Periodic Optical Potential Research Articles

Collective excitations of a periodic Bose condensate in the Wannier representation

We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a renormalization of the s-wave scattering length and the solution of the Bogolubov - de Gennes equations is formulated in terms of the appropriate Wannier functions. Some exact properties of a periodic one-dimensional condensate are easily demonstrated: (i) the lowest band at positive energy refers to phase modulations of the condensate and has a linear dispersion relation near the Brillouin zone centre; (ii) the higher bands arise from the superposition of localized excitations with definite phase relationships; and (iii) the wavenumber-dependent current under a constant force in the semiclassical transport regime vanishes at the zone boundaries. Early results by J. C. Slater [Phys. Rev. 87, 807 (1952)] on a soluble problem in electron energy bands are used to specify the conditions under which the Wannier functions may be approximated by on-site tight-binding orbitals of harmonic- oscillator form. In this approximation the connections between the low-lying excitations in a lattice and those in a harmonic well are easily visualized. Analytic results are obtained in the tight-binding scheme and are illustrated with simple numerical calculations for the dispersion relation and semiclassical transport in the lowest energy band, at values of the system parameters which are relevant to experiment.

Coherent dynamics of Bose-Einstein condensates in high-finesse optical cavities

We study the mutual interaction of a Bose-Einstein condensed gas with a single mode of a high-finesse optical cavity. We show how the cavity transmission reflects condensate properties and calculate the self-consistent intra-cavity light field and condensate evolution. Solving the coupled condensate-cavity equations we find that while falling through the cavity, the condensate is adiabatically transfered into the ground state of the periodic optical potential. This allows time dependent non-destructive measurements on Bose-Einstein condensates with intriguing prospects for subsequent controlled manipulation.

Quantum chaos with cesium atoms: pushing the boundaries

Atomic motion in pulsed, periodic optical potentials provides a unique experimental testing ground for quantum chaos. In the first generation of experiments with sodium atoms we observed dynamical localization, a quantum suppression of chaotic diffusion. To go beyond this work we have constructed an experiment with cold cesium atoms, and report our first results from this system. The larger mass and longer wavelength push out the momentum boundary in phase space that arises from the nonzero duration of the pulses. This feature should enable the study of noise effects and dimensionality on dynamical localization. We propose a new method of quantum state preparation based on stimulated Raman transitions for studies of mixed phase space dynamics.

Bloch oscillations of atoms, adiabatic rapid passage, and monokinetic atomic beams

We study the dynamics of ultracold atoms in a periodic optical potential submitted to a constant external force. Bloch oscillations in the fundamental and first excited bands of the potential are observed. In addition to a solid-state analysis we give a quantum-optics interpretation of this effect in terms of photon exchanges between the atoms and the laser waves. The dynamics of Bloch oscillations are equivalent to a sequence of adiabatic rapid passages between momentum states and can be described using the dressed-atom approach. We demonstrate efficient and dissipation-free acceleration of atoms by coherent transfer of a large number of photon momenta (\ensuremath{\approx}100). This technique produces atomic beams with a very small longitudinal velocity spread that may find applications in atom optics and precision measurements.

Force measurement via dark-state cooling.

We analyze the ``polarization-gradient-assisted velocity-selective coherent population-trapping'' laser cooling scheme in the presence of a homogeneous force. In the limit of a slow rate of cooling this system may be treated using a set of rate equations after applying the secular approximation. This uses a basis of states which form a band structure resulting from the periodic optical potentials. We show that in the presence of a force the secular approximation may be retained, and derive the required modification to the rate equations. This is a density operator method of treating the action of a force on a particle in a band structure, and clearly shows reflections at the band edge. We solve for the steady-state momentum distribution, which provides information on the amount to which the presence of a force limits the achievable temperature. We solve also for the steady-state fluorescence and suggest that the fluorescence from atoms cooled with this scheme could be used as a force meter. \textcopyright{} 1996 The American Physical Society.

Purely optical dark lattice

We study a new type of optical lattice in which the localized atoms experience a much reduced optical pumping and fluorescence rate. An optical standing wave is tuned to the blue of the F = 2 ? F = 2 transition of the (87)Rb D(2) line and induces periodic optical potentials by coupling the F = 2 ground state to both the F = 2 and F = 3 excited states. A Sisyphus mechanism efficiently cools the atoms into the lattice sites. We adiabatically release the atoms from the optical lattice and measure their momentum distribution with a resolution of one third of a single photon recoil. This allows us to determine the population of the two lowest energy bands in the optical lattice (44% and 20%).

Observation of temporal behavior of an atomic wave packet localized in an optical potential.

We have investigated the dynamic temporal behavior of atomic motion in a periodic optical potential by detecting a recoil-induced resonance signal. In the slowly moving optical potential, damped oscillations are observed in the transient signal and the oscillation frequency is found to be independent of the moving speed of the potential. By using a Monte Carlo wave-function method, the signal can be attributed to the oscillatory motion of atomic wave packet localized in the potential, where the oscillation frequency corresponds to the energy separation between vibrational levels.

Observation of a transient response of recoil-induced resonance: A method for the measurement of atomic motion in an optical standing wave.

We demonstrate a method to directly observe the dynamics of motion of cold atoms in an optical standing wave using a recoil-induced resonance. By detecting a transient response of this resonance, we observed the interaction between an atomic population grating and a periodic optical potential. Using this method, we investigated the lifetime of the atomic grating under various conditions in the optical potential. As a result, we obtained the appropriate conditions for the long lifetime and observed the narrowest linewidth in the recoil-induced resonance corresponding to the atomic temperature of 4.4\ifmmode\pm\else\textpm\fi{}0.3 \ensuremath{\mu}K for $^{87}\mathrm{Rb}$ atoms.

Optical thermal ratchet.

We present an optical realization of a thermal ratchet. Directed motion of Brownian particles in water is induced by modulating in time a spatially periodic but asymmetric optical potential. The net drift shows a maximum as a function of the modulation period. The experimental results agree with a simple theoretical model based on diffusion.

Absorption-induced coherence in quantum systems.

We have studied scattering from locally periodic optical potentials. The band-structure characteristics of periodic potentials along with resonances are observed. These features are solely due to the interference from absorptive potentials. Contrary to assertions in the literature, we show that the absorption along with the enhanced reflection induces coherence in quantum systems. We also discuss some conceptual aspects of absorptive potentials.

Dynamics and spatial order of cold cesium atoms in a periodic optical potential.

The spatial distribution and the dynamics of Cs atoms in a 1D optical molasses are probed by measuring the absorption (or amplification) spectrum of a weak laser beam. Narrow (35--50 kHz) Raman lines give access for the first time to the frequency and to the damping of the atom's oscillation in the potential wells associated with light shifts. A narrower (8 kHz) Rayleigh resonance demonstrates the existence of a large-scale spatial order of the atoms, presenting some analogy with an antiferromagnetic medium.