Lasers with wavelengths of the order of the atomic size are becoming available. We explore the behavior of light-matter interactions in this emergent field by considering the atomic Kapitza-Dirac effect. We derive the diffraction patterns, which are in principle experimentally testable. From a fundamental point of view, our proposal provides an example of system where the periodicity of the diffraction grating is comparable to the size of the diffracted object.
A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules and even clusters has been observed. Due to their size and to possible breakup processes optical wave-theory is no longer adequate and a more sophisticated approach is needed. Moreover, surface effects, which can modify the diffraction pattern of atoms and molecules, give rise to further complications. In this article a fully quantum mechanical approach to t…
We suggest the numerical approach to detect eigenfrequencies of trapped modes in waveguides or guided waves in diffraction gratings. At the same time, the approach works perfectly for computation of systems with finitely many scattering channels. The most attractive example concerns the possibility of control on electron transport in nano-dimensions system consisting of a resonator and finitely many adjoined channels due to external variable electric field.
We study diffraction and interference of indistinguishable particles. We consider some examples where the wavefunctions and detection probabilities can be evaluated in an analytical way. The diffraction pattern of a two-particle system shows notorious differences for the cases of bosons, fermions and distinguishable particles. In the example of near-field interferometry, the exchange effects for two-fermion systems lead to the existence of planes at which the probability of double detection is null. We also discuss the relation with the approach to systems of identical particles based on corre…
We report on a detailed investigation of the dynamics and the saturation of a light grating stored in a sample of cold cesium atoms. We employ Bragg diffraction to retrieve the stored optical information impressed into the atomic coherence by the incident light fields. The diffracted efficiency is studied as a function of the intensities of both writing and reading laser beams. A theoretical model is developed to predict the temporal pulse shape of the retrieved signal and compares reasonably well with the observed results.
Molecular beams of rare gas atoms and D_2 have been diffracted from 100 nm period SiN_x transmission gratings. The relative intensities of the diffraction peaks out to the 8th order depend on the diffracting particle and are interpreted in terms of effective slit widths. These differences have been analyzed by a new theory which accounts for the long-range van der Waals -C_3/l^3 interaction of the particles with the walls of the grating bars. The values of the C_3 constant for two different gratings are in good agreement and the results exhibit the expected linear dependence on the dipole pola…
We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in calculating the atomic wavefunction by means of action integrals along the classical trajectories of the atoms in the absence of the modulated part of the potential. The capabilities and the validity condition of the method are illustrated on the well-known case of atomic diffraction by a Gaussian standing wave. We prove that in this situation the perturbation method …
The present study experimentally examines how an electron vortex beam with orbital angular momentum (OAM) undergoes diffraction through a forked grating. The nth-order diffracted electron vortex beam after passing through a forked grating with a Burgers vector of 1 shows an OAM transfer of nh. Hence, the diffraction patterns become mirror asymmetric owing to the size difference between the electron beams. Such a forked grating, when used in combination with a pinhole located at the diffraction plane, could act as an analyzer to measure the OAM of input electrons.
We analyze the diffraction regime of the Kapitza-Dirac effect for particles entangled in momentum. The detection patterns show two-particle interferences. In the single-mode case we identify a discontinuity in the set of joint detection probabilities, associated with the disconnected character of the space of non-separable states. For Gaussian multi-mode states we derive the diffraction patterns, providing an example of the dependence of the light-matter interaction on entanglement. When the particles are identical, we can explore the relation between exchange and entanglement effects. We find…
The five laws of relativistic quantum mechanics, according to Feynman's path integral formulation, are concisely stated and applied to experiments. Reflection diffraction grating experiments for both photons and electrons are analysed, in particular the Davisson-Germer experiment in which the wave-like property of electrons was first established. It is shown how classical, purely spatial, effective wave theories for both photons and electrons are predicted by the path integral formulation of quantum mechanics. The standard Copenhagen interpretation of wave mechanics is critically discussed in …
Diffraction of slow neutrons by nanoparticle-polymer composite gratings has been observed. By carefully choosing grating parameters such as grating thickness and spacing, a three-port beam splitter operation for cold neutrons - splitting the incident neutron intensity equally into the plus-minus first and zeroth diffraction orders - was realized. As a possible application, a Zernike three-path interferometer is briefly discussed.
The size of the helium trimer is determined by diffracting a beam of He-4 clusters from a 100 nm grating inclined by 21 degree. Due to the bar thickness the projected slit width is roughly halved to 27 nm, increasing the sensitivity to the trimer size. The peak intensities measured out to the 8th order are evaluated via a few-body scattering theory. The trimer pair distance is found to be 1.1+0.4/-0.5 nm in agreement with predictions for the ground state. No evidence for a significant amount of Efimov trimers is found. Their concentration is estimated to be less than 6%.
We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, which leads to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a simplified model yielding an analytic formula describing such oscillations for a gas assumed to be at zero temperature. This model is extended to include atoms with initial momenta detuned from our chosen initial value, before analyzing the full finite-temperature response of the system. Finally we present a steady-state soluti…
Atomic diffraction through double slits and transmission gratings is well described in terms of the associated de Broglie waves and classical wave optics. However, for weakly bound and relatively large systems, such as the He_2 dimer, this might no longer hold true due to the possibility of break-up processes and finite-size effects. We therefore study the diffraction of weakly bound two-particle systems. If the bar and slit widths of the grating are much larger than the diameter of the two-particle system we recover the usual optics results. For smaller widths, however, deviations therefrom o…
We consider photo ionization of an atom which, due to passing through a diffraction grating, is prepared in a multi-site state possessing a periodic space structure with alternating maxima and minima. It has been found that this process qualitatively differs from photo ionization of a 'normal' atom. In particular, the spectra of emitted electrons and recoil ions in this process display clear one- and two-particle interference effects. Moreover, there are also striking differences between the momentum distributions of these particles, which no longer mirror each other. The origin of all these f…
Light transmission or diffraction from different quantum phases of cold atoms in an optical lattice has recently come up as a useful tool to probe such ultra cold atomic systems. The periodic nature of the optical lattice potential closely resembles the structure of a diffraction grating in real space, but loaded with a strongly correlated quantum many body state which interacts with the incident electromagnetic wave, a feature that controls the nature of the light transmission or dispersion through such quantum medium. In this paper we show that as one varies the relative angle between the ca…
Reservoir-controlled electromagnetically induced gratings in a weakly driven two-level medium
Abbottabad University of Science and Technology（阿伯塔巴德科学与技术大学）；P. J. Šafárik University（P.J.萨法里克大学）；Government College University（政府学院大学）；Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）
