Quantum systems engineering

Abstract:

We numerically study the behaviour of collapsing and exploding condensates using the parameters of the experiments by Donley et al (2001 Nature 412 295). Our studies are based on a full three-dimensional numerical solution of the Gross-Pitaevskii equation (GPE) including three-body loss. We determine the three-body loss rate from the number of remnant condensate atoms and collapse times, and obtain only one possible value which fits with the experimental results. We then study the formation of jet atoms by interrupting the collapse, and find very good agreement with the experiment. Furthermore, we investigate the sensitivity of the jets to the initial conditions. According to our analysis, the dynamics of the burst atoms is not described by the GPE with three-body loss incorporated.

Abstract:

Dyanamics of the superfluid to Mott-insulator transition in one dimensional lattice was studied numerically. The applicability of time-evolving block decimation (TEBD) algorithm to Bose-Hubbard model was also demonstrated. The results suggest that for slow ramping of the lattice depth the SF growth is consistent with single atom hoping as might naively be expected. It was also suggested that for very rapid ramping of the lattice depth we find that the SF growth is much greater than can be explained by this mechanism.

Abstract:

We study a string of neutral atoms with nearest neighbor interaction in a 1D beam splitter configuration, where the longitudinal motion is controlled by a moving optical lattice potential. The dynamics of the atoms crossing the beam splitter maps to a 1D spin model with controllable time dependent parameters, which allows the creation of maximally entangled states of atoms by crossing a quantum phase transition. Furthermore, we show that this system realizes protected quantum memory, and we discuss the implementation of one- and two-qubit gates in this setup.

Abstract:

We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other, thereby causing hopping between the different columns. By adjusting the laser parameters appropriately we can induce a non-vanishing phase of particles moving along a closed path on the lattice. This phase is proportional to the enclosed area and we thus simulate a magnetic flux through the lattice. This set-up is described by a Hamiltonian identical to the one for electrons on a lattice subject to a magnetic field and thus allows us to study this equivalent situation under very well defined controllable conditions. We consider the limiting case of huge magnetic fields-which is not experimentally accessible for electrons in metals-where a fractal band structure, the Hofstadter butterfly, characterizes the system.

Abstract:

We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d Gross-Pitaevskii equation and obtain a four-parameter model. Identifying 'extreme parameter regimes', the model is accessible to analytical perturbation theory, which justifies formal procedures well known in the physical literature: reduction to 2d and 1d GPEs, approximation of ground state solutions of the GPE and geometrical optics approximations. Then we use a time-splitting spectral method to discretize the time-dependent GPE. Again, perturbation theory is used to understand the discretization scheme and to choose the spatial/temporal grid in dependence of the perturbation parameter. Extensive numerical examples in 1d, 2d and 3d for weak/strong interactions, defocusing/focusing nonlinearity, and zero/nonzero initial phase data are presented to demonstrate the power of the numerical method and to discuss the physics of Bose-Einstein condensation. © 2003 Elsevier Science B.V. All rights reserved.