Skyrmions in a ferromagnetic Bose-Einstein condensate

The recently realized multicomponent Bose-Einstein condensates provide opportunities to explore the rich physics brought about by the spin degrees of freedom. For instance, we can study spin waves and phase separation, macroscopic quantum tunneling, Rabi oscillations, the coupling between spin gradients and superfluid flow, squeezed spin states, vortices and other topological excitations. Theoretically, there have been already some studies of the ground-state properties of these systems and their line-like vortex excitations. In analogy with nuclear physics or the quantum Hall effect, we explore here the possibility of observing point-like topological excitations or skyrmions. These are nontrivial spin textures that in principle can exist in a spinor Bose-Einstein condensate. In particular, we investigate the stability of skyrmions in a fictitious spin-1/2 condensate of Rb87 atoms. We find that skyrmions can exist in this case only as a metastable state, but with a lifetime of the order of, or even longer than, the typical lifetime of the condensate itself. In addition to determining the size and the lifetime of the skyrmion, we also present its spin texture and finally briefly consider its dynamical properties.Comment: 4 pages (REVtex), 3 PDF figures. See also cond-mat/000237

Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate

A central goal in condensed matter and modern atomic physics is the exploration of many-body quantum phases and the universal characteristics of quantum phase transitions in so far as they differ from those established for thermal phase transitions. Compared with condensed-matter systems, atomic gases are more precisely constructed and also provide the unique opportunity to explore quantum dynamics far from equilibrium. Here we identify a second-order quantum phase transition in a gaseous spinor Bose-Einstein condensate, a quantum fluid in which superfluidity and magnetism, both associated with symmetry breaking, are simultaneously realized. $^{87}$Rb spinor condensates were rapidly quenched across this transition to a ferromagnetic state and probed using in-situ magnetization imaging to observe spontaneous symmetry breaking through the formation of spin textures, ferromagnetic domains and domain walls. The observation of topological defects produced by this symmetry breaking, identified as polar-core spin-vortices containing non-zero spin current but no net mass current, represents the first phase-sensitive in-situ detection of vortices in a gaseous superfluid.Comment: 6 pages, 4 figure

Robust Digital Holography For Ultracold Atom Trapping

We have formulated and experimentally demonstrated an improved algorithm for design of arbitrary two-dimensional holographic traps for ultracold atoms. Our method builds on the best previously available algorithm, MRAF, and improves on it in two ways. First, it allows for creation of holographic atom traps with a well defined background potential. Second, we experimentally show that for creating trapping potentials free of fringing artifacts it is important to go beyond the Fourier approximation in modelling light propagation. To this end, we incorporate full Helmholtz propagation into our calculations.Comment: 7 pages, 4 figure

Phase-slip induced dissipation in an atomic Bose-Hubbard system

Phase slips play a primary role in dissipation across a wide spectrum of bosonic systems, from determining the critical velocity of superfluid helium to generating resistance in thin superconducting wires. This subject has also inspired much technological interest, largely motivated by applications involving nanoscale superconducting circuit elements, e.g., standards based on quantum phase-slip junctions. While phase slips caused by thermal fluctuations at high temperatures are well understood, controversy remains over the role of phase slips in small-scale superconductors. In solids, problems such as uncontrolled noise sources and disorder complicate the study and application of phase slips. Here we show that phase slips can lead to dissipation for a clean and well-characterized Bose-Hubbard (BH) system by experimentally studying transport using ultra-cold atoms trapped in an optical lattice. In contrast to previous work, we explore a low velocity regime described by the 3D BH model which is not affected by instabilities, and we measure the effect of temperature on the dissipation strength. We show that the damping rate of atomic motion-the analogue of electrical resistance in a solid-in the confining parabolic potential fits well to a model that includes finite damping at zero temperature. The low-temperature behaviour is consistent with the theory of quantum tunnelling of phase slips, while at higher temperatures a cross-over consistent with the transition to thermal activation of phase slips is evident. Motion-induced features reminiscent of vortices and vortex rings associated with phase slips are also observed in time-of-flight imaging.Comment: published in Nature 453, 76 (2008

Beyond Gross-Pitaevskii Mean Field Theory

A large number of effects related to the phenomenon of Bose-Einstein Condensation (BEC) can be understood in terms of lowest order mean field theory, whereby the entire system is assumed to be condensed, with thermal and quantum fluctuations completely ignored. Such a treatment leads to the Gross-Pitaevskii Equation (GPE) used extensively throughout this book. Although this theory works remarkably well for a broad range of experimental parameters, a more complete treatment is required for understanding various experiments, including experiments with solitons and vortices. Such treatments should include the dynamical coupling of the condensate to the thermal cloud, the effect of dimensionality, the role of quantum fluctuations, and should also describe the critical regime, including the process of condensate formation. The aim of this Chapter is to give a brief but insightful overview of various recent theories, which extend beyond the GPE. To keep the discussion brief, only the main notions and conclusions will be presented. This Chapter generalizes the presentation of Chapter 1, by explicitly maintaining fluctuations around the condensate order parameter. While the theoretical arguments outlined here are generic, the emphasis is on approaches suitable for describing single weakly-interacting atomic Bose gases in harmonic traps. Interesting effects arising when condensates are trapped in double-well potentials and optical lattices, as well as the cases of spinor condensates, and atomic-molecular coupling, along with the modified or alternative theories needed to describe them, will not be covered here.Comment: Review Article (19 Pages) - To appear in 'Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment', Edited by P.G. Kevrekidis, D.J. Frantzeskakis and R. Carretero-Gonzalez (Springer Verlag

Controlled creation of a singular spinor vortex by circumventing the Dirac belt trick

Persistent topological defects and textures are particularly dramatic consequences of superfluidity. Among the most fascinating examples are the singular vortices arising from the rotational symmetry group SO(3), with surprising topological properties illustrated by Dirac’s famous belt trick. Despite considerable interest, controlled preparation and detailed study of vortex lines with complex internal structure in fully three-dimensional spinor systems remains an outstanding experimental challenge. Here, we propose and implement a reproducible and controllable method for creating and detecting a singular SO(3) line vortex from the decay of a non-singular spin texture in a ferromagnetic spin-1 Bose–Einstein condensate. Our experiment explicitly demonstrates the SO(3) character and the unique spinor properties of the defect. Although the vortex is singular, its core fills with atoms in the topologically distinct polar magnetic phase. The resulting stable, coherent topological interface has analogues in systems ranging from condensed matter to cosmology and string theory

Momentum-Resolved Bragg Spectroscopy in Optical Lattices

Strongly correlated many-body systems show various exciting phenomena in condensed matter physics such as high-temperature superconductivity and colossal magnetoresistance. Recently, strongly correlated phases could also be studied in ultracold quantum gases possessing analogies to solid-state physics, but moreover exhibiting new systems such as Fermi-Bose mixtures and magnetic quantum phases with high spin values. Particularly interesting systems here are quantum gases in optical lattices with fully tunable lattice and atomic interaction parameters. While in this context several concepts and ideas have already been studied theoretically and experimentally, there is still great demand for new detection techniques to explore these complex phases in detail. Here we report on measurements of a fully momentum-resolved excitation spectrum of a quantum gas in an optical lattice by means of Bragg spectroscopy. The bandstructure is measured with high resolution at several lattice depths. Interaction effects are identified and systematically studied varying density and excitation fraction.Comment: 13 pages, 5 figure

Atomic “bomb testing”: the Elitzur–Vaidman experiment violates the Leggett–Garg inequality

Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object—in a dramatic scenario, a bomb—without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the “bomb test” with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett–Garg inequality—a quantitative criterion fulfilled by macro-realistic physical theories. To perform interaction-free measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used push-out technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the Leggett–Garg inequality

Isotope shifts in the metastable a5F and excited y5Go terms of atomic titanium

We measure and analyze the isotope shifts in the multiplet of transitions between the metastable a5F and excited y5Go terms of neutral titanium by probing a titanium vapor in a hollow cathode lamp using saturated absorption spectroscopy. We resolve the five J→J+1 and the four J→J transitions within the multiplet for each of the three I=0 stable isotopes (Ti46, Ti48, and Ti50). The isotope shifts on these transitions allow us to determine the isotope-dependent variation in the fine-structure splitting of the a5F and y5Go levels themselves. Combined with existing knowledge of the nuclear charge radii of titanium nuclei, we derive the specific mass and field shifts, which arise from correlated electronic motion and electronic density at the nucleus respectively, and further observe a strong J-dependent variation in each. Our results yield insight into the electronic and nuclear structure of transition metal atoms like titanium and also characterize optical transitions that may allow for optical manipulation of ultracold gases of transition-metal species