Session H6: Artificial Electromagnetism and other Gauge Fields in Cold Atomic Gases

Optically synthesized electric and magnetic fields for ultracold neutral atoms

Ultracold atoms hold great promise in simulating essential models in condensed matter physics. One apparent limitation is the charge neutrality of the atoms, preventing access to a rich source of physics, for example, electrons in magnetic fields. We have circumvented this limitation by generating an effective vector potential with an optical coupling between internal states of the atoms. We have made the first experimental realization of synthetic electric and magnetic fields for ultracold neutral atoms, through the temporal and spatial variation of the vector potential. In our system, we use a two-photon Raman coupling to dress a rubidium 87 Bose-Einstein condensate (BEC), where the momentum difference between two Raman beams results in the modified energy-momentum dispersion of the dressed state, leading to the effective vector potential. We have created a synthetic magnetic field evidenced by the appearance of vortices in the BEC; this field is stable in the laboratory frame and allows for adding optical lattices with ease. Our optical approach is not subject to the limitations of rotating systems; with a suitable lattice configuration, it should be able to create sufficiently large synthetic magnetic fields in the quantum-Hall regime. [Y.-J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto, and I. B. Spielman, Nature,\textbf{ 462}, 628 (2009).]   

A practical scheme for a light-induced gauge field in an atomic Bose gas

Cold atoms can be used to simulate a wide range of pending problems known from condensed matter systems. This should give important insight into phenomena such as high-temperature superconductivity or the fractional quantum Hall effect. Since there the main actors are electrons coupling to electromagnetic fields, it is highly desirable to implement orbital electromagnetism also for neutral alkali atoms. A promising approach is to prepare the atoms in a position-dependent internal state. If the atoms follow this state adiabatically, a geometric (Berry) phase is acquired, corresponding to a gauge field. We will first give a semi-classical interpretation of the emerging Lorentz force and the scalar potential in terms of the quantum-optical radiative forces. We will then discuss a practical scheme to generate a light-induced gauge, which has been designed to minimise losses due to spontaneous emission. We will present results of simulations of the many-body dynamics at the mean field level that validate the adiabatic approximation. In particular we will show that it is possible to attain the Lowest Landau Level regime, and compare the promises of this system with those of a rotating gas. \\[4pt] [1] M.~Cheneau, S.~P.~Rath, T.~Yefsah, K.~J.~G\"unter, G.~Juzeli\=unas, and J.~Dalibard, \emph{Geometric potentials in quantum optics: A semi-classical interpretation}, Eur.~Phys.~Lett.~\textbf{83}, 60001 (2008). \\[0pt] [2] K.~J.~G\"unter, M.~Cheneau, T.~Yefsah, S.~P.~Rath, and J.~Dalibard, \emph{Practical scheme for a light-induced gauge field in an atomic Bose gas}, Phys.~Rev.~A \textbf{79}, 011604 (2009). \\[0pt] [3] G.~Juzeli\=unas, J.~Ruseckas, P.~\"Ohberg, and M.~Fleischhauer, \emph{Light-induced effective magnetic fields for ultracold atoms in planar geometries}, Phys.~Rev.~A \textbf{73}, 025602 (2006). \\[0pt] [4] I.~B.~Spielman, \emph{Raman processes and effective gauge potentials}, Phys.~Rev.~A \textbf{79}, 063613 (2009).   

Correlated Phases in Bose-Hubbard Models with Simulated Magnetic Fields

Proposed methods for imprinting gauge fields (tunneling phases) in optical lattices open up the prospect of experimental studies of atomic Bose gases that are well described by the Bose-Hubbard model in an effective magnetic field. I shall discuss the nature of the groundstates of such systems. The relevant physics involves the interplay between the fractional quantum Hall effect for bosons and the ``Hofstadter butterfly'' spectrum. I shall explain how this interplay can lead to novel strongly correlated phases. [G. M{\" o}ller and N. R. Cooper, Phys. Rev. Lett. {\bf 103}, 105303 (2009).]   

Single particle to many-body physics in rotating optical lattices

Recent progress in creating artificial gauge fields for cold atom systems holds promise for experimental realization of many interesting models. In the presence of a periodic potential, the external gauge fields may be used to realize many lattice-gauge theories for the first time. We consider the simplest of such models, where an artificial magnetic field is coupled to the cold atoms and investigate various scenarios. Such an artificial magnetic field may simply be created by rotating the optical lattice, or by more elaborate means like light induced potentials. The physics of particles moving in a periodic potential in the presence of a magnetic field is rich, as it contains three parameters which control commensurate/incommensurate transitions. The first such parameter, flux quanta per plaquette of the lattice, controls the single particle physics. The energy spectrum as a function of this parameter is a fractal shape known as the Hofstadter butterfly. A second parameter is the number of particles per lattice site, which controls if certain insulating states like the Mott state are possible. The ratio of these two parameters give the filling factor, defined as the number of particles per flux quanta, which controls the quantum Hall physics. We first discuss the single particle physics where we investigate the relation between the Wannier functions and local ground states for each site. We show that the presence of the magnetic field requires a new definition of the Wannier functions, and these functions have large overlaps with local ground states. The Peirels substitution describes the hopping between sites faithfully for the lowest band. We also investigate how Peirels substitution has to be applied to higher bands such as the p- band, and discuss the resulting spectra. We then consider interacting Bosons in a rotating optical lattice and investigate the effect of the external magnetic field on the Mott Insulator- Superfluid transition. The phase boundary for this transition can be calculated exactly within mean-field theory and is shown to be controlled by the minimum eigenvalue of the Hofstadter butterfly. We argue that if one goes beyond mean field theory the Mott Insulator-Superfluid boundary is complex, and there are fractional quantum Hall phases of Bosons near every Mott lobe. As a third model we investigate the density profile for non- interacting fermions in a rotating optical lattice and find that the gaps of the Hofstadter butterfly are reflected as sharp plateaus in the density profile. Each one of these regions are topological insulators with quantized Hall conductivity. We argue that the Hall conductivity can be measured without any transport measurements, as the Streda formula relates Hall conductivity to the response of density to magnetic field change. Finally we investigate the physics of fermions with on-site attraction in a rotating optical lattice. We calculate the critical attraction strength for the transition from a topological insulator to a BCS superfluid. We also calculate the vortex lattice structures after BCS pairing takes place and investigate the transitions between different configurations of vortices.