Browsing by Subject "Vortex lattice"

Now showing 1 - 5 of 5

Open Access
Photonic band gap via quantum coherence in vortex lattices of Bose-Einstein condensates
(The American Physical Society, 2005) Müstecaplioǧlu, O. E.; Oktel, M. Ö.
We investigate the optical response of an atomic Bose-Einstein condensate with a vortex lattice. We find that it is possible for the vortex lattice to act as a photonic crystal and create photonic band gaps, by enhancing the refractive index of the condensate via a quantum coherent scheme. If high enough index contrast between the vortex core and the atomic sample is achieved, a photonic band gap arises depending on the healing length and the lattice spacing. A wide range of experimentally accessible parameters are examined and band gaps in the visible region of the electromagnetic spectrum are found. We also show how directional band gaps can be used to directly measure the rotation frequency of the condensate.
Open Access
Quantum gases in rotating optical lattices
(2010) Umucalılar, Rifat Onur
The thesis is structured into two main parts so as to cover bosons and fermions in rotating optical lattices separately. In the first part, after a brief introduction to ultracold atoms in optical lattices, we review the single-particle physics for the lowest (s) band of a periodic potential under an artificial magnetic field created by rotation. Next, we discuss rotational effects on the first excited (p) band of the lattice, extending the methods available for the lowest band. We conclude the first part with a discussion of many-body physics in rotating lattice systems using a mean-field approach and investigate how the transition boundary between superfluid and Mott insulator phases is affected by the single-particle spectrum. In this context, we also examine a possible coexistent phase of Mott insulator and bosonic fractional quantum Hall states, appearing for certain system parameters near the Mott insulator lobes in the phase diagram. The second part starts with the proposal of a realization and detection scheme for the so-called topological Hofstadter insulator, which basically reveals the single-particle spectrum discussed before. The scheme depends on a measurement of the density profile for noninteracting fermions in a rotating optical lattice with a superimposed harmonic trapping potential. This method also allows one to measure the quantized Hall conductance, a feature which appears when the Fermi energy lies in an energy gap of the lattice potential. Finally, we explore the Bardeen-Cooper-Schrieffer type of pairing of fermionic atoms in optical lattices under an artificial magnetic field by paying special attention to single-particle degeneracies and present our results for the vortex lattice structure of the paired fermionic superfluid phase.
Open Access
Refractive index-enhanced vortex lattices
(SPIE, 2005) Müstecaplıoǧlu, Ö. E.; Öktel, M. Özgür
Light propagation through vortex matter in atomic Bose-Einstein condensates is examined. It is shown that vortex matter can be used as a photonic crystal by a refractive index enhancement scheme. Band structure of the vortex lattice is numerically calculated. Index enhanced vortex matter is shown to exhibit large refractive index contrast with the dilute thermal gas background in the vortex core. Depending on the depth of the index contrast full or directional photonic band gaps are found in the band structure. Experimental parameters required to generate band gaps in the visible region of the electromagnetic spectrum are calculated.
Open Access
Tkachenko modes of the square vortex lattice in a two-component Bose-Einstein condensate
(2006) Keçeli, Murat; Öktel, M. Özgür
We study Tkachenko modes of the square vortex lattice of a two-component Bose-Einstein condensate (BEC) in the mean-field quantum Hall regime, considering the coupling of these modes with density excitations. We derive the hydrodynamic equations and obtain the dispersion relations of the excitation modes. We find that there are two types of excitations, gapped inertial modes and gapless Tkachenko modes. These modes have two branches which we call acoustic and optical modes in analogy with phonons. The former has quadratic while the latter has linear wave-number dependence in both inertial and Tkachenko modes. Acoustic Tkachenko mode is found to be anisotropic while the other three modes are isotropic. The anisotropy of the acoustic Tkachenko mode reflects the four-fold symmetry of the square lattice.
Open Access
A variational approech to stationary and rotating Bose-Einstein condensates
(2006) Keçeli, Murat
After the experimental demonstration of Bose-Einstein condensation (BEC) in alkali gases [6, 7, 18], the number of theoretical and experimental papers on ultracold atomic physics increased enormously [48]. BEC experiments provide a way to manipulate quantum many-body systems, and measure their properties precisely. Although the theory of BEC is simpler compared to other many-body systems due to strong correlation, a fully analytical treatment is generally not possible. Therefore, variational methods, which give approximate analytical solutions, are widely used. With this motivation, in this thesis we study on BEC in stationary and rotating regimes using variational methods. All the atoms in the condensate can be described with a single wave function, and in the dilute regime this wave function satisfies a single nonlinear equation (the Gross-Pitaevskii equation) which resembles the nonlinear Schr¨odinger equation in nonlinear optics. A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser [41, 43] having a similar behavior in the limiting cases of nonlinearity with ground state density profile of BECs, is used as the trial wave function to solve the Gross-Pitaevskii equation with variational principle for a wide range of the interaction parameter. The simple form of the ansatz allowed us to modify it for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground state wave function and energy are in very good agreement with the analytical solutions in the limiting cases of interaction and numerical solutions for the intermediate regime. In the second part, we consider a rapidly rotating two-component BoseEinstein condensate containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to the calculation the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long-wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second-order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first-order and while one of them is accompanied by the softening of an optical mode, the other does not have any dramatic effect on the Tkachenko spectrum. We also find an instability of the vortex lattice when the intercomponent repulsion becomes stronger than the repulsion within the components.