The dynamics of condensate shells: collective modes and expansion

We explore the physics of three-dimensional shell-shaped condensates, relevant to cold atoms in "bubble traps" and to Mott insulator-superfluid systems in optical lattices. We study the ground state of the condensate wavefunction, spherically-symmetric collective modes, and expansion properties of such a shell using a combination of analytical and numerical techniques. We find two breathing-type modes with frequencies that are distinct from that of the filled spherical condensate. Upon trap release and subsequent expansion, we find that the system displays self-interference fringes. We estimate characteristic time scales, degree of mass accumulation, three-body loss, and kinetic energy release during expansion for a typical system of Rb87

Josephson physics mediated by the Mott insulating phase

We investigate the static and dynamic properties of bosonic lattice systems in which condensed and Mott insulating phases co-exist due to the presence of a spatially-varying potential. We formulate a description of these inhomogeneous systems and calculate the bulk energy at and near equilibrium. We derive the explicit form of the Josephson coupling between disjoint superfluid regions separated by Mott insulating regions. We obtain detailed estimates for the experimentally-realized case of alternating superfluid and Mott insulating spherical shells in a radially symmetric parabolically-confined cold atom system.Comment: 4 pages, 1 figur

Shell potentials for microgravity Bose-Einstein condensates

Extending the understanding of Bose-Einstein condensate (BEC) physics to new geometries and topologies has a long and varied history in ultracold atomic physics. One such new geometry is that of a bubble, where a condensate would be confined to the surface of an ellipsoidal shell. Study of this geometry would give insight into new collective modes, self-interference effects, topology-dependent vortex behavior, dimensionality crossovers from thick to thin shells, and the properties of condensates pushed into the ultradilute limit. Here we discuss a proposal to implement a realistic experimental framework for generating shell-geometry BEC using radiofrequency dressing of magnetically-trapped samples. Such a tantalizing state of matter is inaccessible terrestrially due to the distorting effect of gravity on experimentally-feasible shell potentials. The debut of an orbital BEC machine (NASA Cold Atom Laboratory, aboard the International Space Station) has enabled the operation of quantum-gas experiments in a regime of perpetual freefall, and thus has permitted the planning of microgravity shell-geometry BEC experiments. We discuss specific experimental configurations, applicable inhomogeneities and other experimental challenges, and outline potential experiments.Comment: 6 pages, 3 figure

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

QED_3 theory of underdoped high temperature superconductors II: the quantum critical point

We study the effect of gapless quasiparticles in a d-wave superconductor on the T=0 end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to 3D XY phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted XY universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields $N$, and we estimate the correlation length exponent (nu = 0.65) and the vortex field anomalous dimension(eta_Phi=-0.48) at the quantum critical point for the physical case N=2. The stable critical point in the theory disappears for the number of Dirac fermions N > N_c, with N_c ~ 3.4 in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.Comment: 13 pages including figures in tex

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

Quantal phases, disorder effects and superconductivity in spin-Peierls systems

In view of recent developments in the investigation on cuprate high-T${}_{\rm c}$ superconductors and the spin-Peierls compound CuGeO${}_{3}$, we study the effect of dilute impurity doping on the spin-Peierls state in quasi-one dimensional systems. We identify a common origin for the emergence of antiferromagnetic order upon the introduction of static vacancies, and superconductivity for mobile holes.Comment: 4 pages revtex; revised versio

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

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.