arXiv subjects

Mehmet Özgür Oktel

Publications and source records attributed to Mehmet Özgür Oktel.

3 recordsLinked to original sources

arXiv2026

Landau Levels on the Surface of a Cube

We study the quantum mechanics of a charged particle confined to the surface of a cube enclosing a magnetic monopole. The magnetic field is chosen to have a constant magnitude on each face and to point along the outward normal, preserving the rotational symmetry of the cube. We formulate the continuum problem using two gauge patches on the cube surface and show that consistency of the wavefunction gives the Dirac quantization condition. Since an explicit vector potential does not remain invariant under ordinary rotations, we construct gauge-modified rotation operators and use them to classify the eigenstates. Even monopole charges are described by the irreducible representations of the cubic rotation group O, while odd monopole charges require the spinorial representations of the binary octahedral group 2O. We compute the spectrum with a gauge-covariant finite-difference discretization and find Landau-level-like manifolds whose degeneracies are split by the discrete cubic symmetry. We also study the corresponding tight-binding Hofstadter problem on the discretized cube. The resulting spectrum contains the usual magnetic subband structure together with additional gap states localized near the cube corners.

quant-ph↗

arXiv2026

Variational Approach to the Snake Instability of a Bose-Einstein Condensate Soliton

Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long-lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.

cond-mat.quant-gas↗

arXiv2026

Generation of squeezed optical states via stored classical pulses in a Bose gas

We propose and analyze a scheme to generate squeezed light by storing a classical probe pulse in a Bose--Einstein condensate (BEC) and exploiting the nonlinear evolution caused by atom--atom collisions during the storage time. A $Λ$-type optical memory interface maps a chosen temporal probe mode onto a single phase-matched collective spin wave; for a coherent input this prepares a tunable coherent spin state of a two-component BEC, with its initial spin orientation set by the stored mean excitation number and the phase relation between the probe and control fields. Collisional interactions during storage then implement one-axis-twisting dynamics and generate spin squeezing in the atomic ensemble. We account for realistic loss and finite memory and retrieval efficiencies, and model readout as a single-mode beam-splitter mapping that transfers the atomic quadrature squeezing onto a propagating optical mode. We identify optimal storage times and predict that, under realistic conditions, several dB of squeezing can be transferred to the retrieved light.

quant-ph↗