quasi-2D Geometry Research Articles

Interatomic collisions in two-dimensional and quasi-two-dimensional confinements with spin-orbit coupling

We investigate the low-energy scattering and bound states of two two-component fermionic atoms in pure two-dimensional (2D) and quasi-2D confinements with Rashba spin-orbit coupling (SOC). We find that the SOC qualitatively changes the behavior of the 2D scattering amplitude in the low-energy limit. For quasi-2D systems we obtain the analytic expression for the effective-2D scattering amplitude and the algebraic equations for the two-atom bound state energy. Based on these results, we further derive the effective 2D interaction potential between two ultracold atoms in the quasi-2D confinement with Rashba SOC. These results are crucial for the control of the 2D effective physics in quasi-2D geometry via the confinement intensity and the atomic three-dimensional scattering length.

Influence of Particle Shape on Bending Rigidity of Colloidal Monolayer Membranes and Particle Deposition during Droplet Evaporation in Confined Geometries

We investigate the influence of particle shape on the bending rigidity of colloidal monolayer membranes (CMMs) and on evaporative processes associated with these membranes. Aqueous suspensions of colloidal particles are confined between glass plates and allowed to evaporate. Confinement creates ribbonlike air-water interfaces and facilitates measurement and characterization of CMM geometry during drying. Interestingly, interfacial buckling events occur during evaporation. Extension of the description of buckled elastic membranes to our quasi-2D geometry enables the determination of the ratio of CMM bending rigidity to its Young's modulus. Bending rigidity increases with increasing particle anisotropy, and particle deposition during evaporation is strongly affected by membrane elastic properties. During drying, spheres are deposited heterogeneously, but ellipsoids are not. Apparently, increased bending rigidity reduces contact line bending and pinning and induces uniform deposition of ellipsoids. Surprisingly, suspensions of spheres doped with a small number of ellipsoids are also deposited uniformly.

Segregation in quasi-two-dimensional granular systems

Segregation for two granular species is studied numerically in a vertically vibrated quasi-two-dimensional (quasi-2D) box. The height of the box is smaller than two particle diameters so that particles are limited to a submonolayer. Two cases are considered: grains that differ in their density but have equal size, and grains that have equal density but different diameters, while keeping the quasi-2D condition. It is observed that in both cases, for vibration frequencies beyond a certain threshold—which depends on the density or diameter ratios—segregation takes place in the lateral directions. In the quasi-2D geometry, gravity does not play a direct role in the in-plane dynamics and gravity does not point to the segregation directions; hence, several known segregation mechanisms that rely on gravity are discarded. The segregation we observe is dominated by a lack of equipartition between the two species; the light particles exert a larger pressure than the heavier ones, inducing the latter to form clusters. This energy difference in the horizontal direction is due to the existence of a fixed point characterized by vertical motion and hence vanishing horizontal energy. Heavier and bigger grains are more rapidly attracted to the fixed point and the perturbations are less efficient in taking them off the fixed point when compared to the lighter grains. As a consequence, heavier and bigger grains have less horizontal agitation than lighter ones. Although limited by finite size effects, the simulations suggest that the two cases we consider differ in the transition character: one is continuous and the other is discontinuous. In the cases where grains differ in mass on varying the control parameter, partial segregation is first observed, presenting many clusters of heavier particles. Eventually, a global cluster is formed with impurities; namely lighter particles are present inside. The transition looks continuous when characterized by several segregation order parameters. On the other hand, when grains differ in size, there is no partial segregation and the global cluster has a much smaller concentration of impurities. The segregation order parameters change discontinuously and metastability is observed.

Infiltration-mediated combustion in quasi-2D geometry: Stability of front propagation

The stability of infiltration combustion was explored by mathematical modeling under the assumption that the supply rate for gas reagent to the reaction zone is defined by the rate of chemical reaction, with account of changes in the product mass and thermophysical parameters of condensed components. Investigated were the wave structure, stability limits for steady combustion, and the loss of stability caused by 1D and 3D perturbations.

Bidisperse monolayers: Theory and computer simulations

We try to elucidate the microstructure formation in a bidisperse ferrofluid monolayer and understand in detail the difference brought by the geometrical constrains. The system under study consists of soft-sphere magnetic dipolar particles confined to a thin fluid layer. The positions of the particles are constraint to a 2D geometry, whereas the particle magnetic dipole moments are not fixed to the body systems, and are free to rotate in 3 dimensions, hence forming in what we call a quasi-2D geometry (q2D). Unlike the q2D monodisperse case studied in [1] we discover that the presence of small particles inhibit ring formation. Unlike the bidisperse system in bulk thoroughly investigated in [2], small particles can form clusters and can appear in various amounts in the clusters formed by large particles. Finally we come to the conclusion, that geometrical constraints play a crucial role in determining the ferrofluid microstructure, and thus, the direct extrapolation of experimental results obtained for q2D systems to the bulk magnetic fluids might be misleading.

Entanglement of two interacting bosons in a two-dimensional isotropic harmonic trap

We compute the pair entanglement between two interacting bosons in a two-dimensional (2D) isotropic harmonic trap. The interaction potential is modelled by a 2D regularized pseudopotential. By analytically decomposing the wave function into the single particle basis, we show the dependency of the pair entanglement on the scattering length. Our results turn out to be in good agreements with earlier results using a quasi-2D geometry.

Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid

We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz, and Thouless (BKT) transition temperature. By measuring the density profile after time of flight and the coherence length, we identify different states of the gas. We observe that the gas develops a bimodal distribution without long range order. In this regime, the gas presents a longer coherence length than the thermal cloud; it is quasicondensed but is not superfluid. Experimental evidence indicates that we also observe the superfluid transition (BKT transition). For a sufficiently long time of flight, we observe a trimodal distribution when the gas has developed a superfluid component.

Microstructure analysis of monodisperse ferrofluid monolayers: theory and simulation

We try to elucidate the microstructure formation in a monodisperse ferrofluid monolayer. The system under study consists of soft sphere magnetic dipolar particles confined to a thin fluid layer. The positions of the particles are constrained to a 2D geometry, whereas the particle magnetic dipole moments are not fixed to the body systems, and are free to rotate in 3 dimensions, hence forming in what we call a quasi-2D geometry. Using a combination of analytical density functional theory and molecular dynamics (MD) simulations, we find that for the studied range of parameters the majority of aggregates might be divided into two types: chains and rings. Their sizes and area fractions are strongly influenced by the geometrical constraints. We show that for quasi-2D systems the excluded area effects play one of the most important parts in the microstructure formation. The simulation technique and the theoretical model put forward in the present paper agree qualitatively with the results of recent in situ observations of the microstructures observed in ferrofluid monolayers [M. Klokkenberg, R. P. A. Dullens, W. K. Regel, B. H. Erné, A. P. Philipse, Phys. Rev. Lett., 2006, 96, 037203].

Finite-temperature properties of quasi-two-dimensional Bose-Einstein condensates

Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two-dimensional (quasi-2D) geometry. The quantum particles have short-range, $s$-wave interactions described by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interparticle interaction on the equilibrium properties such as the total energy, the density profile, and the superfluid fraction is discussed. We compare our accurate results with both the semiclassical approximation and the exact results of an ideal Bose gas. Our results show that for repulsive interactions (i) the minimum value of the aspect ratio, where the system starts to behave quasi-2D, increases as the two-body interaction strength increases; (ii) the superfluid fraction for a quasi-two-dimensionally Bose gas is distinctly different from that for both a quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true 3D system with increasing temperature, and shows a stronger dependence on the interaction strength; (iii) the superfluid fraction for a quasi-2D Bose gas lies well below the values calculated from the semiclassical approximation; and (iv) the Kosterlitz-Thouless transition temperature decreases as the strength of the interaction increases.

Nonclassical dimension-dependent kinetics of a photobleaching reaction in a focused laser beam “phototrap”

A focused laser beam acts as both a ``phototrap,'' bleaching fluorophore molecules that diffuse into the beam path, and as a confocal probe, detecting the excited, unbleached fluorophore molecules still present in the trap. With this focused laser beam, we observe anomalous asymptotic rate laws similar to those predicted for a diffusion-controlled elementary trapping reaction $A+T\ensuremath{\rightarrow}T$ in both one and two dimensions. One-dimensional diffusion-limited trapping kinetics are observed in capillaries with $10$ $\ensuremath{\mu}$m diameters, while two-dimensional (2D) diffusion limited trapping kinetics are observed with unstirred samples having a quasi-2D geometry. However, in the presence of stirring, the 2D samples exhibit the classical, constant trapping rate.