Fadi Sun

Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential: Gauge Invariance and Experimental Detections

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops.

Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

We study quantum magnetism of interacting spinor bosons at integer fillings hopping in a square lattice in the presence of non-Abelian gauge fields. In the strong coupling limit, it leads to the Rotated ferromagnetic Heisenberg model (RFHM) which is a new class of quantum spin model. We introduce Wilson loops to characterize frustrations and gauge equivalent classes. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground state. It supports not only commensurate magnons, but also a new gapped elementary excitation: in-commensurate magnons with two gap minima continuously tuned by the SOC strength. At low temperatures, these magnons lead to dramatic effects in many physical quantities such as density of states, specific heat, magnetization, uniform susceptibility, staggered susceptibility and various spin correlation functions. The commensurate magnons lead to a pinned central peak in the angle resolved light or atom Bragg spectroscopy. However, the in-commensurate magnons split it into two located at their two gap minima. At high temperatures, the transverse spin structure factors depend on the SOC strength explicitly. The whole set of Wilson loops can be mapped out by measuring the specific heat at the corresponding orders in the high temperature expansion. We argue that one gauge may be realized in current experiments and other gauges may also be realized in near future experiments. The results achieved along the exact solvable line sets up the stage to investigate dramatic effects when tuning away from it by various means. We sketch the crucial roles to be played by these magnons at other equivalent classes, with spin anisotropic interactions and in the presence of finite magnetic fields. Various experimental detections of these new phenomena are discussed. Rotated Anti-ferromagnetic Heisenberg model are also briefly mentioned.

Exciton correlations and input–output relations in non-equilibrium exciton superfluids

The photoluminescence (PL) measurements on photons and the transport measurements on excitons are the two types of independent and complementary detection tools to search for possible exciton superfluids in electron hole semi-conductor bilayer systems. In fact, it was believed that the transport measurements can provide more direct evidences on superfluids than the spectroscopic measurements. It is important to establish the relations between the two kinds of measurements. In this paper, using quantum Heisenberg-Langevin equations, we establish such a connection by calculating various exciton correlation functions in the putative exciton superfluids. These correlation functions include both normal and anomalous greater, lesser, advanced, retarded, and time-ordered exciton Green functions and also various two exciton correlation functions. We also evaluate the corresponding normal and anomalous spectral weights and the Keldysh distribution functions. We stress the violations of the fluctuation and dissipation theorem among these various exciton correlation functions in the non-equilibrium exciton superfluids. We also explore the input output relations between various exciton correlation functions and those of emitted photons such as the angle resolved photon power spectrum, phase sensitive two mode squeezing spectrum and two photon correlations. Applications to possible superfluids in the exciton-polariton systems are also mentioned. For a comparison, using conventional imaginary time formalism, we also calculate all the exciton correlation functions in an equilibrium dissipative exciton superfluid in the electron-electron coupled semi-conductor bilayers at the quantum Hall regime at the total filling factor nu(T) = 1. We stress the analogies and also important differences between the correlations functions in the two exciton superfluid systems

Classification of magnons in rotated ferromagnetic Heisenberg model and their competing responses in transverse fields

Competing orders is a general concept to describe various quantum phases and transitions in various materials. One efficient way to investigate competing orders is to first classify different class of excitations in a given quantum phase, then study their competing responses under various external probes. This strategy may not only lead to deep understanding of the quantum phase itself, but also its deep connections to various other quantum phases nearby. We implement this approach by studying the Rotated Ferromagnetic Heisenberg model (RFHM) in two different transverse fields

Simulating and detecting the quantum spin Hall effect in the kagome optical lattice

h_x

Fermionic Hubbard model with Rashba or Dresselhaus spin–orbit coupling

and

Quantum incommensurate skyrmion crystals and commensurate to in-commensurate transitions in cold atoms and materials with spin–orbit couplings in a Zeeman field

h_z

Abelian flux induced magnetic frustrations of spinor boson superfluids on a square lattice

which can be intuitively visualized as studying spin-orbit couplings (SOC) effects in 2d Ising or anisotropic XY model in a transverse field. At a special SOC class, it was known that the RFHM at a zero field owns an exact ground state called Y-x state. It supports non only the commensurate C-C

Symmetry protected bosonic topological phase transitions: Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice

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Frustrated superfluids in a non-Abelian flux

and C-C