We demonstrate that structures made of light can be used to coherently control the motion of complex molecules. In particular, we show diffraction of the fullerenes C60 and C70 at a thin grating based on a standing light wave. We prove experimentally that the principles of this effect, well known from atom optics, can be successfully extended to massive and large molecules which are internally in a thermodynamic mixed state and which do not exhibit narrow optical resonances. Our results will be important for the observation of quantum interference with even larger and more complex objects.
Exciting experiments in the field of atom and molecule optics have lately drawn much attention to the effects involved in the coherent diffraction of particle beams. We review the influence of the finite size of the particles and of their energy level spectrum on the diffraction pattern. In turn, we demonstrate how experimental diffraction measurements allow to determine these quantities of weakly bound molecules by considering the diffraction of the dimer and trimer of helium, and the deuterium molecule dimer.
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.
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…
We demonstrate Bragg diffraction of the antibiotic ciprofloxacin and the dye molecule phthalocyanine at a thick optical grating. The observed patterns show a single dominant diffraction order with the expected dependence on the incidence angle as well as oscillating population transfer between the undiffracted and diffracted beams. We achieve an equal-amplitude splitting of $14 \hbar k$ (photon momenta) and maximum momentum transfer of $18 \hbar k$. This paves the way for efficient, large-momentum beam splitters and mirrors for hot and complex molecules.
In this paper, we apply the full new method of quantum theory to study the double-slit diffraction of ${C_{60}}$ molecules. We calculate the double-slit wave functions of ${C_{60}}$ molecules by Schrödinger equation, and calculate the diffraction wave function behind the slits with the Feynman path integral quantum theory, and then give the relation between the diffraction intensity of double-slit and diffraction pattern position. We compare the calculation results with two different double-slit diffraction experiments. When the decoherence effects are considered, the calculation results are i…
Diffraction phenomena of large molecules have been studied in many experiments, and these experiments are described by many theoretical works. In this paper, we study $C_{60}$ molecules single and double-slit diffraction with quantum theory approach, and we pay close attention to the $C_{60}$ diffraction experiment carried out by A.Zeilinger et.at in 1999. In double-slit diffraction, we consider the decoherence effect, and find the theoretical results are good agreement with experimental data.
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…
Even 100 years after its introduction by Louis de Broglie, the wave-nature of matter is often regarded as a mind-boggling phenomenon. To give an intuitive introduction to this field, we here discuss the diffraction of massive molecules through a single, double, and triple slit, as well as a nanomechanical grating. While the experiments are in good agreement with undergraduate textbook predictions, we also observe pronounced differences resulting from the molecules' mass and internal complexity. The molecules' polarizability causes an attractive van der Waals interaction with the slit walls, wh…
Homodyne X-ray diffraction signals produced by classical light and classical detectors are given by the modulus square of the charge density in momentum space $\left|σ(\mathbf{q})\right|^{2}$, missing its phase which is required in order to invert the signal to real space. We show that quantum detection of the radiation field yields a linear diffraction pattern that reveals $σ(\mathbf{q})$ itself, including the phase. We further show that repeated diffraction measurements with variable delays constitute a novel multidimensional measure of spontaneous charge-density fluctuations. Classical diff…
We address the feasibility of imaging geometric and orbital structure of a polyatomic molecule on an attosecond time-scale using the laser induced electron diffraction (LIED) technique. We present numerical results for the highest molecular orbitals of the CO2 molecule excited by a near infrared few-cycle laser pulse. The molecular geometry (bond-lengths) is determined within 3% of accuracy from a diffraction pattern which also reflects the nodal properties of the initial molecular orbital. Robustness of the structure determination is discussed with respect to vibrational and rotational motion…
The fringe pattern that allows geometrical and orbital structure information to be extracted from LIED spectra of symmetric molecules is shown to reflect a symmetry conservation principle. We show that under a field polarization which preserves certain symmetry elements of the molecule, the symmetry character of the initial wave function is conserved during its time-evolution. We present a symmetry analysis of a deviation from a perfect alignment by decomposing the field into a major, symmetry-determining part, and a minor, symmetry breaking, part. This decomposition leads to a corresponding f…
We explore the laser-induced ionization dynamics of N2 and CO2 molecules subjected to a few-cycle, linearly polarized, 800\,nm laser pulse using effective two-dimensional single active electron time-dependent quantum simulations. We show that the electron recollision process taking place after an initial tunnel ionization stage results in quantum interference patterns in the energy resolved photo-electron signals. If the molecule is initially aligned perpendicular to the field polarization, the position and relative heights of the associated fringes can be related to the molecular geometrical …
In this paper, we discuss the possibility of imaging molecular orbitals from photoelectron spectra obtained via Laser Induced Electron Diffraction (LIED) in linear molecules. This is an extension of our work published recently in Physical Review A \textbf{94}, 023421 (2016) to the case of the HOMO-1 orbital of the carbon dioxide molecule. We show that such an imaging technique has the potential to image molecular orbitals at different internuclear distances in a sub-femtosecond time scale and with a resolution of a fraction of an Angström.
This chapter reviews recent experiments on matter wave interferometry with large molecules. Starting from an elementary introduction to matter wave physics we discuss far-field diffraction and near-field interferometry with thermally excited many-body systems. We describe the constraints imposed by decoherence and dephasing effects, and present an outlook to the future challenges in macromolecule and cluster interferometry.
We study the effects of strong inter-particle interaction on diffraction of a Bose-Einstein condensate of $^6Li_2$ molecules from a periodic potential created by pulses of a far detuned optical standing wave. For short pulses we observe the standard Kapitza-Dirac diffraction, with the contrast of the diffraction pattern strongly reduced for very large interactions due to interaction dependent loss processes. For longer pulses diffraction shows the characteristic for matter waves impinging on an array of tubes and coherent channeling transport. We observe a slowing down of the time evolution go…
Advances in micro-technology of the last years have made it possible to carry optics textbooks experiments over to atomic and molecular beams, such as diffraction by a double slit or transmission grating. The usual wave-optical approach gives a good qualitative description of these experiments. However, small deviations therefrom and sophisticated quantum mechanics yield new surprising insights on the size of particles and on their interaction with surfaces.
Ubiquitous to most molecular scattering methods is the challenge to retrieve bond distance and angle from the scattering signals since this requires convergence of pattern matching algorithms or fitting methods. This problem is typically exacerbated when imaging larger molecules or for dynamic systems with little a priori knowledge. Here, we employ laser-induced electron diffraction (LIED) which is a powerful means to determine the precise atomic configuration of an isolated gas-phase molecule with picometre spatial and attosecond temporal precision. We introduce a simple molecular retrieval m…
Using single-particle pseudopotential and many-particle configuration interaction methods, we compare various physical quantities of (In,Ga)As/GaAs quantum dot molecules (QDMs) made of dissimilar dots (heteropolar QDMs) with QDMs made of identical dots (homopolar QDMs). The calculations show that the electronic structures of hetero-QDMs and homo-QDMs differ significantly at large inter-dot distance. In particular (i) Unlike those of homo-QDMs, the single-particle molecular orbitals of hetero-QDMs convert to dot localized orbitals at large inter-dot distance. (ii) Consequently, in a hetero-QMD …
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 tho…
Diffraction experiments have moved to ever heavier objects in recent years, now standing at the level of large molecules. Experiments in materials science on the other hand have come down to ever smaller sizes largely due to the success of the scanning tunneling microscope (STM), which allows studying single molecules on surfaces. Since both fields coming from opposite side of the size spectrum are now meeting, there is a need of consistent theories. The simulations presented in the article, which we are referring to, are not consistent with molecular dynamics simulations which are routinely u…
We give an explicit and general description of the energy, linear momentum, angular momentum and boost momentum of a molecule to order $1/c^2$, where it necessary to take account of kinetic contributions made by the electrons and nuclei as well as electromagnetic contributions made by the intramolecular field. A wealth of interesting subtleties are encountered that are not seen at order $1/c^0$, including relativistic Hall shifts, anomalous velocities and hidden momenta. Some of these have well known analogues in solid state physics.
