Diffraction in time (DIT) is a fundamental phenomenon in quantum dynamics due to time-dependent obstacles and slits. It is formally analogous to diffraction of light, and is expected to play an increasing role in the design of coherent matter wave sources, as in the atom laser, to analyze time-of-flight information and emission from ultrafast pulsed excitations, and in applications of coherent matter waves in integrated atom-optical circuits. We demonstrate that DIT emerges robustly in quantum waves emitted by an exponentially decaying source and provide a simple explanation of the phenomenon, as an interference of two characteristic velocities. This allows for its controllability and optimization.
Diffraction in time (DIT) is a fundamental phenomenon in quantum dynamics due to time-dependent obstacles and slits. It is formally analogous to diffraction of light, and is expected to play an increasing role in the design of coherent matter wave sources, as in the atom laser, to analyze time-of-flight information and emission from ultrafast pulsed excitations, and in applications of coherent matter waves in integrated atom-optical circuits. We demonstrate that DIT emerges robustly in quantum waves emitted by an exponentially decaying source and provide a simple explanation of the phenomenon, as an interference of two characteristic velocities. This allows for its controllability and optimization.
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
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.
In analogy to the well-known diffraction of waves at spatial structures, one can also define diffraction in time when a wave is temporarily modulated. In the present paper we investigate this phenomenon starting from a Green's-function approach. Diffraction in time appears for Schr\"odinger waves and not for light in vacuum. Specific cases of diffraction in time investigated here are diffraction at an ``edge in time'' and a Fresnel lens in time. We then investigate in detail the simultaneous diffraction both in space and in time representing a general solution. Then we analyze in detail diffraction at an edge, both in space and in time, of a single slit in space and in time, a double slit in space, and a single slit in time, a single slit in space and a double slit in time, and, finally, a double slit both in space and in time. In all cases we analyze the possibilities of various approximations which can be made, and show the limits and validity of the Fraunhofer approximation both in space and in time. We give explicit results for a gedanken experiment with very cold atoms.
Today, the nature of light is accounted for by one of the jewels of physics, quantum electrodynamics (QED), the fundamental theory of light and matter. Yet owing to its infinite complexity, scientists still debate how its central concept, the photon, can be reconciled with the perceived existence of light waves, emerging 200 years ago in the wake of Young's double slit diffraction experiment. Ever since, the phenomenon of diffraction has been viewed to embody the wave nature of light, leading to the schizophrenic wave-particle duality. The latter does not exist in QED which is photon based without the existence of waves. Here we introduce the new paradigm that diffraction images directly reflect the fundamental quantum states of light. This is revealed by analysis of the evolution of modern versions of Young's experiment performed with differently modified laser light and photon-based detection. In conventional quantum mechanics, corresponding to first order QED, the fundamental photon nature of light remains hidden since different quantum states produce only two basic types of diffraction patterns that may also be explained by coherent and incoherent wave superposition. The true photon based substructure of light is shown to clearly emerge through characteristic diffraction images in second order QED. The degeneracy of the first order images is lifted, the wave-particle equivalence breaks down, and the patterns directly reveal the true quantum substructure of light. This allows the replacement of the conventional concept of wave coherence by a precise order-dependent degree of coherence that quantifies the interference and diffraction behavior of all quantum states of light.
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.