Physics of hollow Bose-Einstein condensates

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.Comment: 8 pages, 4 figure

Inelastic Neutron Scattering Signal from Deconfined Spinons in a Fractionalized Antiferromagnet

We calculate the contribution of deconfined spinons to inelastic neutron scattering (INS) in the fractionalized antiferromagnet (AF*), introduced elsewhere. We find that the presence of free spin-1/2 charge-less excitations leads to a continuum INS signal above the Néel gap. This signal is found above and in addition to the usual spin-1 magnon signal, which to lowest order is the same as in the more conventional confined antiferromagnet. We calculate the relative weights of these two signals and find that the spinons contribute to the longitudinal response, where the magnon signal is absent to lowest order. Possible higher-order effects of interactions between magnons and spinons in the AF* phase are also discussed

Static and dynamic properties of shell-shaped condensates

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.Comment: 26 pages, 13 figure

Quantum Confinement Transition in a D-Wave Superconductor

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

Critical Dynamics of Superconductors in the Charged Regime

The charged regime of the superconductor-metal transition was analyzed by applying a finite temperature critical dynamics. A transverse gage field coupling was applied to the superconducting order parameter. A new dynamic universality class characeterized by a finite fixed point ratio between the transport coefficients associated with the order parameter and gage fields was found by assuming relaxational dynamics for both the order parameter and gage fields within a renormalization group scheme. It was found that various features of the dynamic universality class of the charged superconductor appeared in measurable quantities

Thermodynamics in expanding shell-shaped Bose-Einstein condensates

Inspired by investigations of Bose-Einstein condensates (BECs) produced in the Cold Atom Laboratory (CAL) aboard the International Space Station, we present a study of thermodynamic properties of shell-shaped BECs. Within the context of a spherically symmetric bubble trap potential, we study the evolution of the system from small filled spheres to hollow, large, thin shells via the tuning of trap parameters. We analyze the bubble trap spectrum and states and track the distinct changes in spectra between radial and angular modes across the evolution. This separation of the excitation spectrum provides a basis for quantifying dimensional crossover to quasi-2D physics at a given temperature. Using the spectral data, for a range of trap parameters, we compute the critical temperature for a fixed number of particles to form a BEC. For a set of initial temperatures, we also evaluate the change in temperature that would occur in adiabatic expansion from small filled sphere to large thin shell were the trap to be dynamically tuned. We show that the system cools during this expansion but that the decrease in critical temperature occurs more rapidly, thus resulting in depletion of any initial condensate. We contrast our spectral methods with standard semiclassical treatments, which we find must be used with caution in the thin-shell limit. With regard to interactions, using energetic considerations and corroborated through Bogoliubov treatments, we demonstrate that they would be less important for thin shells due to reduced density but vortex physics would become more predominant. Finally, we apply our treatments to traps that realistically model CAL experiments and borrow from the thermodynamic insights found in the idealized bubble case during adiabatic expansion

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

Small-Network Approximations for Geometrically Frustrated Ising Systems

The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small correlation lengths in frustrated Ising systems, we develop a method for obtaining first approximations to the energetic properties of frustrated two-dimensional Ising systems using small networks of less than 30 spins. These small networks allow much faster numerical simulations, and more importantly, analytical evaluations of their properties are numerically tractable. We choose Ising systems on the triangular lattice, the kagome lattice, and the triangular kagome lattice as prototype systems and find small systems that can serve as good approximations to these prototype systems. Through comparisons between the properties of extended models and small systems, we develop a set of criteria for constructing small networks to approximate general infinite two-dimensional frustrated Ising systems. This method of using small networks provides a different and efficient way to obtain a first approximation to the properties of frustrated spin systems

Probing Condensate Order in Deep Optical Lattices

We study interacting bosons in optical lattices in the weak-tunneling regime in systems that exhibit the coexistence of Mott-insulating and condensed phases. We discuss the nature of the condensed ground state in this regime and the validity of the mean-field treatment thereof. We suggest two experimental signatures of condensate order in the system. (1) We analyze the hyperfine configuration of the system and propose a set of experimental parameters for observing radio-frequency spectra that would demonstrate the existence of the condensed phase between Mott-insulating phases. We derive the structure of the signal from the condensate in a typical trapped system, taking into account Goldstone excitations, and discuss its evolution as a function of temperature. (2) We study matter-wave interference patterns displayed by the system upon release from all confining potentials. We show that as the density profiles evolve very differently for the Mott-insulating phase and the condensed phase, they can be distinguished from one another when the two phases coexist