We explore the effects of artificial U ( 3 ) gauge potentials on ultracold atoms. We study background gauge fields with both non-constant and constant Wilson loops around plaquettes, obtaining the energy spectra in each case. The scenario of metal–insulator transition for irrational fluxes is also examined. Finally, we discuss the effect of such a gauge potential on the superfluid–insulator transition for bosonic ultracold atoms.
We explore the effects of artificial U ( 3 ) gauge potentials on ultracold atoms. We study background gauge fields with both non-constant and constant Wilson loops around plaquettes, obtaining the energy spectra in each case. The scenario of metal–insulator transition for irrational fluxes is also examined. Finally, we discuss the effect of such a gauge potential on the superfluid–insulator transition for bosonic ultracold atoms.
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.
Nowadays it is experimentally feasible to create artificial, and in particular, non-Abelian gauge potentials for ultracold atoms trapped in optical lattices. Motivated by this fact, we investigate the fundamental properties of an ultracold Fermi gas in a non-Abelian U(2) gauge potential characterized by a constant Wilson loop. Under this specific condition, the energy spectrum exhibits a robust band structure with large gaps and reveals a new fractal figure. The transverse conductivity is related to topological invariants and is shown to be quantized when the Fermi energy lies inside a gap of the spectrum. We demonstrate that the analog of the integer quantum Hall effect for neutral atoms survives the non-Abelian coupling and leads to a striking fractal phase diagram. Moreover, this coupling induces an anomalous Hall effect as observed in graphene.
The dynamics of ultracold neutral atoms subject to a non-Abelian gauge field is investigated. In particular we analyze in detail a simple experimental scheme to achieve a con- stant, but non-Abelian gauge field, and discuss in the frame of this gauge field the non-Abelian Aharanov-Bohm effect. In the last part of this paper, we discuss intrinsic non-Abelian effects in the dynamics of cold atomic wavepackets. the implementation of these proposals, ultracold atoms would offer a unique testbed for the analysis of non-trivial non- Abelian effects on the quantum dynamics of multicomponent wavepackets. In this paper, we investigate the wave packet dynam- ics of a cloud of ultracold atoms in the presence of a non- Abelian gauge potential. In Sect. 2 we discuss how this un- doubtedly rather exotic scenario can be envisaged in a sam- ple of cold atoms where the internal electronic energy levels are addressed by laser fields with a nontrivial spatial phase and intensity distribution. This setup opens up a number of new scenarios for ultracold gases, allowing for the study of non-Abelian atom optics, which naturally ties together opti- cal and magnetic effects. Remarkably, as shown in Sect. 2, even very simple laser arrangements may induce non-trivial cold-atom dynamics. As a first example of this non-trivial dynamics, we discuss in Sect. 3 a possible optical tweezer experiment including a non-Abelian flux, for which the pop- ulation transfer between internal states crucially depends on the path taken (non-Abelian Aharonov-Bohm effect). This effect resembles indeed what one would expect from scat- tering protons onto a non-Abelian flux line where the proton can be transferred into a neutron (8). The tweezer experiment discussed in Sect. 3 just involves the internal-state dynamics, without exploring the rich dynamics resulting from the in- terplay between external and internal degrees of freedom in non-Abelian gauge fields. Section 4 is devoted to the analy- sis of this interplay. In particular, we show that the dynamics of cold-atom wavepackets can be significantly affected by in- trinsically non-Abelian effects, which are crucially dependent on the initial momentum distribution of the wavepacket. We consider in particular the relevant examples of wavepacket propagation and wavepacket reflection at an atomic mirror. Finally, we conclude in Sect. 5.
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle-the graviton-that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms 'feeling' laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials-both Abelian and non-Abelian-in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.
The present thesis studies a variety of cold atomic systems in artificial gauge fields. In the first part we focus on fractional quantum Hall effects, asking whether interesting topological states can be realized with cold atoms. We start by making a close connection to solid-state systems and first consider fermionic atoms with dipolar interactions. Assuming the system to be in the Laughlin state, we evaluate the energy gap in the thermodynamic limit as a measure for the robustness of the state. We show that it can be increased by additionally applying a non-Abelian gauge field squeezing the Landau levels. We then switch to bosonic systems with repulsive contact interactions. Artificial magnetic fields for cold bosons have extensively been discussed before in the context of rotating Bose gases. We follow a different approach where the gauge field is due to an atom-laser coupling. Thus, transitions between different dressed states have to be included. They are shown to break the cylindrical symmetry of the system. Modifying the Laughlin state and the Moore-Read state accordingly, we determine the parameter regimes where they are good representations for the ground state of the system obtained via exact diagonalization. One of the most interesting feature of fractional quantum Hall states is the anyonic behavior of their excitations. We therefore also study quasiholes in the Laughlin state and the modified Laughlin state. They are shown to posses anyonic properties, which become manifest even in small systems. Moreover, the dynamics of a single quasihole causes visible traces in the density of the system which allow to clearly distinguish the Laughlin regime from less correlated phases. In the latter, a sequence of collapses and revivals of the quasihole can be observed, which is absent in the Laughlin regime. Extending our study to bosonic systems with a pesudospin-1/2 degree of freedom, we discuss the formation of strongly correlated spin singlets. Strikingly, at filling v=4/3, the system is described by a state with non-Abelian excitations, which is constructed as the zero-energy ground state of repulsive three-body contact interactions. Systems with internal degrees of freedom also allow for implementing artificial spin-orbit coupling. It is shown to give rise to a variety of incompressible states. In the second part of the thesis, we concentrate on condensed system. Bose-Einstein condensates with spin-orbit coupling are shown to have a degeneracy on the mean-field level, which is lifted by quantum and thermal fluctuations. The system becomes experimentally feasible in three dimensions, where the condensate depletion remains finite, and thus allow for an experimental observation of this order-by-disorder mechanism. Finally, we study the influence of Abelian and non-Abelian gauge fields on the quantum phase transitions of bosons in a square optical lattice. Re-entrant superfluid phases and superfluids at finite momenta are interesting properties featured by such systems.
Ultra cold atomic condensate with long range interaction is considered as a possible candidate to realize the supersolid phase. Such a supersolid phase can be subjected to artificial gauge field created either through rotation or by introducing space dependent coupling among hyperfine states of the atoms using Raman lasers. We study the effect of an artificial gauge field on the Supersolid phase in ultracold atomic condensates with long range interactions. Using Mean field approach, we demonstrate the structural differences between vortex in a supersolid and superfluid. We determine analytically the effect of the artificial gauge field on the density wave - supersolid (DW-SS) and the Mott insulator-superfluid (MI-SF) transition boundary. We also point out that in symmetric gauge the momentum distribution structure at these transition boundaries bears distinctive signatures of vortices in supersolid and superfluid phases. We point out that these results can clearly identify such a ultra cold atomic supersolid phase.