arXiv subjects

U. Al Khawaja

Publications and source records attributed to U. Al Khawaja.

51 records · Page 3Linked to original sources

arXiv2006

Vortex Dynamics Near the Surface of a Bose-Einstein Condensate

The center-of-mass dynamics of a vortex in the surface region of a Bose-Einstein condensate is investigated both analytically using a variational calculation and numerically by solving the time-dependent Gross-Pitaevskii equation. We find, in agreement with previous works, that away from the Thomas-Fermi surface, the vortex moves parallel to the surface of the condensate with a constant velocity. We obtain an expression for this velocity in terms of the distance of the vortex core from the Thomas-Fermi surface that fits accurately with the numerical results. We find also that, coupled to its motion parallel to the surface, the vortex oscillates along the direction normal to the surface around a minimum point of an effective potential.

cond-mat.stat-mech↗

arXiv2005

Feshbach resonances in an optical lattice

We present the theory for ultracold atomic gases in an optical lattice near a Feshbach resonance. In the single-band approximation the theory describes atoms and molecules which can both tunnel through the lattice. Moreover, an avoided crossing between the two-atom and the molecular states occurs at every site. We determine the microscopic parameters of the generalized Hubbard model that describes this physics, using the experimentally known parameters of the Feshbach resonance in the absence of the optical lattice. As an application we also calculate the zero-temperature phase diagram of an atomic Bose gas in an optical lattice.

cond-mat.stat-mech↗

arXiv2003

Vortex Stability Near the Surface of a Bose-Einstein Condensate

We investigate energetic stability of vortices near the surface of a Bose-Einstein condensate. From an energy functional of a rotating Bose-Einstein condensate, written in terms of variables local to the surface, and a suitable trial wavefunction we calculate the energy of a moving vortex. The energetic stability of the vortex is investigated in terms of the rotation frequency of the confining potential. The critical frequency at which the vortices enter the condensate is calculated and compared with the experiment where a reasonable agreement is obtained.

cond-mat.stat-mech↗

arXiv2003

Dimensional and Temperature Crossover in Trapped Bose Gases

We investigate the long-range phase coherence of homogeneous and trapped Bose gases as a function of the geometry of the trap, the temperature, and the mean-field interactions in the weakly interacting limit. We explicitly take into account the (quasi)condensate depletion due to quantum and thermal fluctuations, i.e., we include the effects of both phase and density fluctuations. In particular, we determine the phase diagram of the gas by calculating the off-diagonal one-particle density matrix and discuss the various crossovers that occur in this phase diagram and the feasibility of their experimental observation in trapped Bose gases.

cond-mat↗

arXiv2002

Erratum: Low-dimensional Bose gases (PRA 66, 013615 (2002))

We discuss some subtleties regarding the depletion of the condensate in homogeneous two and three-dimensional Bose at zero temperature. We find agreement with the results of Popov theory. Other results in the paper cond-mat/0202085 are not affected by this.

cond-mat↗

arXiv2002

Bright soliton trains of trapped Bose-Einstein condensates

We variationally determine the dynamics of bright soliton trains composed of harmonically trapped Bose-Einstein condensates with attractive interatomic interactions. In particular, we obtain the interaction potential between two solitons. We also discuss the formation of soliton trains due to the quantum mechanical phase fluctuations of a one-dimensional condensate.

cond-mat↗

arXiv2002

Low-dimensional Bose gases

We present an improved many-body T-matrix theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. The resulting mean-field theory is valid in arbitrary dimensions and able to describe the low-temperature crossover between three, two and one-dimensional Bose gases. When applied to a degenerate two-dimensional atomic hydrogen gas, we obtain a reduction of the three-body recombination rate which compares favorably with experiment. Supplementing the mean-field theory with a renormalization-group approach to treat the critical fluctuations, we also incorporate into the theory the Kosterlitz-Thouless transition that occurs in a homogeneous Bose gas in two dimensions. In particular, we calculate the critical conditions for the Kosterlitz-Thouless phase transition as a function of the microscopic parameters of the theory. The proposed theory is further applied to a trapped one-dimensional Bose gas, where we find good agreement with exact numerical results obtained by solving a nonlinear Langevin field equation.

cond-mat↗

arXiv2002

Phase fluctuations in atomic Bose gases

We improve on the Popov theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. As a result, the theory becomes valid in arbitrary dimensions and is able to describe the low-temperature crossover between three, two and one-dimensional Bose gases, which is currently being explored experimentally. We consider both homogeneous and trapped Bose gases.

cond-mat↗

arXiv2001

Nonlinear coupling between scissors modes of a Bose-Einstein condensate

We explore the nonlinear coupling of the three scissors modes of an anisotropic Bose-Einstein condensate. We show that only when the frequency of one of the scissors modes is twice the frequency of another scissors mode, these two modes can be resonantly coupled and a down conversion can occur. We perform the calculation variationally using a gaussian trial wave function. This enables us to obtain simple analytical results that describe the oscillation and resonance behaviour of the two coupled modes.

cond-mat↗

arXiv2001

Skyrmion Physics in Bose-Einstein Ferromagnets

We show that a ferromagnetic Bose-Einstein condensate has not only line-like vortex excitations, but in general also allows for point-like topological excitations, i.e., skyrmions. We discuss the thermodynamic stability and the dynamic properties of these skyrmions for both spin-1/2 and ferromagnetic spin-1 Bose gases.

cond-mat↗

arXiv2001

't Hooft-Polyakov Monopoles in an Antiferromagnetic Bose-Einstein Condensate

We show that an antiferromagnetic spin-1 Bose-Einstein condensate, which can for instance be created with Na-23 atoms in an optical trap, has not only singular line-like vortex excitations, but also allows for singular point-like topological excitations, i.e., 't Hooft-Polyakov monopoles. We discuss the static and dynamic properties ofthese monopoles.

cond-mat.stat-mech↗

arXiv2000

Skyrmions in a ferromagnetic Bose-Einstein condensate

The recently realized multicomponent Bose-Einstein condensates provide opportunities to explore the rich physics brought about by the spin degrees of freedom. For instance, we can study spin waves and phase separation, macroscopic quantum tunneling, Rabi oscillations, the coupling between spin gradients and superfluid flow, squeezed spin states, vortices and other topological excitations. Theoretically, there have been already some studies of the ground-state properties of these systems and their line-like vortex excitations. In analogy with nuclear physics or the quantum Hall effect, we explore here the possibility of observing point-like topological excitations or skyrmions. These are nontrivial spin textures that in principle can exist in a spinor Bose-Einstein condensate. In particular, we investigate the stability of skyrmions in a fictitious spin-1/2 condensate of Rb87 atoms. We find that skyrmions can exist in this case only as a metastable state, but with a lifetime of the order of, or even longer than, the typical lifetime of the condensate itself. In addition to determining the size and the lifetime of the skyrmion, we also present its spin texture and finally briefly consider its dynamical properties.

cond-mat↗

arXiv2000

Kinetic Theory of Collective Excitations and Damping in Bose-Einstein Condensed Gases

We calculate the frequencies and damping rates of the low-lying collective modes of a Bose-Einstein condensed gas at nonzero temperature. We use a complex nonlinear Schrödinger equation to determine the dynamics of the condensate atoms, and couple it to a Boltzmann equation for the noncondensate atoms. In this manner we take into account both collisions between noncondensate-noncondensate and condensate-noncondensate atoms. We solve the linear response of these equations, using a time-dependent gaussian trial function for the condensate wave function and a truncated power expansion for the deviation function of the thermal cloud. As a result, our calculation turns out to be characterized by two dimensionless parameters proportional to the noncondensate-noncondensate and condensate-noncondensate mean collision times. We find in general quite good agreement with experiment, both for the frequencies and damping of the collective modes.

cond-mat↗

arXiv1999

Kinetic Theory of Collective Modes in Atomic Clouds above the Bose-Einstein Transition Temperature

We calculate frequencies and damping rates of the lowest collective modes of a dilute Bose gas confined in an anisotropic trapping potential above the Bose-Einstein transition temperature. From the Boltzmann equation with a simplified collision integral we derive a general dispersion relation that interpolates between the collisionless and hydrodynamic regimes. In the case of axially symmetric traps we obtain explicit expressions for the frequencies and damping rates of the lowest modes in terms of a phenomenological collision time. Our results are compared with microscopic calculations and experiments.

cond-mat↗

arXiv1999

The Surface of a Bose-Einstein Condensed Atomic Cloud

We investigate the structure and collective modes of a planar surface of a trapped Bose-Einstein condensed gas at zero temperature. In the long-wavelength limit we find a mode similar to the gravity wave on the surface of a fluid with the frequency $ω$ and the wavenumber $q$ related by $ω^2=Fq/m$. Here $F$ is the force due to the confining potential at the surface and $m$ is the particle mass. At shorter wavelengths we use a variational approach and find corrections to $ω^2$ of order $q^4 \ln{q}$. We demonstrate the usefulness of the concept of an effective surface tension for describing both static and dynamic properties of condensed atomic clouds.

cond-mat↗