We report on the theoretical investigation of Wigner distribution function (WDF) reconstruction of the motional quantum state of large molecules in de Broglie interference. De Broglie interference of fullerenes and as the like already proves the wavelike behaviour of these heavy particles, while we aim to extract more quantitative information about the superposition quantum state in motion. We simulate the reconstruction of the WDF numerically based on an analytic probability distribution and investigate its properties by variation of parameters, which are relevant for the experiment. Even though the WDF described in the near-field experiment cannot be reconstructed completely, we observe negativity even in the partially reconstructed WDF. We further consider incoherent factors to simulate the experimental situation such as a finite number of slits, collimation, and particle-slit van der Waals interaction. From this we find experimental conditions to reconstruct the WDF from Talbot interference fringes in molecule Talbot-Lau interferometry.
In this article we formulate and solve the problem of molecular beam diffraction when each molecule consists of two interacting bodies. Then, using our results, we present the diffraction patterns for various molecular sizes employing the harmonic oscillator as interaction model between the two atoms. Lastly, we analyze the corrections produced by the internal structure of the molecule in applications that include beam focusing and Talbot carpets.
Wave propagation on the surface of cylinders exhibits interferometric self imaging, much like the Talbot effect in the near-field diffraction at periodic gratings. We report the experimental observation of the cylindrical Talbot carpet in weakly-guiding ring-core fibers for classical light fields. We further show that the ring-core fiber acts as a high-order optical beamsplitter for single photons, whose output can be controlled by the relative phase between the input light fields. By also demonstrating high-quality two-photon interference between indistinguishable photons sent into the ring-c…
Time-frequency Talbot effect as Clifford operations on entangled time-frequency GKP states
Télécom Paris-LTCI, Institut Polytechnique de Paris（巴黎电信学院-LTCI，巴黎理工学院）；Université Côte d’Azur, CNRS, Institut de physique de Nice（蔚蓝海岸大学，法国国家科学研究中心，尼斯物理研究所）
In 1924 Louis de Broglie introduced the concept of wave-particle duality: the Planck constant $h$ relates the momentum $p$ of a massive particle to its de Broglie wavelength $λ=h/p$. The superposition principle is one of the main postulates of quantum mechanics; diffraction and interference phenomena are therefore predicted and have been observed on objects of increasing complexity, from electrons to neutrons and molecules. Beyond the early electron diffraction experiments, the demonstration of single-electron double-slit-like interference was a highly sought-after result. Initially proposed b…
Ultrafast electron diffraction and time-resolved serial crystallography are the basis of the ongoing revolution in capturing at the atomic level of detail the structural dynamics of molecules. However, most experiments employ the classical "ball-and-stick" depictions, and the information of molecular quantum states, such as the density matrix, is missing. Here, we introduce a framework for the preparation and ultrafast coherent diffraction from rotational wave packets of molecules, and we establish a new variant of quantum state tomography for ultrafast electron diffraction to characterize the…
With the ability to directly obtain the Wigner function and density matrix of photon states, quantum tomography (QT) has had a significant impact on quantum optics, quantum computing and quantum information. By an appropriate sequence of measurements on the evolution of each degreeof freedom (DOF), the full quantum state of the observed photonic system can be determined. The first proposal to extend the application of QT to reconstruction of complete quantum states of matter wavepackets had generated enormous interest in ultrafast diffraction imaging and pump-probe spectroscopy of molecules. T…
A unified quantum random walk model for internal crystal effects in dynamical diffraction
Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Department of Physics and Astronomy, University of Waterloo（滑铁卢大学物理与天文学系）；Department of Physics, University at Buffalo, State University of New York（纽约州立大学布法罗分校物理系）；Department of Chemistry, University of Waterloo（滑铁卢大学化学系）；National Institute of Standards and Technology（美国国家标准与技术研究院）
The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple mathematical idea of linearly combining vectors in a Hilbert space. Specifically, the discussion turns around the connection between symmetries characterizing the wave function and the behavior in time displayed by the quantum flux when the latter is analyzed in terms of streamlines (Bohmian trajectories). This is illustrated with a series of analytical results an…
