Visualization of Dimensional Effects in Collective Excitations of Optically Trapped Quasi-Two-Dimensional Bose Gases

We analyze the macroscopic dynamics of a Bose gas axially confined in an optical lattice with a superimposed harmonic trap, taking into account weak tunneling effect. Our results show that upon transition to the quasi-two-dimensional (2D) regime of the trapped gas, the 3D equation of state and equilibrium density profile acquire corrections from 2D many-body effects. The corresponding frequency shift in the transverse breathing mode is accessible within current facilities, suggesting a direct observation of dimensional effects. Comparisons with other relevant effects are also presented.Comment: 4 pages, 1 figur

Noisy Demkov-Kunike model

The Demkov-Kunike (DK) model, in which the Rabi coupling and the on-site detuning depend on time as $J~\text{sech}(t/T)$ and $\Delta_0+\Delta_1\tanh(t/T)$ respectively, provides one of the most general forms of an exactly solvable two-state quantum model. Thus it offers a paradigm for studying the coherent manipulations of the quantum state of a qubit. However, the exploration of the noisy DK model is still lacking. Here, we study the DK model with $J\rightarrow J_{\text{noisy}}(t)$ in the presence of colored Markovian noise sources, as exemplified by the telegraph noise and Gaussian noise. We analytically obtain the exact solutions for the survival probability $Q^{noisy}_{DK}$ of finding the system remained in the initial state. For the fast telegraph noise, surprisingly, we find parameter regimes where the $Q^{noisy}_{DK}$ is suppressed rather than being enhanced by noise, which can be understood through the quantum Zeno effect. For the slow Gaussian noise, we find the noise always leads to an enhanced $Q^{noisy}_{DK}$, due to the absorption of the noise quanta across the gap. Our work complements the studies of the noisy Landau-Zener model. It also offers a new perspective for the control of two-level quantum systems.Comment: 7 pages, 8 figure