Quantum gases in optical lattices allow for fundamental studies in atomic and condensed-matter physics and the exploration of novel effects. After a brief introduction to the fundamentals of quantum gas experiments in optical lattices, we discuss two recent experiments focusing on driven matter waves in a one-dimensional optical lattice. The first experiment uses a tilted bichromatic optical lattice to investigate the interplay of disorder and collisional interactions in the accelerated transport of a Bose-Einstein condensate. Here, a screening effect is observed, in which the interactions effectively cancel the damping of Bloch oscillations induced by a (quasi-)disordered potential. This effect can be understood through a modification of the underlying band structure by the interactions. The second experiment studies the dynamics of a weakly trapped condensate resonantly coupled to the orbitals of a strongly confining state-selective lattice. We observe momentum distributions that correspond to matter wave diffraction from a periodic structure; however, the diffractive dynamics remain strongly linked to the internal-state Rabi oscillations. In the regime investigated, which we call the nonadiabatic regime, no diffracting potential can be defined. We show how only for much stronger coupling, the internal and external dynamics decouple, transitioning from nonadiabatic diffraction to the well-studied Kapitza-Dirac diffraction. We further investigate prospects for realizing dissipative spin models in our ultracold atomic gas experiment. To this end, we develop and test in the laboratory several possible implementations of effective spins with differential coupling to a superfluid background and examine their viability for a realization of the spin-boson model. | 94 pages
Quantum gases in optical lattices allow for fundamental studies in atomic and condensed-matter physics and the exploration of novel effects. After a brief introduction to the fundamentals of quantum gas experiments in optical lattices, we discuss two recent experiments focusing on driven matter waves in a one-dimensional optical lattice. The first experiment uses a tilted bichromatic optical lattice to investigate the interplay of disorder and collisional interactions in the accelerated transport of a Bose-Einstein condensate. Here, a screening effect is observed, in which the interactions effectively cancel the damping of Bloch oscillations induced by a (quasi-)disordered potential. This effect can be understood through a modification of the underlying band structure by the interactions. The second experiment studies the dynamics of a weakly trapped condensate resonantly coupled to the orbitals of a strongly confining state-selective lattice. We observe momentum distributions that correspond to matter wave diffraction from a periodic structure; however, the diffractive dynamics remain strongly linked to the internal-state Rabi oscillations. In the regime investigated, which we call the nonadiabatic regime, no diffracting potential can be defined. We show how only for much stronger coupling, the internal and external dynamics decouple, transitioning from nonadiabatic diffraction to the well-studied Kapitza-Dirac diffraction. We further investigate prospects for realizing dissipative spin models in our ultracold atomic gas experiment. To this end, we develop and test in the laboratory several possible implementations of effective spins with differential coupling to a superfluid background and examine their viability for a realization of the spin-boson model. | 94 pages
Quantum degenerate atomic gases offer a unique platform for the exploration of a wide variety of interacting many-body systems in a pristine environment, based on a set of powerful tools for the coherent control of the atoms' internal and external degrees of freedom. Here, we present experimental studies of strongly interacting bosonic mixtures in one-dimensional (1D) systems, in which the mobilities of the two species are independently controlled with a state-selective optical lattice. In a first experiment, we freeze out the tunneling of one species from a binary mixture, and study the formation of ``quantum emulsion'' states, where immobile atoms serve as a static, random disorder for a more mobile species. We investigate the 1D superfluid-to-insulator transition in the presence of this disorder, and make comparisons to the effects of quasi-disorder from an incommensurate optical lattice. We observe enhanced localization in the more random potential, highlighting the important role of correlations in disordered systems. Through a combined measurement of transport, localization, and excitation spectra, we are able to obtain strong evidence for observation of a disordered, insulating quantum phase, the 1D Bose glass. In a second experiment, we introduce a new experimental technique for the characterization of ultracold gases held in optical lattices. In analogy to neutron diffraction from solids, we use atomic de Broglie waves to non-destructively probe the spatial structure of 1D Mott insulators through elastic Bragg diffraction, and to probe inelastic band-structure excitations of more weakly interacting 1D Bose gases. Furthermore, we use the diffraction of matter waves to detect the formation of forced-antiferromagnetic ordering in a crystalline atomic spin mixture. Lastly, we study the dynamical response of matter waves to a periodically pulsed, incommensurate optical lattice, a situation that realizes a system of two coupled kicked quantum rotors. We observe that the coupling induces a suppression of energy growth at quantum resonances, and a localization-to-delocalization transition in momentum space for off-resonant driving. Our observations confirm a long-standing theoretical prediction for the two-rotor system, and illustrate how classical behavior can emerge from the evolution of a simple quantum system. | 193 pages
In this thesis I report on experiments that enter a new regime in the many body physics of ultracold atomic gases. A Bose-Einstein condensate is loaded into a three-dimensional optical lattice potential formed by a standing wave laser light field. In this novel quantum system we have been able to both realize a quantum phase transition from a superfluid to a Mott insulator, and to observe the collapse and revival of a macroscopic matter wave field. Quantum phase transitions are driven by quantum fluctuations and occur, even at zero temperature, as the relative strength of two competing energy terms in the underlying Hamiltonian is varied across a critical value. In the first part of this work I report on the observation of such a quantum phase transition in a Bose-Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. In the superfluid ground state, each atom is spread-out over the entire lattice, whereas in the Mott insulating state, exact numbers of atoms are localized at individual lattice sites. We observed the reversible transition between those states and detected the gap in the excitation spectrum of the Mott insulator. A Bose-Einstein condensate is usually described by a macroscopic matter wave field. However, a quantized field underlies such a "classical" matter wave field of a Bose-Einstein condensate. The striking behavior of ultracold matter due to the field quantization and the nonlinear interactions between the atoms is the focus of the second part of this work. The matter wave field of a Bose-Einstein condensate is observed to undergo a series of collapses and revivals as time evolves. Furthermore, we show that the collisions between individual pairs of atoms lead to a fully coherent collisional phase shift in the corresponding many-particle state, which is a crucial cornerstone of proposed novel quantum computation schemes with neutral atoms. With these experiments we enter a new field of physics with ultracold quantum gases. In this strongly correlated regime, interactions between atoms dominate the behavior of the many-body system such that it can no longer be described by the usual theories for weakly interacting Bose gases. This novel quantum system offers the unique possibility to experimentally address fundamental questions of modern solid state physics, atomic physics, quantum optics, and quantum information.
Experiments on atomic Bose-Einstein condensates inside quasi-one-dimensional optical lattices and related developments in the realization of atom lasers are currently at the frontiers in atomic physics. We give a short review of theoretical progress in evaluating the coherent transport of matter in such configurations, which has been based on an adaptation of the Wannier function representation of quasi-particle states in periodic potentials and on the use of advanced numerical methods for the solution of the time-dependent Gross-Pitaevskii equation. We present various methods by which the band structure of the elementary excitations of a periodic condensate may be probed and describe in terms of Bloch oscillations the coherent emission of matter pulses from a condensate inside an optical lattice under the force of gravity. A harmonic force can be applied to a condensate inside a magnetic trap by a rapid displacement of the center of the trap and a transition of the condensate from superfluid to dissipative behavior is driven by superposing an optical lattice. Finally, in the superfluid regime the combination of a constant force and a harmonic force in the presence of an optical lattice drives Josephson-type oscillations of the condensate, leading to observable resonances and multimode behavior.
In this thesis I report on experiments on the quantum dynamics of matter waves in a onedimensional lattice potential. A 87Rb Bose-Einstein condensates is prepared in a one-dimensional waveguide in the lowest band of a superimposed optical lattice potential. The action of a weak lattice potential allows to modify the linear wave dispersion. We realized dispersion management by switching from normal to anomalous dispersion during the evolution. In this way the initial expansion of a wave packet is reversed to a compression and thus the effective spreading can be suppressed. By preparing a BEC at the Brillouin zone edge, we observed bright atomic gap solitons – non-spreading wave packets. They form, if the atom number and the lattice potential depth is tuned such that the effect of the repulsive atomic interaction and the anomalous dispersion cancel. For deep lattice potentials our system is described by a discrete nonlinear Schrödinger equation, whose dynamics is determined by the tunneling between adjacent lattice sites and the nonlinear phase evolution. In the main part of this thesis I report on the first experimental observation of nonlinear self-trapping for matter waves. The transition from the diffusive regime, characterized by an continuous expansion of the condensate, to the self-trapping regime is accomplished by increasing the atomic density. Due to the corresponding increase of the repulsive atomic interaction the initial expansion stops and the width of the wave packet remains finite. The comparison with a numerical analysis reveals that the effect is due to an inhibition of the site-to-site tunneling induced by the nonlinear phase evolution.
From time to time in physics, single technical achievements have spawned an explosion of research activity and have led to the genesis of entirely new avenues of investigation. Precisely this occurred in the field of quantum gases - the topic of this Focus Issue - following the achievement of Bose-Einstein condensation in a dilute alkali gas in 1995. These experiments built on the foundational work on quantum fluids in dense systems, such as superfluid helium, and the technical achievements of laser cooling in atomic physics. Dilute quantum gases have already proved to be an incredibly fertile ground for exploring a wide range of macroscopic quantum phenomena. The rapid pace of experimental discovery and theoretical advance is evident and every year continues to bring significant achievements. A great advantage is that microscopic observations can be made directly and compared with the predictions of many-body theoretical formulations founded on interaction parameters which are completely determined - something which is not possible in their dense fluid counterparts. This Focus Issue brings together papers which cover many of the topical aspects of quantum gases: optical lattices, quantum degenerate fermions, quantum atom optics, molecular Bose-Einstein condensation, vorticity, and quantum fluctuations in systems of reduced dimensionality. One pervasive theme is the flexibility which arises from the ability to control the interactions, even dynamically if necessary. In quantum gases, this can be effected in two ways, either by changing the internal nature of the pairwise potentials by a Feshbach resonance, or by changing the nature of external potentials in which the atoms are confined and supported against gravity. The external potential may be used to spin gases to high vorticity, imprint on the system a periodic optical lattice potential, or even change the effective dimensionality. Optical lattices are particularly well represented in this Focus Issue. This is where there is the strongest connection with the physics of solids and strongly correlated fluids. Interest in optical lattices is partly due to the recent experimental demonstration that in these systems one can study the quantum phase transition from a Mott insulator, where the atoms are localized to individual sites of the optical potential, to a superfluid phase with long-range order. In contrast to a condensed matter system, the transition can be easily dynamically controlled since it is induced by simply varying the depth of the optical potential. Another area of focused interest is in fermionic gases where there is an ongoing effort, both experimentally and theoretically, to observe and characterize the high-temperature superfluid transition that should occur with enhanced pairwise interactions. If realized, this quantum system would allow experimental investigation of the crossover from Bose-Einstein condensation of dilute weakly-interacting composite bosons to the superconducting-like transition that occurs in a system of weakly interacting fermions. The topics of this Focus Issue represent well the building blocks of quantum gas studies which should allow the exploration of a wide range of macroscopic quantum phenomena in a highly controllable and clean system in which the effects of disorder may be completely absent. Given the recent progress, it will be intriguing to see where this field leads in the future. Focus on Quantum Gases Contents Anisotropic dissipation of superfluid flow in a periodically dressed Bose-Einstein condensate D M Stamper-Kurn Rapidly rotating Bose-Einstein condensates in anharmonic potentials G M Kavoulakis and Gordon Baym Feshbach resonances and collapsing Bose-Einstein condensates J N Milstein, C Menotti and M J Holland Three-body recombination of cold fermionic atoms H Suno, B D Esry and Chris H Greene Bogoliubov spectrum and Bragg spectroscopy of elongated Bose-Einstein condensates C Tozzo and F Dalfovo Quantum atom optics with Bose-Einstein condensates Klaus Mølmer Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms D Jaksch and P Zoller The Josephson frequency of resonantly coupled atomic and molecular condensates R A Duine and H T C Stoof Superfluid current disruption in a chain of weakly coupled Bose–Einstein condensates F S Cataliotti, L Fallani, F Ferlaino, C Fort, P Maddaloni and M Inguscio Bright matter wave solitons in Bose–Einstein condensates K E Strecker, G B Partridge, A G Truscott and R G Hulet Spin dynamics for bosons in an optical lattice Juan José García-Ripoll and Juan Ignacio Cirac Mean field ground state of a spin-1 condensate in a magnetic field Wenxian Zhang, Su Yi and Li You Atom resonant tunnelling through a moving barrier M L Chiofalo, M Artoni and G C La Rocca Local correlations in a strongly interacting one-dimensional Bose gas D M Gangardt and G V Shlyapnikov Shift of the molecular bound state threshold in dense ultracold Fermi gases with Feshbach resonance R Combescot Landau damping in trapped Bose condensed gases B Jackson and E Zaremba An exact reformulation of the Bose–Hubbard model in terms of a stochastic Gutzwiller ansatz Iacopo Carusotto and Yvan Castin Chemical potential standard for atomic Bose–Einstein condensates Sigmund Kohler and Fernando Sols The short-distance first-order correlation function of the interacting one-dimensional Bose gas Maxim Olshanii and Vanja Dunjko The relation between the Gross–Pitaevskii and Bogoliubov descriptions of a dilute Bose gas A J Leggett Superfluidity of Bose–Einstein condensate in an optical lattice: Landau–Zener tunnelling and dynamical instability B Wu and Q Niu Density-optimized efficiency for magneto-optical production of a stable molecular Bose–Einstein condensate Matt Mackie, Anssi Collin, Kalle-Antti Suominen and Juha Javanainen A two-atom picture of coherent atom–molecule quantum beats Bogdan Borca, D Blume and Chris H Greene Superfluid dynamics of a Bose–Einstein condensate in a periodic potential C Menotti, A Smerzi and A Trombettoni Phase diagram of two-component bosons on an optical lattice Ehud Altman, Walter Hofstetter, Eugene Demler and Mikhail D Lukin Murray J Holland University of Colorado at Boulder, USA
Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.