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arXiv:0711.3102 · Journal of Physics Conference Series

Atom laser dynamics in a tight waveguide

A del Campo, I Lizuain, M. Ll. Pons, J G Muga, M. Moshińsky

Published Feb 1, 2008• 4 citations
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Abstract

We study the transient dynamics that arise during the formation of an atom laser beam in a tight waveguide. The time dependent density profile develops a series of wiggles which are related to the diffraction in time phenomenon. The apodization of matter waves, which relies on the use of smooth aperture functions, allows to suppress such oscillations in a time interval, after which there is a revival of the diffraction in time. The revival time scale is directly related to the inverse of the harmonic trap frequency for the atom reservoir.

DOI
10.1088/1742-6596/99/1/012003

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We study the transient dynamics that arise during the formation of an atom laser beam in a tight waveguide. The time dependent density profile develops a series of wiggles which are related to the diffraction in time phenomenon. The apodization of matter waves, which relies on the use of smooth aperture functions, allows to suppress such oscillations in a time interval, after which there is a revival of the diffraction in time. The revival time scale is directly related to the inverse of the harmonic trap frequency for the atom reservoir.
We study the transient dynamics that arise during the formation of an atom laser beam in a tight waveguide. The time dependent density profile develops a series of wiggles which are related to the diffraction in time phenomenon. The apodization of matter waves, which relies on the use of smooth aperture functions, allows to suppress such oscillations in a time interval, after which there is a revival of the diffraction in time. The revival time scale is directly related to the inverse of the harmonic trap frequency for the atom reservoir. PACS numbers: Atom lasers have recently been created in the laboratory and stand up for their applications in atom lithography and interferometry. Similar to their light analogues, they consist in coherent and directed (matter-) wave beams, which are extracted from a Bose-Einstein condensate (BEC). Different schemes have been proposed to out-couple the atoms from the BEC reservoir. One of the prototypes uses two-photon Raman excitation to create “output coupled ” atomic pulses with well defined mean momentum which overlap and form a quasi-continuous beam [1, 2] (For other approaches see e.g. [3] or [4]). The features of the beam profile are of outmost importance for applications [5, 6, 7], and depend on the pulse shape, duration, emission frequency, and initial phase [8]. We study the dynamics of a beam created by multiple overlapping pulses, transversely confined in a tight waveguide and with negligible interactions between the out-coupled atoms. It is found that an oscillatory pattern appears in the density profile of the beam which is closely related to the diffraction in time phenomenon. If the switching process is slow, such oscillations are suppressed on a time window after which there is a revival of the diffraction in time. The time scale in which the spatial fringes appear is related to the the spatial width of the out-coupled pulses.
Abstract. Sudden turn-on of a matter-wave source leads to characteristic oscillations of the probability density which are the hallmark feature of diffraction in time. The apodization of matter waves relies on the use of smooth aperture functions which suppress such oscillations. The analytical dynamics arising with different aperture functions are discussed systematically for switching-on processes, and for single and many-pulse formation procedures. The possibility and time scale of a revival of the diffraction-in-time pattern is also analysed. Similar modulations in time of the pulsed output coupling in atom-lasers are responsible for the dynamical evolution and characteristics of the beam profile. For multiple pulses, different phase schemes and regimes are described and compared. Strongly overlapping pulses lead to a saturated, constant beam profile in time and space, up to the revival phenomenon. Coherent matter-wave pulse formation and dynamics have been studied traditionally in the context of scattering and interferometric experiments with mechanical shutters. Suddenly switching-on and off matter-wave sources leads to an oscillatory pattern in the probability density which was discovered by one of the authors
Sudden turn-on of a matter-wave source leads to characteristic oscillations of the density profile which are the hallmark feature of diffraction in time. We show how the use of smooth aperture functions suppresses the diffraction oscillations. The analytical dynamics of non-interacting bosons arising with different aperture functions are discussed systematically for switching-on processes and for single- and many-pulse formation procedures. The possibility and timescale of a revival of the diffraction-in-time pattern is also analysed. Similar modulations in time of the pulsed output coupling in atom lasers are responsible for the dynamical evolution and characteristics of the beam profile. For multiple pulses, different phase schemes and regimes are described and compared. Strongly overlapping pulses lead to a saturated, constant beam profile in time and space, up to the revival phenomenon.
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.
Although there are many kinds of different techniques developed to manipulate atomic matter waves, a laser beam is still considered as the most effective `optical element' to manipulate atomic waves in atom optics. In the laser-based atom optic devices, the spatial profiles of a laser beam play a central role in controlling the motion of atoms. By choosing different spatial profiles of laser beams, one can construct atom optic devices for different purposes. Recently experimental demonstrations of manipulation of center of mass motion of atoms by time-dependent light field were reported. In this paper we theoretically study the transient effects in atom optics by using a laser pulse train. The reflection and transmission of atoms through the laser pulse train are studied in detail. We find that the laser pulse train acts as both a spatial beam splitter and a `temporal grating' which can both reflect or transmit atoms in spatial domain and `diffract' atoms in the time domain.
The objective of this presentation is to discuss a simple model of laser in which the atoms can undergo diffusive motion and to characterize the main dynamic effects associated with this often ignored feature of theoretical models. For this purpose we reconsider a laser cavity with flat mirrors1 and special geometry that allows diffraction along only one of the transverse directions to the resonator axis. As already found in an earlier model, here we also show that low threshold instabilities can lead to a departure from the homogeneous stationary state, to the creation of complex spatial patterns, and to cooperative frequency locking, a state of operation in which several transverse modes can oscillate synchronously. There are significant differences, however, in the shape of the domains of instability and in details of the laser dynamics following the destabilization of the homogeneous state. In addition, for selected parameter values the operation of the laser may actually become more stable in the presence of atomic diffusion.