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Physical Review A

Atom-laser coherence length and atomic standing waves

Iacopo Carusotto, M. Artoni, Giuseppe Carlo La Rocca

Published Nov 14, 2000• 6 citations
Publisher

Abstract

We consider the dynamical Bragg reflection of an atomic matter wave from a finite optical lattice; the resulting energy dependence of the transmittivity allows us to filter out the velocities of the incident atoms. In particular, we show how the coherence length of the incident beam can be inferred from the sharpness of the transmittivity as a function of the lattice intensity. For incident frequencies well inside the reflecting window, the interference of incident and reflected matter waves gives rise to an oscillatory density profile in front of the lattice which can be observed by means of light diffraction. The angular width of the diffracted peaks also provides information on the coherence length of the incident atomic beam.

DOI
10.1103/physreva.62.063606

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We consider the dynamical Bragg reflection of an atomic matter wave from a finite optical lattice; the resulting energy dependence of the transmittivity allows us to filter out the velocities of the incident atoms. In particular, we show how the coherence length of the incident beam can be inferred from the sharpness of the transmittivity as a function of the lattice intensity. For incident frequencies well inside the reflecting window, the interference of incident and reflected matter waves gives rise to an oscillatory density profile in front of the lattice which can be observed by means of light diffraction. The angular width of the diffracted peaks also provides information on the coherence length of the incident atomic beam.
Bragg diffraction of atoms at thick standing light waves requires that the wave-matching condition is fulfilled. This usually means that the atomic beam crosses the light wave exactly at the Bragg angle. Nevertheless, our experiments also demonstrate Bragg diffraction at detuned angles if the amplitude of the standing light wave is temporally modulated with an appropriate frequency. If, on the other hand, the phase of the light wave is modulated no diffraction is observed. Both modulation processes produce frequency sidebands which set up `slowly travelling standing waves' in front of a retro-reflection mirror. Atoms are diffracted at these `almost standing' light waves in a similar way to photons at the travelling sound waves in an acousto-optic modulator. The frequency of the diffracted de Broglie waves is assumed to be shifted by the intensity modulation frequency. The different results using amplitude- and phase-modulated light waves are due to interference between the diffraction contributions of the individual frequency sidebands contained in the standing light wave.
When a stationary reflecting wall acting as a perfect mirror for an atomic beam with well-defined incident velocity is suddenly removed, the density profile develops during the time evolution an oscillatory pattern known as diffraction in time. The interference fringes are suppressed or their visibility is diminished by several effects such as averaging over a distribution of incident velocities, apodization of the aperture function, atom-atom interactions, imperfect reflection, or environmental noise. However, when the mirror moves with finite velocity along the direction of propagation of the beam, the visibility of the fringes is enhanced. For mirror velocities below beam velocity, as used for slowing down the beam, the matter wave splits into three regions separated by space-time points with classical analogs. For mirror velocities above beam velocity a visibility enhancement occurs without a classical counterpart. When the velocity of the beam approaches that of the mirror the density oscillations rise by a factor 1.8 over the stationary value.
We study Bragg scattering at one-dimensional atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated inside a laser-driven cavity. The atoms arrange themselves into an array of lens-shaped layers located at the antinodes of the standing wave. Light incident on this array at a well-defined angle is partially Bragg reflected. We measure reflectivities as high as 3030%30. In contrast to a previous experiment devoted to the thin grating limit [S. Slama et al., Phys. Rev. Lett. 94, 193901 (2005)] we now investigate the thick grating limit characterized by multiple reflections of the light beam between the atomic layers. In principle, multiple reflections give rise to a photonic stop band, which manifests itself in the Bragg diffraction spectra as asymmetries and minima due to destructive interference between different reflection paths. We show that close to resonance however disorder favors diffuse scattering, hinders coherent multiple scattering and impedes the characteristic suppression of spontaneous emission inside a photonic band gap.
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.
We consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.