We study the nature of the zero-temperature phase transition between a d-wave superconductor and a Mott insulator in two dimensions. In this "quantum confinement transition", spin and charge are confined to form the electron in the Mott insulator. Within a dual formulation, direct transitions from d-wave superconductors at half-filling to insulators with spin-Peierls (as well as other) order emerge naturally. The possibility of striped superconductors is also discussed within the dual formulation. The transition is described by nodal fermions and bosonic vortices, interacting via a long-ranged statistical interaction modeled by two, coupled Chern-Simons gauge fields, and the critical properties of this model are discussed.

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 propose 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.

Static, dynamic, and topological properties of hollow systems differ from those that are fully filled as a result of the presence of a boundary associated with an inner surface. Hollow Bose-Einstein condensates (BECs) naturally occur in various ultracold atomic systems and possibly within neutron stars but have hitherto not been experimentally realized in isolation on Earth because of gravitational sag. Motivated by the expected first realization of fully closed BEC shells in the microgravity conditions of the Cold Atomic Laboratory aboard the International Space Station, we present a comprehensive study of spherically symmetric hollow BECs as well as the hollowing transition from a filled sphere BEC into a thin shell through central density depletion. We employ complementary analytic and numerical techniques in order to study equilibrium density profiles and the collective mode structures of condensate shells hosted by a range of trapping potentials. We identify concrete and robust signatures of the evolution from filled to hollow structures and the effects of the emergence of an inner boundary, inclusive of a dip in breathing-mode-type collective mode frequencies and a restructuring of surface mode structure across the transition. By extending our analysis to a two-dimensional transition of a disk to a ring, we show that the collective mode signatures are an essential feature of hollowing, independent of the specific geometry. Finally, we relate our work to past and ongoing experimental efforts and consider the influence of gravity on thin condensate shells. We identify the conditions under which gravitational sag is highly destructive and study the mode-mixing effects of microgravity on the collective modes of these shells.arXiv:1712.04428v2 [cond-mat.quant-gas]

Figure 6 contains an error in the placement of the uppermost parabola of allowed transitions. A corrected figure is given below. Related errors are found in the first column of text on p. 10: ͑i͒ line 12 should read "that is U aa ͑␤ −1͒ / ប −␥R 2 2 wide in frequency," ͑ii͒ line 15 should read "as the frequency is increased past 0 +2U aa ͑␤ −1͒ / ប." ͑iii͒ the third and fourth sentences in the second complete paragraph should read "The width of each gap where atoms are not transferred to ͉b͘ as the frequency is changed isThe highest frequency where atoms are transferred is determined by the occupancy m at the core and is 0 + ͑m −1͒U aa ͑␤ −1͒ / ប,"None of the above corrections changes the conclusions of the paper, and in particular, the simulations reported in Fig. 7 did not contain these errors. FIG. 6. ͑Color online͒ The spectrum for transitions between ͉a͘ and ͉b͘ for n =1,2,3. The transition frequency between states with different n a and n b is shown by the thick line. The dashed lines indicate the boundaries between sites with different n in the lattice, which occur at radii R 0 , R 1 , and R 2 . Sites with n =1,2,3 are indicated with green, blue, and red coloring, respectively ͑color available online͒. The interaction energy shifts are indicated, and the figure is drawn assuming ␤ Ͼ 1.PHYSICAL REVIEW A 73, 049903͑E͒ ͑2006͒

We consider the feasibility of creating a phase of neutral bosonic atoms in which multiple Mottinsulating states coexist in a shell structure and propose an experiment to spatially resolve such a structure. This spatially-inhomogeneous phase of bosons, arising from the interplay between the confining potential and the short-ranged repulsion, has been previously predicted. While the Mottinsulator phase has been observed in an atomic gas, the spatial structure of this phase in the presence of an inhomogeneous potential has not yet been directly probed. In this paper, we give a simple recipe for creating a structure with any desired number of shells, and explore the stability of the structure under typical experimental conditions. The stability analysis gives some constraints on how successfully these states can be employed for quantum information experiments. The experimental probe we propose for observing this phase exploits transitions between two species of bosons, induced by applying a frequency-swept, oscillatory magnetic field. We present the expected experimental signatures of this probe, and show that they reflect the underlying Mott configuration for large lattice potential depth.

PACS 03.75.Kk -Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow PACS 67.85.De -Dynamic properties of condensates; excitations, and superfluid flow Abstract -Bose-Einstein condensate shells, while occurring in ultracold systems of coexisting phases and potentially within neutron stars, have yet to be realized in isolation on Earth due to the experimental challenge of overcoming gravitational sag. Motivated by the expected realization of hollow condensates by the space-based Cold Atomic Laboratory in microgravity conditions, we study a spherical condensate undergoing a topological change from a filled sphere to a hollow shell. We argue that the collective modes of the system show marked and robust signatures of this hollowing transition accompanied by the appearance of a new boundary. In particular, we demonstrate that the frequency spectrum of the breathing modes shows a pronounced depression as it evolves from the filled sphere limit to the hollowing transition. Furthermore, when the center of the system becomes hollow surface modes show a global restructuring of their spectrum due to the availability of a new, inner, surface for supporting density distortions. We pinpoint universal features of this topological transition as well as analyse the spectral evolution of collective modes in the experimentally relevant case of a bubble-trap.Quantum matter, when subject to transitions of a topological nature, undergoes fundamental changes in its properties [1]. Such transitions involve singular deformations of the underlying space inhabited by the system, be it real or abstract. For instance, the ripping action required to convert a sphere into a torus. In topological materials, which have recently gained prominent attention, matter can transform from being a trivial insulator to one having gapless surface states. The topological nature of the transition can be pinpointed through the calculation or measurement of an abstract Berry phase type global invariant associated with non-trivial winding, for instance, in momentum space [2]. Cold atomic systems, given their spectacular trapping and tuning capabilities, not only enable measuring such topological invariants [3-5], they offer a much more direct, real space version of a topological transition through purely changing physical geometry. As a pioneering instance, the realization of toroidal BoseEinstein condensates (BECs) [6,7] corresponds to a topo-(a) kuei.sun@utdallas.edu (b) clannert@smith.edu (c) smivish@illinois.edu logical structure characterized by a homotopy group that is not equivalent to that of a disk. Here we explore salient features associated with the hollowing out of a spherically filled BEC and subsequent formation of a closed, hollow shell. The filled and hollow BECs are topologically inequivalent in that they correspond to different second homotopy groups. In other words, unlike for the filled spherically symmetric BEC, a spherical surface within the hollow BEC that surrounds its center cannot be continuousl...

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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 87 Rb.