Cold collisions between atoms in optical lattices

We have simulated binary collisions between atoms in optical lattices during Sisyphus cooling. Our Monte Carlo Wave Function simulations show that the collisions selectively accelerate mainly the hotter atoms in the thermal ensemble, and thus affect the steady state which one would normally expect to reach in Sisyphus cooling without collisions.Comment: 4 pages, 1 figur

Quantum-Enhanced continuous-wave stimulated Raman spectroscopy

Stimulated Raman spectroscopy has become a powerful tool to study the spatiodynamics of molecular bonds with high sensitivity, resolution and speed. However, sensitivity and speed of state-of-the-art stimulated Raman spectroscopy are currently limited by the shot-noise of the light beam probing the Raman process. Here, we demonstrate an enhancement of the sensitivity of continuous-wave stimulated Raman spectroscopy by reducing the quantum noise of the probing light below the shot-noise limit by means of amplitude squeezed states of light. Probing polymer samples with Raman shifts around 2950 $cm^{-1}$ with squeezed states, we demonstrate a quantum-enhancement of the stimulated Raman signal-to-noise ratio (SNR) of 3.60 dB relative to the shot-noise limited SNR. Our proof-of-concept demonstration of quantum-enhanced Raman spectroscopy paves the way for a new generation of Raman microscopes, where weak Raman transitions can be imaged without the use of markers or an increase in the total optical power.Comment: 6 pages, 6 figure

Stabilization of the number of Bose-Einstein condensed atoms in evaporative cooling via three-body recombination loss

The dynamics of evaporative cooling of magnetically trapped $^{87}$Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. We carried out the quantitative calculations of the time evolution of conventional evaporative cooling where the frequency of the radio-frequency magnetic field is swept exponentially. This "exponential-sweep cooling" is known to become inefficient at the final stage of the cooling process due to a serious three-body recombination loss. We precisely examine how the growth of a Bose-Einstein condensate depends on the experimental parameters of evaporative cooling, such as the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. It is shown that three-body recombination drastically depletes the trapped $^{87}$Rb atoms as the system approaches the quantum degenerate region and the number of condensed atoms finally becomes insensitive to these experimental parameters. This result indicates that the final number of condensed atoms is well stabilized by a large nonlinear three-body loss against the fluctuations of experimental conditions in evaporative cooling.Comment: 7 pages, REVTeX4, 8 eps figures, Phys. Rev A in pres

Atomic collision dynamics in optical lattices

We simulate collisions between two atoms, which move in an optical lattice under the dipole-dipole interaction. The model describes simultaneously the two basic dynamical processes, namely the Sisyphus cooling of single atoms, and the light-induced inelastic collisions between them. We consider the J=1/2 -> J=3/2 laser cooling transition for Cs, Rb and Na. We find that the hotter atoms in a thermal sample are selectively lost or heated by the collisions, which modifies the steady state distribution of atomic velocities, reminiscent of the evaporative cooling process.Comment: 17 pages, 15 figure

Loop structure of the lowest Bloch band for a Bose-Einstein condensate

We investigate analytically and numerically Bloch waves for a Bose--Einstein condensate in a sinusoidal external potential. At low densities the dependence of the energy on the quasimomentum is similar to that for a single particle, but at densities greater than a critical one the lowest band becomes triple-valued near the boundary of the first Brillouin zone and develops the structure characteristic of the swallow-tail catastrophe. We comment on the experimental consequences of this behavior.Comment: 4 pages, 7 figure

Modulational instability in cigar shaped Bose-Einstein condensates in optical lattices

A self consistent theory of a cigar shaped Bose-Einstein condensate (BEC) periodically modulated by a laser beam is presented. We show, both theoretically and numerically, that modulational instability/stability is the mechanism by which wavefunctions of soliton type can be generated in cigar shaped BEC subject to a 1D optical lattice. The theory explains why bright solitons can exist in BEC with positive scattering length and why condensate with negative scattering length can be stable and give rise to dark solitary pulses.Comment: Submitted, 4 pages, 3 figures. Revised versio

Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential

We present a new family of stationary solutions to the cubic nonlinear Schroedinger equation with a Jacobian elliptic function potential. In the limit of a sinusoidal potential our solutions model a dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided the ratio of the height of the variations of the condensate to its DC offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Numerical simulations suggest such stationary states are experimentally observable.Comment: 4 pages, 4 figure

Modulated Amplitude Waves in Bose-Einstein Condensates

We analyze spatio-temporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions. A coherent structure ansatz yields a parametrically forced nonlinear oscillator, to which we apply Lindstedt's method and multiple-scale perturbation theory to determine the dependence of the intensity of periodic orbits (``modulated amplitude waves'') on their wave number. We explore BEC band structure in detail using Hamiltonian perturbation theory and supporting numerical simulations.Comment: 5 pages, 4 figs, revtex, final form of paper, to appear in PRE (forgot to include \bibliography command in last update, so this is a correction of that; the bibliography is hence present again

Bogoliubov sound speed in periodically modulated Bose-Einstein condensates

We study the Bogoliubov excitations of a Bose-condensed gas in an optical lattice. Of primary interest is the long wavelength phonon dispersion for both current-free and current-carrying condensates. We obtain the dispersion relation by carrying out a systematic expansion of the Bogoliubov equations in powers of the phonon wave vector. Our result for the current-carrying case agrees with the one recently obtained by means of a hydrodynamic theory.Comment: 16 pages, no figure