Gravity-induced Wannier-Stark ladder in an optical lattice

We discuss the dynamics of ultracold atoms in an optical potential accelerated by gravity. The positions and widths of the Wannier-Stark ladder of resonances are obtained as metastable states. The metastable Wannier-Bloch states oscillate in a single band with the Bloch period. The width of the resonance gives the rate transition to the continuum.Comment: 5 pages + 8 eps figures, submitted to Phys. Rev.

Damped Bloch oscillations of cold atoms in optical lattices

The paper studies Bloch oscillations of cold neutral atoms in the optical lattice. The effect of spontaneous emission on the dynamics of the system is analyzed both analytically and numerically. The spontaneous emission is shown to cause (i) the decay of Bloch oscillations with the decrement given by the rate of spontaneous emission and (ii) the diffusive spreading of the atoms with a diffusion coefficient depending on {\em both} the rate of spontaneous emission and the Bloch frequency.Comment: 10 pages, 8 figure

Theory of nonlinear Landau-Zener tunneling

A nonlinear Landau-Zener model was proposed recently to describe, among a number of applications, the nonadiabatic transition of a Bose-Einstein condensate between Bloch bands. Numerical analysis revealed a striking phenomenon that tunneling occurs even in the adiabatic limit as the nonlinear parameter $C$ is above a critical value equal to the gap $V$ of avoided crossing of the two levels. In this paper, we present analytical results that give quantitative account of the breakdown of adiabaticity by mapping this quantum nonlinear model into a classical Josephson Hamiltonian. In the critical region, we find a power-law scaling of the nonadiabatic transition probability as a function of $C/V-1$ and $\alpha$, the crossing rate of the energy levels. In the subcritical regime, the transition probability still follows an exponential law but with the exponent changed by the nonlinear effect. For $C/V>>1$, we find a near unit probability for the transition between the adiabatic levels for all values of the crossing rate.Comment: 9 figure

Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis $-\infty<E<\infty$ instead of being bounded from below $0\leq E <\infty$ (``Fermi's approximation''). Then the Fourier transform of the extended Lorentzian becomes the exponential, but only for times $t\geq 0$, a time asymmetry which is in conflict with the unitary group time evolution of standard quantum mechanics. Extending the Fourier transform from distributions to generalized vectors, we are led to Gamow kets, which possess a Lorentzian energy distribution with $-\infty<E<\infty$ and have exponential time evolution for $t\geq t_0 =0$ only. This leads to probability predictions that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.

Squeezing of Atoms in a Pulsed Optical Lattice

We study the process of squeezing of an ensemble of cold atoms in a pulsed optical lattice. The problem is treated both classically and quantum-mechanically under various thermal conditions. We show that a dramatic compression of the atomic density near the minima of the optical potential can be achieved with a proper pulsing of the lattice. Several strategies leading to the enhanced atomic squeezing are suggested, compared and optimized.Comment: Latex, 9 pages, 10 figures, submitted to PR

Momentum state engineering and control in Bose-Einstein condensates

We demonstrate theoretically the use of genetic learning algorithms to coherently control the dynamics of a Bose-Einstein condensate. We consider specifically the situation of a condensate in an optical lattice formed by two counterpropagating laser beams. The frequency detuning between the lasers acts as a control parameter that can be used to precisely manipulate the condensate even in the presence of a significant mean-field energy. We illustrate this procedure in the coherent acceleration of a condensate and in the preparation of a superposition of prescribed relative phase.Comment: 9 pages incl. 6 PostScript figures (.eps), LaTeX using RevTeX, submitted to Phys. Rev. A, incl. small modifications, some references adde

Driving the resonant quantum kicked rotor via extended initial conditions

We study the resonances of the quantum kicked rotor subjected to an extended initial distribution. For the primary resonances we obtain the dispersion relation for the map of this system. We find an analytical dependence of the statistical moments on the shape of the initial distribution. For the secondary resonances we obtain numerically a similar dependence. This allows us to devise an extended initial condition which produces an average angular momentum pointing in a preset direction which increases with time with a preset ratio.Comment: 6 pages, 5 figures, send to EPJ