We discuss the line shape for an internal state transition for bosonic atoms confined as a one-dimensional gas, using a method by Haldane. Typical line shape is an edge singularity due to the absence of Bose-Einstein condensation in such systems.

Bose-Einstein condensates of sodium atoms have been prepared in optical and magnetic traps in which the energy-level spacing in one or two dimensions exceeds the interaction energy between atoms, realizing condensates of lower dimensionality. The crossover into two-dimensional and one-dimensional condensates was observed by a change in aspect ratio and by the release energy converging to a nonzero value when the number of trapped atoms was reduced.

We show that even in three dimensions an antiferromagnetic spin-1 Bose-Einstein condensate, which can, for instance, be created with ${}^{23}\mathrm{Na}$ atoms in an optical trap, has not only singular linelike vortex excitations, but also allows for singular pointlike topological excitations, i.e., monopoles similar to the ’t Hooft–Polyakov monopoles. We discuss the static and dynamic properties of these monopoles.

We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium ( ${}^{40}\mathrm{K}$), and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about ${0.5T}_F$. Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly coupled fermions to the Bose-Einstein condensation of strongly bound composite bosons.

Using ensembles of two, three, and four spheres immersed in a fermionic background we evaluate the (integrated) density of states and the Casimir energy. We thus infer that for sufficiently smooth objects, whose various geometric characteristic lengths are larger then the Fermi wave length one can use the simplest semiclassical approximation (the contribution due shortest periodic orbits only) to evaluate the Casimir energy. We also show that the Casimir energy for several objects can be represented fairly accurately as a sum of pairwise Casimir interactions between pairs of objects.

We investigate the ground states of weakly interacting bosons in a rotating trap as a function of the number of bosons, $N$, and the average number of vortices, $N_V$. We identify the filling fraction $\nu \equiv {N/N}_V$ as the parameter controlling the nature of these states. We present results indicating that, as a function of $\nu$, there is a zero temperature phase transition between a triangular vortex lattice phase, and strongly correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states.

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount $\Delta T_c\simeq {\mathrm{ca}}_{\mathrm{sc}}{n}^{1/3}{T}_0$ from the ideal gas result $T_0$, where $a_{\mathrm{sc}}$ is the scattering length, $n$ is the density, and $c$ is a pure number. There have been several different theoretical estimates for $c$. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) ${\phi }^4$ field theory in three dimensions—an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce nonuniversal quantities such as the critical temperature. We find $c=1.32\mathrm{}\pm 0.02$.

With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional $|\psi {|}^4$ theory (which includes quantum Bose gas). In terms of critical density, $n_c$, mass, $m$, interaction, $U$, and temperature, $T$, this shift is universal: $\Delta n_c\left(T\right){=-Cm}^3{T}^{2}U$, the constant $C$ found to be equal to $0.0140\pm 0.0005$. For quantum Bose gas with the scattering length $a$ this implies $\Delta T_c{/T}_c{=C}_0{\mathrm{an}}^{1/3}$, with $C_0=1.29\mathrm{}\pm 0.05$.

We show that the shift in the transition temperature of the dilute homogeneous Bose gas is nonanalytic in the scattering amplitude $a$. The first correction beyond the positive linear shift in $a$ is negative and of order $a^2\ln a$. This nonuniversal nonanalytic structure indicates how the discrepancies between numerical calculations at finite $a$ can be reconciled with calculations of the limit $a\to 0$, since the linearity is apparent only for anomalously small $a$.

We derive exact expressions for a number of aging functions that are scaling limits of nonequilibrium correlations, $R(t_w{,t}_w+t)$ as $t_w\to \infty$, ${t/t}_w\to \theta$, in the 1D homogenous $q$-state Potts model for all $q$ with $T=0\mathrm{}$ dynamics following a quench from $T=\infty$. One such quantity is $〈{\overrightarrow{\sigma }}_0\left(t_w\right)̇{\overrightarrow{\sigma }}_n(t_w+t)〉$ when $n/\sqrt{t_w}\to z$. Exact, closed-form expressions are also obtained when an interlude of $T=\infty$ dynamics occurs. Our derivations express the scaling limit via coalescing Brownian paths and a “Brownian space-time spanning tree,” which also yields other aging functions, such as the persistence probability of no spin flip at $0$ between $t_w$ and $t_w+t$.

We show that the superselection rule in the Galilean transformation, forbidding the superposition of states of different mass, in inconsistent with the nonrelativistic limit of the Lorentz transformation. We also point out that the extra Galilean phase is merely the residue of the “twin-paradox” effect, which does not vanish nonrelativistically. In general, there are phase effects due to proper time differences, and effects due to mass-energy equivalence, that do not vanish nonrelativistically but that are not handled adequately by the Galilean transformation.

We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.

We study the superfluid properties of (quasi) one-dimensional bosonic atom gases/liquids in traps with finite geometries in the presence of strong quantum fluctuations. Driving the condensate with a moving defect we find the nucleation rate for phase slips using instanton techniques. While phase slips are quenched in a ring resulting in a superfluid response, they proliferate in a tube geometry where we find Bloch oscillations in the chemical potential. These Bloch oscillations describe the individual tunneling of atoms through the defect and thus are a consequence of particle quantization.

The dynamics of a trapped Bose-condensed gas at finite temperatures is described by a generalized Gross-Pitaevskii equation for the condensate order parameter and a semiclassical kinetic equation for the thermal cloud, solved using $N$-body simulations. The two components are coupled by mean fields as well as collisional processes that transfer atoms between the two. We use this scheme to investigate scissors modes in anisotropic traps as a function of temperature. Frequency shifts and damping rates of the condensate mode are extracted, and are found to be in good agreement with recent experiments.

In this Letter, the problem of the existence of a state localized on a weak short-range attractive potential in the presence of dissipation is considered. It is shown that, contrary to the pure quantum case, a localized state is produced in any number of dimensions, while in low dimensions dissipation leads to much stronger localization. The results have physical implications for the dissipative dynamics of objects such as heavy particles in Fermi liquids and for superconductivity in high- $T_c$ materials.

We report the observation of coexisting Bose-Einstein condensate (BEC) and Fermi gas in a magnetic trap. With a very small fraction of thermal atoms, the ${}^7\mathrm{Li}$ condensate is quasipure and in thermal contact with a ${}^6\mathrm{Li}$ Fermi gas. The lowest common temperature is $0.28\mu \mathrm{K}\simeq 0.2\left(1\right)T_{\mathrm{C}}=0.2\mathrm{}\left(1\right)T_{\mathrm{F}}$ where $T_{\mathrm{C}}$ is the BEC critical temperature and $T_{\mathrm{F}}$ the Fermi temperature. The ${}^7\mathrm{Li}$ condensate has a one-dimensional character.

We study spin correlations in Bose-Einstein condensates of spin 1 bosons with scatterings dominated by a total spin equal $2$ channel. We show that the low energy spin dynamics in the system can be mapped into an $o\left(n\right)$ nonlinear sigma model. $n=3\mathrm{}$ at the zero magnetic field limit and $n=2\mathrm{}$ in the presence of weak magnetic fields. In an ordered phase, the ground state has a discrete $Z_2$ symmetry and is degenerate under the group $\left[U\right(1)\times S^{n-1\mathrm{}}]{/Z}_2$. We explore consequences of the discrete symmetry and propose some measurements to probe it.

We have observed phase singularities due to vortex excitation in Bose-Einstein condensates. Vortices were created by moving a laser beam through a condensate. They were observed as dislocations in the interference fringes formed by the stirred condensate and a second unperturbed condensate. The velocity dependence for vortex excitation and the time scale for re-establishing a uniform phase across the condensate were determined.

The nearest neighbor contacts between the two halves of an $N$-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for $N\to \infty$ they are strictly finite in number but their radius of gyration $R_c$ is power law distributed $\propto R_c^{-\tau }$, where $\tau >1\mathrm{}$ is a novel exponent characterizing universal behavior. A continuum of diverging length scales is associated with the $R_c$ distribution. A possibly superuniversal $\tau =2\mathrm{}$ is also expected for the contacts of a self-avoiding or random walk with a confining wall.

Off-diagonal geometric phases acquired by an evolution of a $1/2$-spin system have been observed by means of a polarized neutron interferometer. We have successfully measured the off-diagonal phase for noncyclic evolutions even when the diagonal geometric phase is undefined. Our data confirm theoretical predictions and the results illustrate the significance of the off-diagonal phase.