the contribution of Higgs field, the interaction of spin and orbital angular momentum of moving fermion also contributes to the energy operator.