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Register a new userObservation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
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Because global topological properties are robust against local perturbations, understanding and manipulating the topological properties of physical systems is essential in advancing quantum science and technology. For quantum computation, topologically protected qubit operations can increase computational robustness, and for metrology the quantized Hall effect directly defines the von Klitzing constant. Fundamentally, topological order is generated by singularities called topological defects in extended spaces, and is quantified in terms of Chern numbers, each of which measures different sorts of fields traversing surfaces enclosing these topological singularities. Here, inspired by high energy theories, we describe our synthesis and characterization of a singularity present in non-Abelian gauge theories - a Yang monopole - using atomic Bose-Einstein condensates in a five-dimensional space, and quantify the monopole in terms of Chern numbers measured on enclosing manifolds. While the well-known 1st Chern number vanished, the 2nd Chern number, measured for the first time in any physical settings, did not. By displacing the manifold, we then observed a phase transition from topological to trivial as the monopole left the manifold.
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We observe monopole oscillations in a mixture of Bose-Einstein condensates, where the usually dominant mean-field interactions are canceled. In this case, the system is governed by the next-order Lee-Huang-Yang (LHY) correction to the ground state energy, which describes the effect of quantum fluctuations. Experimentally such a LHY fluid is realized by controlling the atom numbers and interaction strengths in a $^{39}$K spin mixture confined in a spherical trap potential. We measure the monopole oscillation frequency as a function of the LHY interaction strength as proposed recently by J{o}rgensen et al. [Phys. Rev. Lett. 121, 173403 (2018)] and find excellent agreement with simulations of the complete experiment including the excitation procedure and inelastic losses. This confirms that the system and its collective behavior are initially dominated by LHY interactions. Moreover, the monopole oscillation frequency is found to be stable against variations of the involved scattering lengths in a broad region around the ideal values, confirming the stabilizing effect of the LHY interaction. These results pave the way for using the non-linearity provided by the LHY term in quantum simulation experiments and for investigations beyond the LHY regime.
Here, we provide a simple Hubbard-like model of spin-$1/2$ fermions that gives rise to the SU(2) symmetric Thirring model that is equivalent, in the low-energy limit, to Yang-Mills-Chern-Simons model. First, we identify the regime that simulates the SU(2) Yang-Mills theory. Then, we suitably extend this model so that it gives rise to the SU(2) level $k$ Chern-Simons theory with $kgeq2$ that can support non-Abelian anyons. This is achieved by introducing multiple fermionic species and modifying the Thirring interactions, while preserving the SU(2) symmetry. Our proposal provides the means to theoretically and experimentally probe non-Abelian SU(2) level $k$ topological phases.
For decades, the topological phenomena in quantum systems have always been catching our attention. Recently, there are many interests on the systems where topologically protected edge states exist, even in the presence of non-Hermiticity. Motivated by these researches, the topological properties of a non-Hermitian dice model are studied in two non-Hermitian cases, viz. in the imbalanced and the balanced dissipations. Our results suggest that the topological phases are protected by the real gaps and the bulk-edge correspondence readily seen in the real edge-state spectra. Besides, we show that the principle of the bulk-edge correspondence in Hermitian case is still effective in analyzing the three-band non-Hermitian system. We find that there are topological non-trivial phases with large Chern numbers $C=-3$ robust against the dissipative perturbations.
The Su-Schrieffer-Heeger (SSH) model, which captures the most striking transport properties of the conductive organic polymer $trans$-polyacetylene, provides perhaps the most basic model system supporting topological excitations. The alternating bond pattern of polyacetylene chains is captured by the bipartite sublattice structure of the SSH model, emblematic of one-dimensional chiral symmetric topological insulators. This structure supports two distinct nontrivial topological phases, which, when interfaced with one another or with a topologically trivial phase, give rise to topologically-protected, dispersionless boundary states. Using $^{87}$Rb atoms in a momentum-space lattice, we realize fully-tunable condensed matter Hamiltonians, allowing us to probe the dynamics and equilibrium properties of the SSH model. We report on the experimental quantum simulation of this model and observation of the localized topological soliton state through quench dynamics, phase-sensitive injection, and adiabatic preparation.
Magnetic monopoles --- particles that behave as isolated north or south magnetic poles --- have been the subject of speculation since the first detailed observations of magnetism several hundred years ago. Numerous theoretical investigations and hitherto unsuccessful experimental searches have followed Diracs 1931 development of a theory of monopoles consistent with both quantum mechanics and the gauge invariance of the electromagnetic field. The existence of even a single Dirac magnetic monopole would have far-reaching physical consequences, most famously explaining the quantization of electric charge. Although analogues of magnetic monopoles have been found in exotic spin-ices and other systems, there has been no direct experimental observation of Dirac monopoles within a medium described by a quantum field, such as superfluid helium-3. Here we demonstrate the controlled creation of Dirac monopoles in the synthetic magnetic field produced by a spinor Bose-Einstein condensate. Monopoles are identified, in both experiments and matching numerical simulations, at the termini of vortex lines within the condensate. By directly imaging such a vortex line, the presence of a monopole may be discerned from the experimental data alone. These real-space images provide conclusive and long-awaited experimental evidence of the existence of Dirac monopoles. Our result provides an unprecedented opportunity to observe and manipulate these quantum-mechanical entities in a controlled environment.
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