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Time modulation of atom sources

A. Del Campo, J. G. Muga, M. Moshińsky

Published Jan 1, 2006• 19 citations
OpenAlex

Abstract

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

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Time modulation of atom sources

A del Campo, J G Muga, M. Moshińsky

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.

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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. 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.

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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.

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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.

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In recent years, matter-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and the study of fundamental aspects of quantum theory. Diffraction and interference of matter waves can be observed not only at a spatial aperture (such as a screen edge, slit, or grating), but also at a time-domain aperture (such as an absorbing barrier, or ``shutter,'' that is being periodically switched on and off). The wave phenomenon of the latter type is commonly referred to as ``diffraction in time.'' Here, we introduce a versatile, exactly solvable model of diffraction in time. It describes time evolution of an arbitrary initial quantum state in the presence of a time-dependent absorbing barrier, governed by an arbitrary aperture function. Our results enable a quantitative description of diffraction and interference patterns in a large variety of setups, and may be used to devise new diffraction and interference experiments with atoms and molecules.

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We study the properties of quantum single-particle wave pulses created by sharp-edged or apodized shutters with single or periodic openings. In particular, we examine the following: the visibility of diffraction fringes depending on evolution time and temperature; the purity of the state depending on the opening-time window; the accuracy of a simplified description which uses 'source' boundary conditions instead of solving an initial value problem; and the effects of apodization on the energy width.

arXiv:quant-ph/0506103•Journal of Physics A Mathematical and General•Oct 26, 2005•25 citations
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.
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.
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.
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.
In recent years, matter-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and the study of fundamental aspects of quantum theory. Diffraction and interference of matter waves can be observed not only at a spatial aperture (such as a screen edge, slit, or grating), but also at a time-domain aperture (such as an absorbing barrier, or ``shutter,'' that is being periodically switched on and off). The wave phenomenon of the latter type is commonly referred to as ``diffraction in time.'' Here, we introduce a versatile, exactly solvable model of diffraction in time. It describes time evolution of an arbitrary initial quantum state in the presence of a time-dependent absorbing barrier, governed by an arbitrary aperture function. Our results enable a quantitative description of diffraction and interference patterns in a large variety of setups, and may be used to devise new diffraction and interference experiments with atoms and molecules.
We study the properties of quantum single-particle wave pulses created by sharp-edged or apodized shutters with single or periodic openings. In particular, we examine the following: the visibility of diffraction fringes depending on evolution time and temperature; the purity of the state depending on the opening-time window; the accuracy of a simplified description which uses 'source' boundary conditions instead of solving an initial value problem; and the effects of apodization on the energy width.