Controlling quasiparticle excitations in a trapped Bose-Einstein condensate

We describe an approach to quantum control of the quasiparticle excitations in a trapped Bose-Einstein condensate based on adiabatic and diabatic changes in the trap anisotropy. We describe our approach in the context of the Landau-Zener transition at the avoided crossings in the quasiparticle excitation spectrum. We find also that there can be population oscillation between different modes at the specific aspect ratios of the trapping potential at which the mode energies are almost degenerate. These effects may have implications in the expansion of an excited condensate as well as the dynamics of a moving condensate in an atomic waveguide with a varying width.

Figure 1

(Color online) Energy spectrum of hydrodynamic modes of the BEC in a strong trap potential along the $z$ axis with respect to the aspect ratio $\lambda ={\omega }_y∕{\omega }_x$. Each spectral line is given a set of quantum numbers $(n_x,n_y)$ corresponding to its slope and the intercept at the energy axis. In the circle is the avoided crossing between the (10, 0) and the (2, 2) modes. The excitation frequency $\omega$ is in the unit of ${\omega }_x$.

Figure 2

(Color online) Change in the density fluctuation $n^{\prime }$ for the adiabatic states along the lower spectral line associated with the avoided crossing in the circle drawn into Fig. 1.

Figure 3

Distribution function in the frequency space for each value of $\lambda$ while $\lambda$ increases from 3.1 to 3.5 (a) adiabatically $(\dot{\lambda }=0.001)$ and (c) diabatically $(\dot{\lambda }=0.1)$; (b) is for the intermediate case $(\dot{\lambda }=0.01)$. The excitation frequency $\omega$ is in the unit of ${\omega }_x$.

Figure 4

(a) The population growth of the (10, 0) mode while the ground state of BEC is driven by $V_{\mathrm{dr}}\left(t\right)\sim \sin \left(\omega t\right)$. The other mode (2, 2) is clearly suppressed, and (b) the follow-up population oscillation between the (10, 0) and the (2, 2) modes near the avoided level crossing.

Figure 5

Schematic diagram of an avoided crossing. ${\varphi }_i$ indicate asymptotic shape eigenstates and ${\chi }_i$ exact energy eigenstates.