Observation of ultracold atomic bubbles in orbital microgravity

Substantial leaps in the understanding of quantum systems have been driven by exploring geometry, topology, dimensionality and interactions in ultracold atomic ensembles1–6. A system where atoms evolve while confined on an ellipsoidal surface represents a heretofore unexplored geometry and topology. Realizing an ultracold bubble—potentially Bose–Einstein condensed—relates to areas of interest including quantized-vortex flow constrained to a closed surface topology, collective modes and self-interference via bubble expansion7–17. Large ultracold bubbles, created by inflating smaller condensates, directly tie into Hubble-analogue expansion physics18–20. Here we report observations from the NASA Cold Atom Lab21 facility onboard the International Space Station of bubbles of ultracold atoms created using a radiofrequency-dressing protocol. We observe bubble configurations of varying size and initial temperature, and explore bubble thermodynamics, demonstrating substantial cooling associated with inflation. We achieve partial coverings of bubble traps greater than one millimetre in size with ultracold films of inferred few-micrometre thickness, and we observe the dynamics of shell structures projected into free-evolving harmonic confinement. The observations are among the first measurements made with ultracold atoms in space, using perpetual freefall to explore quantum systems that are prohibitively difficult to create on Earth. This work heralds future studies (in orbital microgravity) of the Bose–Einstein condensed bubble, the character of its excitations and the role of topology in its evolution

Thermally generated vortices, gauge invariance and electron spectral function in the pseudo-gap regime

Starting from classical vortex fluctuation picture, we study the single electron properties in the pseudogap regime. We show that it is the gauge invariant Green function of spinon which is directly related to ARPES data in the pseudogap regime instead of the non-gauge invariant one. We find that the random gauge field from the thermally generated vortices completely destroys the coherent spinon motion and leads to excitations pertinent to non-Fermi liquid behaviors. The Energy Distribution Curves (EDC) show broad peaks, while the Momentum Distribution Curve (MDC) show sharp peaks with Lorenz form. The local density of state at zero energy scales as the inverse of Kosterlize-Thouless length. These results are qualitatively consistent with the ARPES data in the pseudo-gap regime.Comment: Phys. Rev. Lett. 87, 22700

Unconventional particle-hole mixing in the systems with strong superconducting fluctuations

Development of the STM and ARPES spectroscopies enabled to reach the resolution level sufficient for detecting the particle-hole entanglement in superconducting materials. On a quantitative level one can characterize such entanglement in terms of the, so called, Bogoliubov angle which determines to what extent the particles and holes constitute the spatially or momentum resolved excitation spectra. In classical superconductors, where the phase transition is related to formation of the Cooper pairs almost simultaneously accompanied by onset of their long-range phase coherence, the Bogoliubov angle is slanted all the way up to the critical temperature Tc. In the high temperature superconductors and in superfluid ultracold fermion atoms near the Feshbach resonance the situation is different because of the preformed pairs which exist above Tc albeit loosing coherence due to the strong quantum fluctuations. We discuss a generic temperature dependence of the Bogoliubov angle in such pseudogap state indicating a novel, non-BCS behavior. For quantitative analysis we use a two-component model describing the pairs coexisting with single fermions and study their mutual feedback effects by the selfconsistent procedure originating from the renormalization group approach.Comment: 4 pages, 4 figure

Electronic structure of the trilayer cuprate superconductor Bi2_2Sr2_2Ca2_2Cu3_3O10+δ_{10+\delta}

The low-energy electronic structure of the trilayer cuprate superconductor Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ near optimal doping is investigated by angle-resolved photoemission spectroscopy. The normal state quasiparticle dispersion and Fermi surface, and the superconducting d-wave gap and coherence peak are observed and compared with those of single and bilayer systems. We find that both the superconducting gap magnitude and the relative coherence-peak intensity scale linearly with $T_c$ for various optimally doped materials. This suggests that the higher $T_c$ of the trilayer system should be attributed to parameters that simultaneously enhance phase stiffness and pairing strength.Comment: 5 pages, 5 figre

QED3 theory of underdoped high temperature superconductors

Low-energy theory of d-wave quasiparticles coupled to fluctuating vortex loops that describes the loss of phase coherence in a two dimensional d-wave superconductor at T=0 is derived. The theory has the form of 2+1 dimensional quantum electrodynamics (QED3), and is proposed as an effective description of the T=0 superconductor-insulator transition in underdoped cuprates. The coupling constant ("charge") in this theory is proportional to the dual order parameter of the XY model, which is assumed to be describing the quantum fluctuations of the phase of the superconducting order parameter. The principal result is that the destruction of phase coherence in d-wave superconductors typically, and immediately, leads to antiferromagnetism. The transition can be understood in terms of the spontaneous breaking of an approximate "chiral" SU(2) symmetry, which may be discerned at low enough energies in the standard d-wave superconductor. The mechanism of the symmetry breaking is analogous to the dynamical mass generation in the QED3, with the "mass" here being proportional to staggered magnetization. Other insulating phases that break chiral symmetry include the translationally invariant "d+ip" and "d+is" insulators, and various one dimensional charge-density and spin-density waves. The theory offers an explanation for the rounded d-wave-like dispersion seen in ARPES experiments on Ca2CuO2Cl2 (F. Ronning et. al., Science 282, 2067 (1998)).Comment: Revtex, 20 pages, 5 figures; this is a much extended follow-up to the Phys. Rev. Lett. vol.88, 047006 (2002) (cond-mat/0110188); improved presentation, many additional explanations, comments, and references added, sec. IV rewritten. Final version, to appear in Phys. Rev.

Quantum magnetism and criticality

Magnetic insulators have proved to be fertile ground for studying new types of quantum many body states, and I survey recent experimental and theoretical examples. The insights and methods transfer also to novel superconducting and metallic states. Of particular interest are critical quantum states, sometimes found at quantum phase transitions, which have gapless excitations with no particle- or wave-like interpretation, and control a significant portion of the finite temperature phase diagram. Remarkably, their theory is connected to holographic descriptions of Hawking radiation from black holes.Comment: 39 pages, 10 figures, review article for non-specialists; (v2) added clarifications and references; (v3) minor corrections; (v4) added footnote on hydrodynamic long-time tail

Quantum phases and phase transitions of Mott insulators

This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. The simplest class of Mott insulators have an even number of S=1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S=1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S=1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations.Comment: 51 pages, 13 figure

Order and quantum phase transitions in the cuprate superconductors

It is now widely accepted that the cuprate superconductors are characterized by the same long-range order as that present in the Bardeen-Cooper-Schrieffer (BCS) theory: that associated with the condensation of Cooper pairs. We argue that many physical properties of the cuprates require interplay with additional order parameters associated with a proximate Mott insulator. We review a classification of Mott insulators in two dimensions, and contend that the experimental evidence so far shows that the class appropriate to the cuprates has collinear spin correlations, bond order, and confinement of neutral, spin S=1/2 excitations. Proximity to second-order quantum phase transitions associated with these orders, and with the pairing order of BCS, has led to systematic predictions for many physical properties. We use this context to review the results of recent neutron scattering, fluxoid detection, nuclear magnetic resonance, and scanning tunnelling microscopy experiments.Comment: 20 pages, 13 figures, non-technical review article; some technical details in the companion review cond-mat/0211027; (v3) added refs; (v4) numerous improvements thanks to the referees, to appear in Reviews of Modern Physics; (v6) final version as publishe

Bond operator theory of doped antiferromagnets: from Mott insulators with bond-centered charge order, to superconductors with nodal fermions

The ground states and excitations of two-dimensional insulating and doped Mott insulators are described by a bond operator formalism. While the method represents the degrees of freedom of an arbitrary antiferromagnet exactly, it is especially suited to systems in which there is a natural pairing of sites into bonds, as in states with spontaneous or explicit spin-Peierls order (or bond-centered charge order). In the undoped insulator, as discussed previously, we obtain both paramagnetic and magnetically-ordered states. We describe the evolution of superconducting order in the ground state with increasing doping--at low doping, the superconductivity is weak, can co-exist with magnetic order, and there are no gapless spin 1/2 fermionic excitations; at high doping, the magnetic order is absent and we obtain a BCS d-wave superconductor with gapless spin 1/2, nodal fermions. We present the critical theory describing the onset of these nodal fermionic excitations. We discuss the evolution of the spin spectrum, and obtain regimes where a spin 1 exciton contributes a sharp resonance in the dynamic spin susceptiblity. We also discuss the experimental consequences of low-energy, dynamically fluctuating, spin-Peierls order in an isotropic CuO_2 plane--we compute consequences for the damping and dispersion of an optical phonon involving primarily the O ions, and compare the results with recent neutron scattering measurements of phonon spectra.Comment: 16 pages + 14 pages of appendices, 18 figures; (v3) expanded discussion of theory and experimental implications; (v4) Removed some introductory review discussion and moved it to cond-mat/010823