S. Gautam

Critical temperature for Bose-Einstein condensation in quartic potentials

Abstract.The quartic confining potential has emerged as a key ingredient to obtain fast rotating vortices in BEC as well as observation of quantum phase transitions in optical lattices. We calculate the critical temperature Tc of bosons at which normal to BEC transition occurs for the quartic confining potential. Further more, we evaluate the effect of finite particle number on Tc and find that ΔTc/Tc is larger in quartic potential as compared to quadratic potential for number of particles <105. Interestingly, the situation is reversed if the number of particles is

Ground state geometry of binary condensates in axisymmetric traps

\gtrsim

Phase separation of binary condensates in harmonic and lattice potentials

105.

Goldstone modes and bifurcations in phase-separated binary condensates at finite temperature

We show that the ground state interface geometry of binary condensates in the phase-separated regime undergoes a smooth transition from planar to ellipsoidal to cylindrical geometry. This occurs for the condensates with repulsive interactions as the trapping potential is changed from prolate to oblate. The correct ground state geometry emerges when the interface energy is included in the energy minimization, whereas energy minimization based on the Thomas–Fermi approximation gives incorrect geometry. The planar and cylindrical interface geometries have less interface area and minimize the interface energy. These are the preferred ground states in the cigar- and pan-cake-shaped trap configurations.

Scattering length for fermionic alkali atoms

We propose a modified Gaussian ansatz to study binary condensates, trapped in harmonic and optical lattice potentials, both in miscible and immiscible domains. The ansatz is an apt one as it leads to a smooth transition from miscible to immiscible domains without any a priori assumptions. In optical lattice potentials, we analyse the squeezing of the density profiles due to the increase in the depth of the optical lattice potential. For this we develop a model with three potential wells, and define the relationship between the lattice depth and profile of the condensate.Vortex dipoles are generated when an obstacle moves through a superfluid. In case of phase-separated binary condensates, with appropriate interaction parameters in pan-cake shaped traps, we show that coreless vortex dipoles are created when a Gaussian obstacle beam traverses across them above a critical speed. As the obstacle passes through the inner component, it carries along a bubble of the outer component. Using Thomas-Fermi approximation, we show that phase-separated binary condensates can either support vortices with empty or filled cores. For time dependent obstacle potentials, ramped down in the present case, relative energy scales of the system influence the dynamical evolution of the binary condensate.

Finite-temperature dynamics of vortices in Bose-Einstein condensates

We show that the third Goldstone mode, which emerges in binary condensates at phase separation, persists to higher interspecies interaction for density profiles where one component is surrounded on both sides by the other component. This is not the case with symmetry-broken density profiles where one species is entirely to the left and the other is entirely to the right. We, then, use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution at T not equal 0 and demonstrate the existence of mode bifurcation near the critical temperature. The Kohn mode, however, exhibits deviation from the natural frequency at finite temperatures after the phase separation. This is due to the exclusion of the noncondensate atoms in the dynamics.

Coreless vortex dipoles and trapped droplets in phase-separated binary condensates

We have calculated the p-wave phase shifts and scattering length of Li. For this we solve the p partial wave Schrödinger equation and analyze the validity of adopting the semiclassical solution to evaluate the constant factors in the solution. Unlike in the s wave case, the semiclassical solution does not provide unique value of the constants. We suggest an approximate analytic solution, which provides reliable results in special cases. Further more, we also use the variable phase method to evaluate the phase shifts. The p-wave scattering lengths of Cs and Cs are calculated to validate the schemes followed. Based on our calculations, the value of the p wave scattering length of Li is −45ao.

Position swapping and pinching in Bose-Fermi mixtures with two-color optical Feshbach resonances

We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross-Pitaevskii equation, which is the Langevin equation for the Bose-Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.

Vortex reconnections between coreless vortices in binary condensates

Vortex dipoles are generated when an obstacle moves through a superfluid above a critical speed. In the case of phase-separated binary condensates, with appropriate interaction parameters in pancake-shaped traps, we show that coreless vortex dipoles are created when a Gaussian obstacle beam traverses across them above a critical speed. As the obstacle passes through the inner component, it carries along a droplet of the outer component. Using the Thomas–Fermi approximation, we show that phase-separated binary condensates can either support vortices with empty or filled cores.

Anisotropic merging and splitting of dipolar Bose-Einstein condensates

We examine the density profiles of the quantum degenerate Bose-Fermi mixture of