Session C3: Quantum Gases in Two Dimensions

Excitations and behavior of a trapped two component Bose Einstein Condensate

We present an analysis of the excitation spectrum for a two-component quasi-two-dimensional Bose-Einstein condensate (BEC). We study how excitations change character across the miscible to immiscible phase transition. We find that the bulk excitations are typical of a single-component BEC with the addition of interface bending excitations. We further study the characteristic behavior of the gas across the miscible to immiscible phase transition.   

Anderson localization in 2D using point-like disorder

Anderson localization is a general phenomenon that has been seen in a variety of media, and particularly in ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of localization in a two-dimensional geometry has been elusive. We show that a major cause of this difficulty is the relatively high percolation threshold of a speckle potential in 2D, resulting in strong classical localization, and propose instead a point-like disorder that can avoid this percolation limit. Required disorder strength in this potential is examined, going beyond the weak-scattering approximation, and realistic experimental setups that could observe this localization are discussed.   

Density Fluctuations in a 2D Bose gas near Feshbach resonance

Here we report our progress towards using the local fluctuations determined from the in-situ density profiles of a 2D gas to determine its local properties. This allows for a method to determine the distribution of temperature and chemical potential regardless of the geometry of the trapping potential. This technique will provide a generic probe to characterize non-equilibrium systems, and allow for a complete characterization of the transport phenomena. Near a Feshbach resonance, the density fluctuations may also offer new insight into the universal behavior of unitary Bose gas.   

Relaxation of Two-dimensional Turbulent Superflow and Vortex Pair Annihilation

We study relaxation dynamics of two-dimensional turbulent superflow in highly oblate Bose-Einstein condensates. Turbulent superflow is generated by moving a Gaussian repulsive laser beam in a trapped condensate and the relaxation dynamics is characterized by measuring the temporal evolution of the vortex number in the condensate. We observe non-exponential decay behavior of the vortex number. The initial fast decay is attributed to the vortex-anti-vortex pair annihilation at high vortex density, and furthermore, the vortex pair annihilation is directly demonstrated by observing a crescent-shape, density-depleted region in the condensate. We quantitatively investigate the pair annihilation rate for various sample conditions and present a simple model to explain our experimental results.   

Breakdown of scale invariance in a quasi-two-dimensional Bose gas due to the presence of the third dimension

In this presentation, we describe how the presence of the third dimension may break the scale invariance in a two-dimensional Bose gas in a pancake-shaped trap. From the two-dimensional perspective, the possibility of a weak spilling of the atomic density beyond the ground-state of the confinement alters the two-dimensional chemical potential; in turn, this correction no longer supports scale invariance. We compare experimental data with numerical and analytic perturbative results and find a good agreement.   

Investigating the Sliding Phase in Strongly and Randomly Coupled Quasi-2D Bose Gasses

Asymptotic analytical [Mohan et al 2010] functional RNG [Pekker et al 2010] and Monte Carlo [Laflorencie 2012] methods identified an anomalous Griffiths phase in the 3D XY model in the presence of disorder. A stack of cold 2D Bose gasses with random nearest neighbor inter-planar couplings should pass through two phase transitions as one increases temperature, first from a 3D superfluid to a stack of 2D superfluids, and then to a thermal state. We discuss our investigation of this intermediate phase in a stack of strongly coupled quasi-2D Rb 87 pancakes generated by a truly disordered 1D optical potential.   

Dynamics of Correlations in a quasi-2D Dipolar Bose gas

Experiments on highly magnetic atoms such as Dysprosium and Erbium have opened up the possibility of studying the non-equilibrium dynamics of gases with long range dipole-dipole interactions. Of particular relevance are questions such as: How do correlations evolve in a gas with long range interactions? Can quench dynamics provide clues to the underlying excitation spectrum of a long range interacting system? In this talk I will discuss how the evolution of the momentum distribution in a quasi-2D dipolar gas displays striking features related to the existence of rotons in the excitation spectrum. I will show how one can obtain the roton gap directly from the dynamics of the excited fraction of atoms, which can be readily probed in time-of-flight. I will also discuss how density-density correlations develop between uncorrelated regions in a dipolar system, finding that correlations spread much more slowly in a dipolar gas as compared to a non-dipolar gas.   

The 2D Bose gas in box potential(s)

In this talk, we will present our experiments with a 2D gas of bosons in box potentials with various geometries. The appearance of degeneracy in a 2D Bose gas is fundamentally different from the 3D case. We investigate the appearance of a bimodal distribution when the cloud is prepared in a flat bottom potential to test the relevance of the Berezinskii-Kosterlitz-Thouless mechanism with respect to the Bose-Einstein condensation mechanism. This measurement of degeneracy can then be confronted to the appearance of fringes when two similar systems interefere. Our technique also enables us to create various geometries for the clouds, helping to reveal vortices through interferometric measurement or short time-of-flight expansion.   

Pairing effects in the nondegenerate limit of the two-dimensional Fermi gas

I present results on the spectral function of a two-dimensional Fermi gas in the non-degenerate or high-temperature limit which are obtained by means of a quantum cluster expansion. Our findings are in good qualitative agreement with a recent experiment by Feld et al. [Nature (London) 480, 75 (2011)]. The spectral function displays two distinct branches, a particle branch and a bound-state branch, both of which have a quadratic dispersion. Interestingly, in the occupied part of the spectral function, the weight of the bound-state branch is shifted to higher frequencies with increasing momentum but bends backwards at high momentum. This shows that this ``back-bending'' cannot be taken as a phenomenological sign of a conjectured pseudogap phase but can be explained by bound-state pairing. I also show that the virial expansion gives expressions for the quasiparticle properties, the momentum distribution, and the radio-frequency spectrum that are in excellent agreement with exact universal results.   

Accurate quantum states for a 2D-dipole

Edge dislocations are crucial in understanding both mechanical and electrical transport in solid and are modeled as linear distributions of dipole moments. The calculation of the electronic spectrum for the two dimensional dipole, represented by the potential energy $V(r,\theta) = p \cos\theta/r$ has been the topic of several studies that show significant difficulties in obtaining accurate results. In this work we show that the source of these difficulties is a logarithmic contribution to the behavior of the wave function at the origin that was neglected by previous authors. By taking into account this non-analytic deviation of the solution of Schr\"odinger's equation superior results, with the expected rate of convergence, are obtained. This goal is accomplished by ``adapting" general algorithms for solving partial derivative differential equations to include the desired asymptotic behavior. We demonstrate this principle for the variational principle and finite difference methods.